Guilherme Filipe de Jesus Félix das Neves Loureiro

Livre

0
0
130
1 year ago
Preview
Full text

    Guilherme Filipe de Jesus Félix das Neves Loureiro

  Licenciado em Engenharia Civil        

  Impulsos activos sobre estruturas de suporte   em consola

      Dissertação para obtenção do Grau de Mestre em Engenharia Civil  

  Perfil Estruturas e Geotecnia      

  Orientador: Professor Doutor Nuno Manuel da Costa Guerra        

  Júri:   Presidente: Professor Doutor Corneliu Cismasiu  

  Arguente: Professor Doutor Jorge Nuno Veiga de Almeida e Sousa Vogal: Professor Doutor Nuno Manuel da Costa Guerra      

  ✐✐

  ✏❈♦♣②r✐❣❤t✑ ●✉✐❧❤❡r♠❡ ❋✐❧✐♣❡ ❞❡ ❏❡s✉s ❋é❧✐① ❞❛s ◆❡✈❡s ▲♦✉r❡✐r♦✱ ❋❈❚✴❯◆▲ ❡ ❯◆▲ ❆ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛ ❡ ❛ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛ tê♠ ♦ ❞✐r❡✐t♦✱ ♣❡r♣ét✉♦ ❡ s❡♠ ❧✐♠✐t❡s ❣❡♦❣rá✜❝♦s✱ ❞❡ ❛rq✉✐✈❛r ❡ ♣✉❜❧✐❝❛r ❡st❛ ❞✐ss❡rt❛çã♦ ❛tr❛✈és ❞❡ ❡①❡♠♣❧❛r❡s ✐♠♣r❡ss♦s r❡♣r♦❞✉③✐❞♦s ❡♠ ♣❛♣❡❧ ♦✉ ❞❡ ❢♦r♠❛ ❞✐❣✐t❛❧✱ ♦✉ ♣♦r q✉❛❧q✉❡r ♦✉tr♦ ♠❡✐♦ ❝♦♥❤❡❝✐❞♦ ♦✉ q✉❡ ✈❡♥❤❛ ❛ s❡r ✐♥✈❡♥t❛❞♦✱ ❡ ❞❡ ❛ ❞✐✈✉❧❣❛r ❛tr❛✈és ❞❡ r❡♣♦s✐tór✐♦s ❝✐❡♥tí✜❝♦s ❡ ❞❡ ❛❞♠✐t✐r ❛ s✉❛ ❝ó♣✐❛ ❡ ❞✐str✐❜✉✐çã♦ ❝♦♠ ♦❜❥❡❝t✐✈♦s ❡❞✉❝❛❝✐♦♥❛✐s ♦✉ ❞❡ ✐♥✈❡st✐❣❛çã♦✱ ♥ã♦ ❝♦♠❡r❝✐❛✐s✱ ❞❡s❞❡ q✉❡ s❡❥❛ ❞❛❞♦ ❝ré❞✐t♦ ❛♦ ❛✉t♦r ❡ ❡❞✐t♦r✳

  ✐✈

  ❆❣r❛❞❡❝✐♠❡♥t♦s

  ❊♠ ♣r✐♠❡✐r♦ ❧✉❣❛r✱ ♥ã♦ ♣♦❞❡ ♦ ❛✉t♦r ❞❛ ♣r❡s❡♥t❡ ❞✐ss❡rt❛çã♦ ❞❡✐①❛r ❞❡ ❛❣r❛❞❡❝❡r t♦❞❛ ❛ ❞✐s♣♦♥✐❜✐✲ ❧✐❞❛❞❡✱ ✐♥t❡r❡ss❡✱ ♠♦t✐✈❛çã♦ ❡ ❛♣♦✐♦ ❞❡♠♦♥str❛❞♦s ♣❡❧♦ Pr♦❢❡ss♦r ◆✉♥♦ ▼❛♥✉❡❧ ❞❛ ❈♦st❛ ●✉❡rr❛ ♥♦ ❛❝♦♠♣❛♥❤❛♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳

  ❆ t♦❞♦s ♦s ❝♦❧❡❣❛s q✉❡ ❞❡ ❛❧❣✉♠❛ ❢♦r♠❛ ❝♦♥tr✐❜✉ír❛♠✱ ❝♦♠ ✐♥❝❡♥t✐✈♦ ❡ ❛♠✐③❛❞❡✱ ♥♦♠❡❛❞❛♠❡♥t❡ ❛♦s ❊♥❣❡♥❤❡✐r♦s ❊❞❣❛r ❉♦♠✐♥❣✉❡s✱ ❋✐❧✐♣❡ ❈♦rr❡✐❛✱ ❏♦ã♦ ❈❛♠õ❡s✱ ▼✐❣✉❡❧ P✐r❡s✱ ◆✉♥♦ P✐r❡s✱ P❡❞r♦ P✐r❡s ❡ ❘✉✐ ●♦♥ç❛❧✈❡s✳

  ➚ ♠ã❡✱ ♣♦r t♦❞❛ ❛ ❢♦rç❛✱ ❞❡❞✐❝❛çã♦ ❡ ♣❛❝✐ê♥❝✐❛ q✉❡ s❡♠♣r❡ ❞❡♠♦♥str♦✉ ♥♦ ❞❡❝♦rr❡r ❞♦ tr❛❜❛❧❤♦✳ ▼✉✐t♦ ♦❜r✐❣❛❞♦ ♣❡❧♦s ❡s❢♦rç♦s ❢❡✐t♦s ❛♦ ❧♦♥❣♦ ❞❡ t♦❞♦ ♦ ♣❡r❝✉rs♦ ❛❝❛❞é♠✐❝♦✳

  ❆♦ ♣❛✐ ❡ ✐r♠ã♦✱ ♣❡❧❛ ♠♦t✐✈❛çã♦ ❞❡♠♦♥str❛❞❛ ❡ ♣❡❧♦ s❡✉ ❛♣♦✐♦✳ ➚ r❡st❛♥t❡ ❢❛♠í❧✐❛✱ ♥♦♠❡❛❞❛♠❡♥t❡✱ ❛✈ô✱ ♣r✐♠♦s✱ t✐♦s ❡✱ ❞❡ ♠♦❞♦ ❡s♣❡❝✐❛❧ à ❘♦s❛✱ ♣❡❧♦ ❝♦♥st❛♥t❡ ✐♥❝❡♥t✐✈♦ ❡ ❝❛r✐♥❤♦ ❝♦♠ q✉❡ s❡♠♣r❡ ❛♣♦✐❛r❛♠✳

  ❆♦ Pr♦❢❡ss♦r ❏♦r❣❡ ◆✉♥♦ ❱❡✐❣❛ ❞❡ ❆❧♠❡✐❞❛ ❡ ❙♦✉s❛ ♣❡❧❛ r❡✈✐sã♦ ❞♦ tr❛❜❛❧❤♦ ❛♣ós ❛ ❡♥tr❡❣❛ ❞❛ ✈❡rsã♦ ♣r♦✈✐sór✐❛✳

  ❆♦s ❛♠✐❣♦s✱ ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ❡ ❛♠✐③❛❞❡ ❞❡♠♦♥str❛❞♦s✳ ❆ t♦❞♦s ✉♠ ♣r♦❢✉♥❞♦ ❡ s✐♥❝❡r♦ ♦❜r✐❣❛❞♦✳

  ✈✐

  ❘❡s✉♠♦

  ❆s ❡str✉t✉r❛s ❞❡ s✉♣♦rt❡ ❡♠ ❝♦♥s♦❧❛ ♥ã♦ tê♠ ✉♠ ♣❛r❛♠❡♥t♦ ❜❡♠ ❞❡✜♥✐❞♦ ♥♦ q✉❛❧ s❡ ♣♦ss❛ ❝♦♥s✐❞❡r❛r q✉❡ ♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s sã♦ ❛♣❧✐❝❛❞♦s✳ ❈♦♠ ❡❢❡✐t♦✱ ❡①✐st❡✱ ♣♦r ✈❡③❡s✱ ❛ ❞❡s✐❣♥❛❞❛ ✏❝✉♥❤❛ ♠♦rt❛✑✱ q✉❡ tr❛❞✉③ ♦ s♦❧♦ q✉❡ ❛❝♦♠♣❛♥❤❛ ♦ ♠✉r♦ ❞❡ s✉♣♦rt❡ q✉❛♥❞♦ ❡st❡ s♦❢r❡ ❛❧❣✉♠ ♠♦✈✐♠❡♥t♦✳ ❘❡✈ê❡♠✲s❡ ♦s ♠ét♦❞♦s ❞❡ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ✐♠♣✉❧s♦s ❞❡ t❡rr❛s s♦❜r❡ ❡str✉t✉r❛s ❞❡ s✉♣♦rt❡ ❡♠ ❝♦♥s♦❧❛ ❡ ❞❛ ❣❡♦♠❡tr✐❛ ❞❛ r❡❢❡r✐❞❛ ❝✉♥❤❛✳ ❈♦♠♣❛r❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ❛ q✉❡ ❝♦♥❞✉③❡♠ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ❝♦♠♣♦♥❡♥t❡ ❤♦r✐③♦♥t❛❧ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❡ ❞❛ r❡❧❛çã♦ ❡♥tr❡ ❡st❛ ❝♦♠♣♦♥❡♥t❡ ❡ ❛ ❢♦rç❛ t♦t❛❧ ✈❡rt✐❝❛❧ s♦❜r❡ ❛ ❜❛s❡ ❞♦ ♠✉r♦✳ ❆♣❧✐❝❛✲s❡ ♦ ♠ét♦❞♦ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ❛tr❛✈és ❞❡ ❝á❧❝✉❧♦ ❡❧❛st♦✲♣❧ást✐❝♦✱ à ❞❡t❡r♠✐♥❛çã♦ ❞❛s ❞✉❛s ❣r❛♥❞❡③❛s r❡❢❡r✐❞❛s ❡ ❝♦♠♣❛r❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥✉♠❡r✐❝❛♠❡♥t❡ ❝♦♠ ♦s ❞♦s ♠ét♦❞♦s ❞✐s♣♦♥í✈❡✐s✳ ❈♦♥❝❧✉✐✲s❡ ❞❛ ❛❞❡q✉❛❜✐❧✐❞❛❞❡ ❞❛ ❛♣❧✐❝❛çã♦ ❞♦s ♠ét♦❞♦s tr❛❞✐❝✐♦♥❛❧♠❡♥t❡ ✉s❛❞♦s✳

  P❛❧❛✈r❛s✲❝❤❛✈❡✿

  ▼✉r♦s ❞❡ s✉♣♦rt❡❀ ♠✉r♦s ❡♠ ❝♦♥s♦❧❛❀ ✐♠♣✉❧s♦ ❛❝t✐✈♦❀ ✈❡r✐✜❝❛çã♦ ❞♦ ❞❡s❧✐③❛♠❡♥t♦✳

  ✈✐✐✐

  ❆❜str❛❝t

  ❚❤❡ ❝❛♥t✐❧❡✈❡r r❡t❛✐♥✐♥❣ str✉❝t✉r❡s ❞♦♥✬t ❤❛✈❡ ❛ ✇❡❧❧ ❞❡✜♥❡❞ ❢❛❝❡ ✐♥ ✇❤✐❝❤ ✐t ❝❛♥ ❜❡ ❝♦♥s✐❞❡r❡❞ t❤❛t t❤❡ ❛❝t✐✈❡ ❡❛rt❤ ♣r❡ss✉r❡s ❛r❡ ❛♣♣❧✐❡❞✳ ❚❤❡r❡❢♦r❡✱ ❛ ✏❞❡❛❞ ✇❡❞❣❡✑ ✐s ❢♦r♠❡❞✱ ❝♦♥s✐st✐♥❣ ❜② t❤❡ t❤❡ ♣♦rt✐♦♥ ♦❢ t❤❡ s♦✐❧ t❤❛t ♠♦✈❡s ✇✐t❤ t❤❡ ✇❛❧❧✳ ❚❤❡ ♠❡t❤♦❞s ❢♦r t❤❡ ❞❡t❡r♠✐♥❛t✐♦♥ ♦❢ ❛❝t✐✈❡ ❡❛rt❤ ♣r❡ss✉r❡s ♦♥ ❝❛♥t✐❧❡✈❡r r❡t❛✐♥✐♥❣ ✇❛❧❧s ❛♥❞ ♦❢ t❤❡ ❣❡♦♠❡tr② ♦❢ t❤✐s ✇❡❞❣❡ ❛r❡ r❡✈✐❡✇❡❞✳ ❘❡s✉❧ts ♦❢ t❤❡ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ t❤❡s❡ ♠❡t❤♦❞s t♦ t❤❡ ❞❡t❡r♠✐♥❛t✐♦♥ ♦❢ t❤❡ ❤♦r✐③♦♥t❛❧ ❝♦♠♣♦♥❡♥t ♦❢ t❤❡ ❛❝t✐✈❡ ❡❛rt❤ ♣r❡ss✉r❡ ❛♥❞ t❤❡ r❛t✐♦ ❜❡t✇❡❡♥ t❤✐s ❝♦♠♣♦♥❡♥t ❛♥❞ t❤❡ t♦t❛❧ ✈❡rt✐❝❛❧ ❢♦r❝❡ ❛❝t✐♥❣ ♦♥ t❤❡ ❜❛s❡ ♦❢ t❤❡ ✇❛❧❧ ❛r❡ ❝♦♠♣❛r❡❞✳ ❚❤❡ ✜♥✐t❡ ❡❧❡♠❡♥t ♠❡t❤♦❞ ✐s ❛♣♣❧✐❡❞✱ ✉s✐♥❣ ❡❧❛st✐❝✲♣❡r❢❡❝t❧② ♣❧❛st✐❝ ❝❛❧❝✉❧❛t✐♦♥s✱ t♦ ❞❡t❡r♠✐♥❡ t❤❡ t✇♦ q✉❛♥t✐t✐❡s ♠❡♥t✐♦♥❡❞ ❛❜♦✈❡ ❛♥❞ t❤❡ r❡s✉❧ts ❛r❡ ❝♦♠♣❛r❡❞ ✇✐t❤ t❤❡ r❡s✉❧ts ♦❜t❛✐♥❡❞ ❜② t❤❡ ❛✈❛✐❧❛❜❧❡ ♠❡t❤♦❞s✳

  ❑❡②✇♦r❞s✿

  ❘❡t❛✐♥✐♥❣ ✇❛❧❧s❀ ❝❛♥t✐❧❡✈❡r ✇❛❧❧s❀ ❛❝t✐✈❡ ❡❛rt❤ ♣r❡ss✉r❡❀ s❧✐❞✐♥❣ ✈❡r✐✜❝❛t✐♦♥✳

  ①

  ❙✐♠❜♦❧♦❣✐❛

  a ❉✐♠❡♥sã♦ ❞❛ ♣❛r❡❞❡ ❞❛ ❡str✉t✉r❛ ❬L❪

  B ❉✐♠❡♥sã♦ ❞❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡ ❬L❪ b ▼❡♥♦r ❡s♣❡ss✉r❛ ❞❛ ♣❛r❡❞❡ ❞♦ ♠✉r♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❬L❪ b

  1 ▼❛✐♦r ❡s♣❡ss✉r❛ ❞❛ ♣❛r❡❞❡ ❞❛ ❡str✉t✉r❛ ❬L❪

  B

  1

  ✱ B

  2

  ✱ B

3 P❛r❝❡❧❛s ❞❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡ ❬L❪

  2

  1

  i ■♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦

  2 ❬L❪

  ❉✐♠❡♥sã♦ ❛✉①✐❧✐❛r ❞❛ ❛❧t✉r❛ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ✲ ▼ét♦❞♦ C

  3

  ′

  h

  3 ❈♦♠♣♦♥❡♥t❡ ❞❛ ❛❧t✉r❛ t♦t❛❧ ❞❛ ❡str✉t✉r❛ ✲ ▼ét♦❞♦ C 2 ❬L❪

  h

  2 ❈♦♠♣♦♥❡♥t❡ ❞❛ ❛❧t✉r❛ t♦t❛❧ ❞❛ ❡str✉t✉r❛ ✲ ▼ét♦❞♦ C 2 ❬L❪

  h

  1 ❈♦♠♣♦♥❡♥t❡ ❞❛ ❛❧t✉r❛ t♦t❛❧ ❞❛ ❡str✉t✉r❛ ✲ ▼ét♦❞♦ C 2 ❬L❪

  ❬L❪ h

  2

  ❆❧t✉r❛ t♦t❛❧ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ✲ ▼ét♦❞♦ C

  ❆❧t✉r❛ t♦t❛❧ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ✲ ▼ét♦❞♦ ❘ ❬L❪ H

  ▼❡♥♦r ❡s♣❡ss✉r❛ ❞❛ ♣❛r❡❞❡ ❞❛ ❡str✉t✉r❛ ❬L❪ c

  ′

  H

  2 ❬L❪

  ❆❧t✉r❛ ❞❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡ ❬L❪ h ❉✐♠❡♥sã♦ ❛✉①✐❧✐❛r ❞❛ ❛❧t✉r❛ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ✲ ▼ét♦❞♦ C

  b

  a ❋♦rç❛ ❞❡ ❛tr✐t♦ ♥❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ ❬F L −1

  F

  ❪ e ❊s♣❡ss✉r❛ ❞❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ ❬L❪

  −2

  E ▼ó❞✉❧♦ ❞❡ ❨♦✉♥❣ ❬F L

  ❪ d ❉❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧ ❬L❪

  

−2

  ❈♦❡sã♦ ❡❢❡❝t✐✈❛ ❞♦ s♦❧♦ ❬F L

  ′

  ❪ H

  ①✐✐ K a

  1

  β ■♥❝❧✐♥❛çã♦ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❡♠ r❡❧❛çã♦ à ❤♦r✐③♦♥t❛❧

  β

  B ■♥❝❧✐♥❛çã♦ ❞❛ ❝✉♥❤❛ ❞❡ s♦❧♦ ✲ ❇❛r❣❤♦✉t❤✐

  β

  ′ B

  ■♥❝❧✐♥❛çã♦ ✈❛r✐á✈❡❧ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❡♠ r❡❧❛çã♦ à ❤♦r✐③♦♥t❛❧ ✲ ❇❛r❣❤♦✉t❤✐ β

  ′ ∗ B

  ■♥❝❧✐♥❛çã♦ ✜①❛ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❡♠ r❡❧❛çã♦ à ❤♦r✐③♦♥t❛❧ ✲ ❇❛r❣❤♦✉t❤✐ β

  C1 ■♥❝❧✐♥❛çã♦ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❡♠ r❡❧❛çã♦ à ❤♦r✐③♦♥t❛❧ ✲ ♠ét♦❞♦ C

  β

  ❪ z Pr♦❢✉♥❞✐❞❛❞❡ ❞♦ s♦❧♦ ❬L❪

  C2 ■♥❝❧✐♥❛çã♦ ✈❛r✐á✈❡❧ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❡♠ r❡❧❛çã♦ à ❤♦r✐③♦♥t❛❧ ✲ ♠ét♦❞♦ C

  2

  β

  ∗ C2

  ■♥❝❧✐♥❛çã♦ ✜①❛ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❡♠ r❡❧❛çã♦ à ❤♦r✐③♦♥t❛❧ ✲ ♠ét♦❞♦ C

  2

  β

  C2,I H a

  ■♥❝❧✐♥❛çã♦ ✈❛r✐á✈❡❧ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧✱ ❡♠ r❡❧❛çã♦ à ❤♦r✐③♦♥t❛❧ ✲ ❝♦♠♣♦♥❡♥t❡ ❤♦r✐③♦♥t❛❧ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦

  β

  α ❈♦♠♣♦♥❡♥t❡ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞❛ ❢❛❝❡ ❡①t❡r✐♦r ❞❛ ♣❛r❡❞❡ ❞❛ ❡str✉t✉r❛

  −1

  ❈♦❡✜❝✐❡♥t❡ ❞❡ ✐♠♣✉❧s♦ ❛❝t✐✈♦ L

  P❡s♦ t♦t❛❧ ❞❛ ❝✉♥❤❛ ❞❡ s♦❧♦ ❡ ❞♦ ♠✉r♦ ❬F ❪ w

  ❚✐♣♦ ❞❡ s❡❝çã♦ ❞♦ ♠✉r♦ ❞❡ s✉♣♦rt❡ l ❉✐♠❡♥sã♦ ❛✉①✐❧✐❛r ❞❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ ❬L❪ l

  2 ❉✐♠❡♥sã♦ ❛✉①✐❧✐❛r ❞❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ ❬L❪

  l

  3

  ❉✐♠❡♥sã♦ ❛✉①✐❧✐❛r ❞❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ ❬L❪ R inter

  ❋❛❝t♦r ❞❡ r❡❞✉çã♦ ❞❡ r❡s✐stê♥❝✐❛ ❞❡ ✐♥t❡r❢❛❝❡ T

  ❚✐♣♦ ❞❡ s❡❝çã♦ ❞♦ ♠✉r♦ ❞❡ s✉♣♦rt❡

  V ❘❡s✉❧t❛♥t❡ ❞❛s ❝❛r❣❛s ✈❡rt✐❝✐❛✐s ❬F L

  −1

  ❪ W

  1

  w s P❡s♦ ❞♦ s♦❧♦ ♥❛ ❝✉♥❤❛ ♠♦rt❛ ❬F L

  ❈♦♠♣♦♥❡♥t❡ ❞♦ ♣❡s♦ t♦t❛❧ ❞❛ ❡str✉t✉r❛ ❬F L

  −1

  ❪ w

  2 ❈♦♠♣♦♥❡♥t❡ ❞♦ ♣❡s♦ t♦t❛❧ ❞❛ ❡str✉t✉r❛ ❬F L −1

  ❪ w

  s1 ❈♦♠♣♦♥❡♥t❡ ❛✉①✐❧✐❛r ❞♦ ♣❡s♦ ❞♦ s♦❧♦ ♥❛ ❝✉♥❤❛ ♠♦rt❛ ❬F ❪

  w

  s2 ❈♦♠♣♦♥❡♥t❡ ❛✉①✐❧✐❛r ❞♦ ♣❡s♦ ❞♦ s♦❧♦ ♥❛ ❝✉♥❤❛ ♠♦rt❛ ❬F ❪

  w

  s3 ❈♦♠♣♦♥❡♥t❡ ❛✉①✐❧✐❛r ❞♦ ♣❡s♦ ❞♦ s♦❧♦ ♥❛ ❝✉♥❤❛ ♠♦rt❛ ❬F ❪

  

C2,tan δ ■♥❝❧✐♥❛çã♦ ✈❛r✐á✈❡❧ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧✱ ❡♠ r❡❧❛çã♦ à ❤♦r✐③♦♥t❛❧ ✲ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦

  ①✐✐✐ ε

  ′ h,a

  ■♥❝❧✐♥❛çã♦ ✐♥t❡r✐♦r ❞❛ ♣❛r❡❞❡ ❞❛ ❡str✉t✉r❛ ψ

  ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❡❢❡❝t✐✈♦ ❞♦ s♦❧♦ ϕ

  ′

  ❈♦❡✜❝✐❡♥t❡ ❞❡ P♦✐ss♦♥ φ

  ❪ υ

  −2

  ❚❡♥sã♦ ❞❡ ❝♦rt❡ t❛♥❣❡♥❝✐❛❧ ❬F L

  ❪ τ

  −2

  ❚❡♥sã♦ ❡❢❡❝t✐✈❛ ✈❡rt✐❝❛❧ ❬F L

  ′ v

  ❪ σ

  −2

  ❚❡♥sã♦ ❡❢❡❝t✐✈❛ ❤♦r✐③♦♥t❛❧ ❛❝t✐✈❛ ❬F L

  ❪ σ

  ❉❡❢♦r♠❛çã♦ ❞♦ s♦❧♦ ❬L❪ θ

  −2

  ❚❡♥sã♦ ❡❢❡❝t✐✈❛ ❬F L

  ′

  σ

  ξ ❈♦♠♣♦♥❡♥t❡ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞❛ ❢❛❝❡ ❡①t❡r✐♦r ❞❛ ♣❛r❡❞❡ ❞❛ ❡str✉t✉r❛

  2

  ■♥❝❧✐♥❛çã♦ ✜①❛ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❡♠ r❡❧❛çã♦ à ✈❡rt✐❝❛❧ ✲ ♠ét♦❞♦ C

  ∗ C2

  θ

  2

  C2 ■♥❝❧✐♥❛çã♦ ✈❛r✐á✈❡❧ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❡♠ r❡❧❛çã♦ à ✈❡rt✐❝❛❧ ✲ ♠ét♦❞♦ C

  θ

  1

  C1 ■♥❝❧✐♥❛çã♦ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❡♠ r❡❧❛çã♦ à ✈❡rt✐❝❛❧ ✲ ♠ét♦❞♦ C

  ➶♥❣✉❧♦ ❞❡ ❞✐❧❛tâ♥❝✐❛ ❞♦ s♦❧♦

  ①✐✈

  ❈♦♥t❡ú❞♦

  ✶ ■♥tr♦❞✉çã♦ ✶

  ✷ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ✸

  ✷✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✷✳✷ ▼ét♦❞♦s ❝❧áss✐❝♦s ❞❡ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ✐♠♣✉❧s♦s ❛❝t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸

  ✷✳✷✳✶ ❆ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✷✳✷✳✷ ❆ t❡♦r✐❛ ❞❡ ❈♦✉❧♦♠❜ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

  ✷✳✸ ❚✐♣♦s ❞❡ ♠✉r♦s ❞❡ s✉♣♦rt❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✸✳✶ ▼✉r♦s ❞❡ ❣r❛✈✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✸✳✷ ▼✉r♦s ❡♠ ❝♦♥s♦❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵

  ✷✳✹ ■♠♣✉❧s♦s ❛❝t✐✈♦s s♦❜r❡ ❡str✉t✉r❛s ❞❡ s✉♣♦rt❡ ❡♠ L ♦✉ T ✐♥✈❡rt✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✹✳✶ ▼ét♦❞♦ ❜❛s❡❛❞♦ ♥❛ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡ ✭▼ét♦❞♦ R✮ ✭❚❡r③❛❣❤✐ ❡t ❛❧✳✱ ✶✾✹✽✮ ✳ ✳ ✳ ✶✷ ✷✳✹✳✷ ▼ét♦❞♦ ❜❛s❡❛❞♦ ♥♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜ ✭▼ét♦❞♦ C

  1 ✮ ✭▼✐♥❡✐r♦✱ ✶✾✼✽✮ ✳ ✳ ✳ ✳ ✳ ✶✸

  ✷✳✹✳✸ ▼ét♦❞♦ ❜❛s❡❛❞♦ ♥♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜ ✭▼ét♦❞♦ C

  2 ✮ ✭▼❛t♦s ❋❡r♥❛♥❞❡s ❡t ❛❧✳✱

  ✶✾✾✼✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✸ ❆♥á❧✐s❡ ❞❡ ❡str✉t✉r❛s ❞❡ s✉♣♦rt❡ ❡♠ ▲

  ✶✾ ✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✷ ❉❡✜♥✐çã♦ ❞❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✸ ❈á❧❝✉❧♦ ❞♦s ✐♠♣✉❧s♦s s♦❜r❡ ❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

  ✸✳✸✳✶ ▼ét♦❞♦ R ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✸✳✷ ▼ét♦❞♦ C

  1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶

  ✸✳✸✳✸ ▼ét♦❞♦ C

  2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷

  ✸✳✹ ❈♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✹✳✶ ▼ét♦❞♦ R ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✹✳✷ ▼ét♦❞♦ C

  1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾

  ✸✳✹✳✸ ▼ét♦❞♦ C

  2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ′

  1

  ✸✳✺ ❆♥á❧✐s❡ ♣❛r❛♠étr✐❝❛✿ ✐♥❢✳ ❞❡ φ ✱ i ❡ ❝♦♠♣✳ ❞❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✺✳✶ ■♠♣✉❧s♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷

  ✸✳✺✳✶✳✶ ▼ét♦❞♦s R ❡ C

  1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷

  ①✈✐ ❈❖◆❚❊Ú❉❖

  ✸✳✺✳✸✳✷ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✺✳✹ ❘❡s✉❧t❛❞♦s ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻

  ✸✳✺✳✹✳✶ ❆♣r❡s❡♥t❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✺✳✹✳✷ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

  ✸✳✻ ❆♥á❧✐s❡ ♣❛r❛♠étr✐❝❛✿ ✐♥✢✉ê♥❝✐❛ ❞❡ δ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✸✳✻✳✶ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✸✳✻✳✷ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✸✳✻✳✸ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

  e H

  / ✸✳✼ ❆♥á❧✐s❡ ♣❛r❛♠étr✐❝❛✿ ✐♥✢✉ê♥❝✐❛ ❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

  ✸✳✼✳✶ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✼✳✷ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✼✳✸ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹

  ✹ ❆♣❧✐❝❛çã♦ ❞❡ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ✻✺

  ✹✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✷ ▼♦❞❡❧♦ ❝♦♥st✐t✉t✐✈♦ ▼♦❤r✲❈♦✉❧♦♠❜ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✸ ❈❛s♦ ❜❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼

  ✹✳✸✳✶ ❉❡s❝r✐çã♦ ❞♦ ❝❛s♦ ❜❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✸✳✷ ❘❡s✉❧t❛❞♦s ❡ ❛♥á❧✐s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾

  ✹✳✹ ❆♥á❧✐s❡ ♣❛r❛♠étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✹✳✹✳✶ ❉❡s❝r✐çã♦ ❞♦s ❝❛s♦s ❛♥❛❧✐s❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✹✳✹✳✷ ❆♥á❧✐s❡ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞♦ ❢❛❝t♦r R inter ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷

  ✹✳✹✳✷✳✶ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✹✳✹✳✷✳✷ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✹✳✷✳✸ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼

  ′

  ✹✳✹✳✸ ❆♥á❧✐s❡ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦✱ φ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✹✳✹✳✸✳✶ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✹✳✹✳✸✳✷ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✹✳✹✳✸✳✸ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷

  ✹✳✹✳✹ ❆♥á❧✐s❡ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ B

  1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷

  ✹✳✹✳✹✳✶ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✹✳✹✳✹✳✷ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✹✳✹✳✹✳✸ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼

  ✹✳✹✳✺ ❆♥á❧✐s❡ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ i ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✹✳✹✳✺✳✶ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✹✳✹✳✺✳✷ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✹✳✹✳✺✳✸ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵

  ✺ ❈♦♥❝❧✉sõ❡s ❡ ❢✉t✉r♦s ❞❡s❡♥✈♦❧✈✐♠❡♥t♦s ✶✵✶

  ✺✳✶ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✺✳✷ ❋✉t✉r♦s ❞❡s❡♥✈♦❧✈✐♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷

  ▲✐st❛ ❞❡ ❋✐❣✉r❛s

  ✶✳✶ ▼✉r♦ ❡♠ ❝♦♥s♦❧❛✳ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ✏❝✉♥❤❛ ♠♦rt❛✑ ❡ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✷✳✶ ■♠♣✉❧s♦ ❞❡ t❡rr❛s✿ ❆ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✷✳✷ ❉❡t❡r♠✐♥❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛tr❛✈és ❞❛ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡ ✭❛❞❛♣t❛❞♦ ❞❡ ▼✐♥❡✐r♦✱

  ✶✾✼✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✷✳✸ ■♠♣✉❧s♦ ❞❡ t❡rr❛s✿ ❛ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡ ❛♣❧✐❝❛❞❛ ❛ t❡rr❡♥♦ ❝♦♠ ✐♥❝❧✐♥❛çã♦ ✭❛❞❛♣t❛❞♦ ❞❡

  ❈❡r♥✐❝❛✱ ✶✾✾✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✹ ❈✉♥❤❛ ❞❡ s♦❧♦ ❛❝t✐✈❛ ❛tr❛✈és ❞❛ t❡♦r✐❛ ❞❡ ❈♦✉❧♦♠❜ ✭❛❞❛♣t❛❞♦ ❞❡ ❈❡r♥✐❝❛✱ ✶✾✾✹✮✳ ✳ ✳ ✳ ✻ ✷✳✺ ●❡♦♠❡tr✐❛ ❞❡ ♠✉r♦s ❞❡ ❣r❛✈✐❞❛❞❡ ✭❈❡r♥✐❝❛✱ ✶✾✾✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✻ ▼✉r♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❝♦♠ ♣❡r✜❧ r❡❝t❛♥❣✉❧❛r ✭❛❞❛♣t❛❞♦ ❞❡ ❉♦♠✐♥❣✉❡s ✭✶✾✾✼✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✼ ▼✉r♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❝♦♠ ♣❡r✜❧ tr❛♣❡③♦✐❞❛❧ ✭❛❞❛♣t❛❞♦ ❞❡ ❉♦♠✐♥❣✉❡s ✭✶✾✾✼✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✽ ▼✉r♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❝♦♠ ♣❡r✜❧ ❡♠ ❡s❝❛❞❛ ✭❛❞❛♣t❛❞♦ ❞❡ ❉♦♠✐♥❣✉❡s ✭✶✾✾✼✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✾ ❚✐♣♦❧♦❣✐❛ ❞❛s ❣❛✐♦❧❛s ❡ ❣❡♦♠❡tr✐❛ ❞❛ ♠❛❧❤❛ ✭❇❙ ✽✵✵✷✿✶✾✾✹ ✭✷✵✵✷✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✶✵ ▼✉r♦ ❞❡ ❣❛❜✐õ❡s ✭❆❣✉✐❛r ❡ ▼❛rt✐♥s✱ ✷✵✵✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✶✶ ●❡♦♠❡tr✐❛ ❞❡ ♠✉r♦s ❡♠ ❝♦♥s♦❧❛ ✭❈❡r♥✐❝❛✱ ✶✾✾✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✶✷ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ♠✉r♦ ❝♦♠ ❛♥❝♦r❛❣❡♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✶✸ ❙✉♣❡r❢í❝✐❡ ❞❡ r♦t✉r❛✿ ❊st❛❞♦ ❛❝t✐✈♦ ✭❚❡r③❛❣❤✐ ❡t ❛❧✳✱ ✶✾✹✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✶✹ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♠ét♦❞♦ ❜❛s❡❛❞♦ ♥❛ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡ ✲ ♠ét♦❞♦ R ✭❛❞❛♣✲ t❛❞♦ ❞❡ ❚❡r③❛❣❤✐ ❡t ❛❧✳✱ ✶✾✹✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✶✺ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♠ét♦❞♦ ❜❛s❡❛❞♦ ♥♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜ ✲ ♠ét♦❞♦ C

  1 ✳ ✳ ✶✸

  ✷✳✶✻ ▼ét♦❞♦ ❞❡ ❛✈❛❧✐❛çã♦ ❞♦s ✐♠♣✉❧s♦s ❡♠ ♠✉r♦s ❞❡ ❜❡tã♦ ❛r♠❛❞♦ ✭▼❛t♦s ❋❡r♥❛♥❞❡s ❡t ❛❧✳ ✭✶✾✾✼✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹

  2

  ✷✳✶✼ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♠ét♦❞♦ C ✿ ✐♥❝❧✐♥❛çã♦ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❞♦ ♠✉r♦✳ ✳ ✶✺ ✷✳✶✽ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♠ét♦❞♦ C

  2 ✿ ❞✐❛❣r❛♠❛s ❞❡ t❡♥sõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

  ✷✳✶✾ ▼✉r♦ ❡♠ ❝♦♥s♦❧❛ ❡ ❝✉♥❤❛s ❞❡ t❡rr❛s ❡♠ ❡st❛❞♦ ❛❝t✐✈♦ ✭❛❞❛♣t❛❞♦ ❞❡ ▼❛t♦s ❋❡r♥❛♥❞❡s✱ ✷✵✶✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

  ✷✳✷✵ ❆✈❛❧✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❡♠ ♠✉r♦s ❡♠ ❝♦♥s♦❧❛✳ ❈❛s♦ ❡♠ q✉❡ ❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ♦ ♣❛r❛♠❡♥t♦ s❡ ❡♥❝♦♥tr❛ ❛❝✐♠❛ ❞♦ t♦♣♦ ❞♦ ♠✉r♦ ✭❛❞❛♣t❛❞♦ ❞❡ ▼❛t♦s ❋❡r♥❛♥❞❡s✱ ✷✵✶✶✮✳ ✶✼

  ✷✳✷✶ ❆✈❛❧✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❡♠ ♠✉r♦s ❡♠ ❝♦♥s♦❧❛✳ ❈❛s♦ ❡♠ q✉❡ ❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ♦ ♣❛r❛♠❡♥t♦ s❡ ❡♥❝♦♥tr❛ ❛❜❛✐①♦ ❞♦ t♦♣♦ ❞♦ ♠✉r♦ ✭❛❞❛♣t❛❞♦ ❞❡ ▼❛t♦s ❋❡r♥❛♥❞❡s✱ ✷✵✶✶✮✳ ✶✼

  ①✈✐✐✐ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙

  ✿ ♠ét♦❞♦ C

  = 30

  ′

  ✸✳✷✺ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

  = 0, 125 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

  

H

  /

  

e

  ❀

  o

  = 20

  ′

  ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

  ✳ ✳ ✹✻ ✸✳✷✹ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

  2

  o

  ❀

  = 0, 125 ❡ i = 5

  H

  /

  e

  ✱

  o

  = 20

  

  ✸✳✷✸ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ✐♥❝❧✐♥❛çã♦ β C2,I H a ♣❛r❛ φ

  = 0, 125 ✳ ✹✺

  H

  /

  2 ✿ e

  ✸✳✷✷ ❱❛r✐❛çã♦ ❞❛ ✐♥❝❧✐♥❛çã♦ β C2,I H a ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ â♥❣✉❧♦s ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦ ✿ ♠ét♦❞♦ C

  o

  

e

  2 ✿ e

  

H

  o

e

  = 45

  ′

  ✸✳✷✾ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

  = 0, 125 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

  

H

  /

  

e

  ❀

  o

  = 45

  ′

  ✸✳✷✽ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

  = 0, 125 ✭❝♦♥t✐♥✉❛çã♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

  /

  /

  ❀

  

H

  = 0, 125 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽

  ✸✳✷✻ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

  ′

  = 40

  o

  

e

  

e

  / H = 0, 125 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

  ✸✳✷✼ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

  ′

  = 40

  o

  ❀

  / H = 0, 125 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹

  ✸✳✷✶ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs♦s â♥❣✉❧♦s ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❡ ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❡❧♦ ♠ét♦❞♦ C

  ✸✳✻ P♦r♠❡♥♦r ❞❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ ❣r❛♥❞❡③❛s✿ ▼ét♦❞♦ C

  ′

  /

  e

  ❀

  o

  = 30

  ′

  ✸✳✶✻ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

  = 0, 125 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼

  H

  /

  e

  ❀

  o

  = 20

  ✸✳✶✺ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

  = 0, 125 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

  2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

  ✸✳✶✹ ▲❛②♦✉t ❞♦ ♦✉t♣✉t✿ ▼ét♦❞♦ C

  2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✶✸ ▲❛②♦✉t ❞♦ ✐♥♣✉t✿ ▼ét♦❞♦ C

  2

  ✸✳✶✷ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ♣❡s♦ ♣r❡s❡♥t❡ ♥❛ ❝✉♥❤❛ ❞❡ s♦❧♦✿ ♠ét♦❞♦ C

  2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

  ✸✳✶✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ❣r❛♥❞❡③❛s✿ ♠ét♦❞♦ C

  1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾

  ✸✳✾ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ❣r❛♥❞❡③❛s✿ ♠ét♦❞♦ R✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✶✵ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ❣r❛♥❞❡③❛s✿ ♠ét♦❞♦ C

  ✸✳✽ ■❧✉str❛çã♦ ❣❡♥ér✐❝❛ ❞❛s ♣r✐♥❝✐♣❛✐s ❣r❛♥❞❡③❛s ❡♥✈♦❧✈✐❞❛s ♥♦ ❡st✉❞♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s✲ ❧✐③❛♠❡♥t♦✿ ❡①❡♠♣❧♦ ♠ét♦❞♦ R✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

  2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✼ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ✐♠♣✉❧s♦s ♣❛r❝✐❛✐s✿ ▼ét♦❞♦ C

  2

  H

  ✸✳✶✼ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

  = 0, 125 ✭❝♦♥t✐♥✉❛çã♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷

  = 45

  H

  /

  e

  ❀

  o

  = 45

  ′

  ✸✳✷✵ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ φ

  = 0, 125 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶

  H

  /

  e

  ❀

  o

  ′

  ′

  = 0, 125 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾

  = 40

  o

  ❀

  e

  /

  H

  ✸✳✶✽ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

  ✸✳✶✾ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

  ′

  = 40

  o

  ❀

  e

  / H = 0, 125 ✭❝♦♥t✐♥✉❛çã♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

  / H = 0, 125

  ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ 2 ①✐①

  B 1 = 2 m = 0, 188

  ✸✳✸✷ ■♥✢✉ê♥❝✐❛ ❞♦ ♣❛râ♠❡tr♦ δ s−e ♥♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ♣❛r❛ B ❀

  H ′ o ∗

  φ = 30 > β ✳ ❈❛s♦ β C2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

  C2 2 B

  = 7 m = 0, 813 ✸✳✸✸ ■♥✢✉ê♥❝✐❛ ❞♦ ♣❛râ♠❡tr♦ δ ♥♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ♣❛r❛ B

  1 ❀ s−e H ′ o ∗

  φ = 30 < β ✳ ❈❛s♦ β C2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽

  C2

  = 2 m ✸✳✸✹ ■♥✢✉ê♥❝✐❛ ❞♦ ♣❛râ♠❡tr♦ δ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦ ♣❛r❛ B

  1 2 s−e B ′ o ∗

  = 0, 188 = 30 > β ❀ φ ✳ ❈❛s♦ β C2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾

  C2 H

  = 7 m ✸✳✸✺ ■♥✢✉ê♥❝✐❛ ❞♦ ♣❛râ♠❡tr♦ δ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦ ♣❛r❛ B

  1 2 s−e B ′ o ∗

  = 0, 813 = 30 < β ❀ φ ✳ ❈❛s♦ β C2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵

  C2 H

  ✸✳✸✻ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦

  

′ o ′ o

e

  

2

H

  3

  / = 30 / φ ♣❛r❛ ❞✐✈❡rs♦s ✈❛❧♦r❡s ❞❡ ✿ φ ❀ δ = ❀ i = 0 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷

  ✸✳✸✼ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

  ′ o ′ o e

2 H

  3

  / = 30 / φ ❞✐✈❡rs♦s ✈❛❧♦r❡s ❞❡ ✿ φ ❀ δ = ❀ i = 0 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

  ✹✳✶ ▼♦❞❡❧♦ ❡❧ást✐❝♦ ♣❡r❢❡✐t❛♠❡♥t❡ ♣❧ást✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✷ ❈r✐tér✐♦ ❞❡ ❝❡❞ê♥❝✐❛ ❞❡ ▼♦❤r✲❈♦✉❧♦♠❜ ✭❇r✐♥❦❣r❡✈❡ ❡t ❛❧✳✱ ✷✵✵✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✸ ❙✉♣❡r❢í❝✐❡ ❞❡ r♦t✉r❛ ❞♦ ♠♦❞❡❧♦ ▼♦❤r✲❈♦✉❧♦♠❜✱ ♥♦ ❡s♣❛ç♦ ❞❛s t❡♥sõ❡s ♣r✐♥❝✐♣❛✐s✱ ♣❛r❛ s♦❧♦s ♥ã♦ ❝♦❡s✐✈♦s ✭❇r✐♥❦❣r❡✈❡ ❡t ❛❧✳✱ ✷✵✵✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✹ ❉✐♠❡♥sõ❡s ❞❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡✿ ♠♦❞❡❧♦ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳ ❈❛s♦ ❜❛s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✺ ▼❛❧❤❛ ❞♦ ♠♦❞❡❧♦ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✿ ❝❛s♦ ❜❛s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✻ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❤♦r✐③♦♥t❛❧ ❡♠ ❢✉♥çã♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧✿ ❝❛s♦ ❜❛s❡✳ ✻✾ ✹✳✼ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ r❡❧❛çã♦ ❡♥tr❡ ❛s ❝❛r❣❛s ❤♦r✐③♦♥t❛✐s ❡ ✈❡rt✐❝❛✐s ✭❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛✲

  ♠❡♥t♦ ❞♦ ♠✉r♦✮ ❡♠ ❢✉♥çã♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧✿ ❝❛s♦ ❜❛s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✽ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❞❡❢♦r♠❛çã♦ ❞♦ s♦❧♦ ❛♣ós ❛ ✐♠♣♦s✐çã♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧

  ✭d = 15 mm✮✿ ❝❛s♦ ❜❛s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✾ ❘❡♣r❡s❡♥t❛çã♦✱ ♣♦r ❣r❛❞❛çã♦ ❞❡ ❝♦r❡s✱ ❞♦s ❞❡s❧♦❝❛♠❡♥t♦s ❤♦r✐③♦♥t❛✐s ♥♦ ♠❛❝✐ç♦ ✭d = 15 mm

  ✮✿ ❝❛s♦ ❜❛s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ =

  ✹✳✶✵ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❛♣❧✐❝❛❞♦ ♣❛r❛ B 2

  1 B ′ o 2 o

  4 m = 0, 438 = 30 = ❀ φ ❀ R inter ❀ i = 0 ✳ ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s q✉❡

  H

  3

  ❞❡❝♦rr❡♠ ❞♦ ♠ét♦❞♦ C

  2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ 2 B ′ o

  = 0, 438 = 30 ✹✳✶✶ ■♥✢✉ê♥❝✐❛ ❞♦ ❢❛❝t♦r R inter ♥♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ♣❛r❛ ❀ φ ✳

  H

  ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ 2 B = 0, 438

  ✹✳✶✷ ■♥✢✉ê♥❝✐❛ ❞♦ ❢❛❝t♦r R inter ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦ ♣❛r❛ ❀

  H ′ o

  φ = 30 ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹

  ′ o

  = 4 m = 30 ✹✳✶✸ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞❡ R inter ♣❛r❛ B

  1 ❀ φ ❀ o

  i = 0 ✳ ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ C

  2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ′ o

  = 4 m = 30 ✹✳✶✹ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞❡ R inter ♣❛r❛ B

  1 ❀ φ ❀ o

  i = 15 ✳ ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ C

  2 ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ 2 B ′

  = ✹✳✶✺ ■♥✢✉ê♥❝✐❛ ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ φ ♥♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ♣❛r❛

  H

  2

  0, 438 = ❀ R inter ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽

  3 ′

  ①① ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙

  ✹✳✶✾ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧✱ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦✱ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐✲

  ′ o

  2

  = /

  3 = 30

  ③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R inter ❀ φ ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸

  ✹✳✷✵ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧✱ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦✱ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐✲

  ′ o

  2

  3 inter = / = 40

  ③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R ❀ φ ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹

  ✹✳✷✶ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧✱ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦✱ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐✲

  o ′

  2

  3 inter = / = 40

  ③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R ❀ φ ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s ✭❝♦♥t✐♥✉❛çã♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺

  ✹✳✷✷ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧✱ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦✱ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐✲

  o ′

  2

  3 inter = / = 45

  ③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R ❀ φ ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻

  ✹✳✷✸ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧✱ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦✱ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐✲

  o ′

  2

  3 inter = / = 45

  ③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R ❀ φ ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s ✭❝♦♥t✐♥✉❛çã♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼

  ✹✳✷✹ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

  o ′

  

2

  3

  = / = 30 ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R inter ❀ φ ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽

  ✹✳✷✺ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

  ′

  

2

  3

  = / = 40 ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R inter ❀ φ ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾

  ✹✳✷✻ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

  ′

  

2

  3

  = / = 40 ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R inter ❀ φ ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s ✭❝♦♥t✐♥✉❛çã♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵

  ✹✳✷✼ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

  ′ o

  

2

  3

  = / = 45 ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R inter ❀ φ ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶

  ✹✳✷✽ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

  ′ o

  

2

  3

  = / = 45 ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R inter ❀ φ ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s ✭❝♦♥t✐♥✉❛çã♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷

  ′ o

  = 30 ✹✳✷✾ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ♣❛r❛ φ ❀

  o

  2

  3 R = /

inter ❀ i = 0 ✳ ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ C

2 ✳ ✾✸ ′ o

  = 40 ✹✳✸✵ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ♣❛r❛ φ ❀

  o

  2

  3 R = /

inter ❀ i = 0 ✳ ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ C

2 ✳ ✾✹ ′ o

  = 30 ✹✳✸✶ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ♣❛r❛ φ ❀

  o

  3

inter ❀ i = 15 ✳ ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦

  2 R = /

  C

  2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ′ o

  = 40 ✹✳✸✷ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ♣❛r❛ φ ❀

  o

  3

inter ❀ i = 20 ✳ ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦

  2 R = /

  ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ①①✐

  ✹✳✸✺ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦

  ′ o

  2

  = 4 m = 30 = /

  3

  ♣❛r❛ B

  1 ❀ φ ❀ R inter ✳ ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s r❡s✉❧t❛♥t❡s ❞❛

  ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ C

  2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾

  ①①✐✐ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙

  ▲✐st❛ ❞❡ ❚❛❜❡❧❛s

  ❀ φ

  o

  ❀ i = 0

  3

  2

  ❀ R inter =

  o

  = 30

  ′

  = 0, 438

  ✷✳✶ ❉✐♠❡♥sõ❡s ♣❛r❛ ♦ ♣ré✲❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ✭▼♦❧✐t❡r♥♦✱ ✶✾✽✵✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✸✳✶ P❛râ♠❡tr♦s ✐♥✐❝✐❛✐s ✉s❛❞♦s ♥❛s ❛♥á❧✐s❡s ❞♦s ♠ét♦❞♦s R ❡ C

  B 2 H

  / 1 2 γH 2 ❡ tan δ✳ ❈❛s♦ ❜❛s❡✿

  I H a

  ✸✳✹ P❡s♦s ♣r❡s❡♥t❡s ♥♦ ♠♦❞❡❧♦ ❞❡ ❝á❧❝✉❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✶ P❛râ♠❡tr♦s ✉t✐❧✐③❛❞♦s ♣❡❧♦ ♠♦❞❡❧♦ ▼♦❤r✲❈♦✉❧♦♠❜✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✷ ❈❛r❛❝t❡ríst✐❝❛s ❞♦ s♦❧♦ ❡ ❡str✉t✉r❛ ❝♦♥s✐❞❡r❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✸ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❛tr❛✈és ❞♦s ❞✐❢❡r❡♥t❡s ♠ét♦❞♦s✿

  2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

  ♦s r❡s✉❧t❛❞♦s ❞♦ ♠ét♦❞♦ C

  ✸✳✷ ❱❛❧♦r❡s ❞♦s â♥❣✉❧♦s ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦ ❡ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ ❛♥❛❧✐s❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✸ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣♦r ❇❛r❣❤♦✉t❤✐ ✭✶✾✾✵✮ ✭✐♥❞✐❝❛❞♦s ❝♦♠ ♦ í♥❞✐❝❡ B✮❀ ❝♦♠♣❛r❛çã♦ ❝♦♠

  1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

  ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✹✳✹ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷

  ①①✐✈ ▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙

  ❈❛♣ít✉❧♦ ✶ ■♥tr♦❞✉çã♦

  ▼✉✐t♦s ❞♦s ♠✉r♦s ❞❡ s✉♣♦rt❡ ❛❝t✉❛❧♠❡♥t❡ ♣r♦❥❡❝t❛❞♦s ❡ ❡①❡❝✉t❛❞♦s sã♦ ♠✉r♦s ❡♠ ❝♦♥s♦❧❛✱ ♦✉ s❡❥❛✱ ❡♠ L ♦✉ ❡♠ T ✐♥✈❡rt✐❞♦✱ ❞♦ t✐♣♦ ❞♦ r❡♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✶✳✶✳ ❊st❡s ♠✉r♦s ❞❡ s✉♣♦rt❡ ❛♣r❡s❡♥t❛♠ ❝♦♠♦ ❞✐✜❝✉❧❞❛❞❡✱ ♥❛ s✉❛ ❛♥á❧✐s❡✱ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s q✉❡ s♦❜r❡ ❡❧❡s ❛❝t✉❛♠✳

  ❋✐❣✉r❛ ✶✳✶✿ ▼✉r♦ ❡♠ ❝♦♥s♦❧❛✳ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ✏❝✉♥❤❛ ♠♦rt❛✑ ❡ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧✳ ❈♦♠ ❡❢❡✐t♦✱ ❛ ❣❡♦♠❡tr✐❛ ❞♦ ♠✉r♦ ❞❡ s✉♣♦rt❡ ♣r♦♣♦r❝✐♦♥❛ q✉❡✱ ♥♦r♠❛❧♠❡♥t❡✱ ✉♠ ♣❡q✉❡♥♦ ♠♦✈✐✲

  ♠❡♥t♦ ❞♦ ♠✉r♦ s❡❥❛ ❛❝♦♠♣❛♥❤❛❞♦ ♣♦r ✉♠❛ ❝✉♥❤❛ ❞❡ s♦❧♦✱ ❤❛❜✐t✉❛❧♠❡♥t❡ ❞❡s✐❣♥❛❞❛ ♣♦r ✏❝✉♥❤❛ ♠♦rt❛✑✱ q✉❡ ❛❝t✉❛ s❡♠♣r❡ ❝♦♠ ♦ s❡✉ ♣❡s♦ ❡ ♠♦✈✐♠❡♥t♦ ❝♦♠♦ ♣❛rt❡ ❞♦ ♠✉r♦✱ ♦r✐❣✐♥❛♥❞♦ ✉♠ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❝✉❥❛ ❣❡♦♠❡tr✐❛ s❡ ❞❡s❝♦♥❤❡❝❡✳

  ❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ♣r❡t❡♥❞❡ ❡st✉❞❛r ❡ ❝♦♠♣❛r❛r ❡♥tr❡ s✐ ♦s ♠ét♦❞♦s ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ❞❡✜♥✐r ❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❡ ❞❡t❡r♠✐♥❛r ♦s ✐♠♣✉❧s♦s s♦❜r❡ ❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡✳ ❱✐s❛✱ ✐❣✉❛❧♠❡♥t❡✱ ❝♦♠♣❛r❛r ♦s r❡s✉❧t❛❞♦s ❞❛ ❛♥á❧✐s❡ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ✐♥❢❡r✐❞❛ ❞♦s ♠ét♦❞♦s ❞✐s♣♦♥í✈❡✐s✳ ❖s ♠ét♦❞♦s ❞✐s♣♦♥í✈❡✐s sã♦ ❞❡s❝r✐t♦s ♥♦ ❈❛♣ít✉❧♦ ✷ ❡ ❛s ❝♦♠♣❛r❛çõ❡s r❡❢❡r✐❞❛s ❢❡✐t❛s ♥♦ ❈❛♣ít✉❧♦ ✸✳

  ❈♦♠ ✈✐st❛ ❛ ❛♥❛❧✐s❛r ❛ ❛❞❡q✉❛❜✐❧✐❞❛❞❡ ❞♦s ♠ét♦❞♦s ❞✐s♣♦♥í✈❡✐s✱ t❛♥t♦ ♣❛r❛ ❡st✐♠❛r ♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s ❝♦♠♦ ♣❛r❛ ❛♥❛❧✐s❛r ❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦✱ ❝♦♠♦✱ ❛✐♥❞❛✱ ♣❛r❛ ❞❡✜♥✐r ❛ ❧♦❝❛❧✐③❛çã♦ ❞♦

  ✷ ❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖

  ❈❛♣ít✉❧♦ ✷ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ✷✳✶ ■♥tr♦❞✉çã♦

  ❖s ♠✉r♦s ♣♦❞❡♠ s❡r ❝♦♥str✉í❞♦s ❡♠ ❛❧✈❡♥❛r✐❛✱ ❜❡tã♦✱ ❜❡tã♦ ❛r♠❛❞♦ ♦✉ ♦✉tr♦s ♠❛t❡r✐❛✐s✳ ❖s ♠✉r♦s ❞❡ s✉♣♦rt❡ ❡♠ L ♦✉ ❡♠ T ✐♥✈❡rt✐❞♦ sã♦ ❡str✉t✉r❛s ❢r❡q✉❡♥t❡♠❡♥t❡ ✉t✐❧✐③❛❞❛s ❡♠ ♦❜r❛s ❞❡ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧✳ ❖s ✐♠♣✉❧s♦s ❞❡ t❡rr❛s ❤❛❜✐t✉❛❧♠❡♥t❡ ❝♦♥s✐❞❡r❛❞♦s ♥♦ s❡✉ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ r❡❝♦rr❡♠✱ ❝♦♠ r❡❣✉❧❛r✐❞❛❞❡✱ às t❡♦r✐❛s ❝❧áss✐❝❛s ❞❡ ❘❛♥❦✐♥❡ ✭✶✽✺✼✮ ❡ ❈♦✉❧♦♠❜ ✭✶✼✼✻✮✳

  ◆♦ ♣r❡s❡♥t❡ ❝❛♣ít✉❧♦ ♣r❡t❡♥❞❡✲s❡ ❢❛③❡r ✉♠ ❜r❡✈❡ ❧❡✈❛♥t❛♠❡♥t♦ ❞♦ t✐♣♦ ❞❡ ♠✉r♦s ❡①✐st❡♥t❡s ❡ ❛♣r❡s❡♥t❛♠✲s❡ ❛s t❡♦r✐❛s ❝❧áss✐❝❛s ❞❡ ❝á❧❝✉❧♦ ❞❡ ✐♠♣✉❧s♦s ♣❛r❛ ♦s ❝❛s♦s ❞❡ s♦❧♦s ❝♦♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❛❞♠✐t✐❞♦ ♣✉r❛♠❡♥t❡ ❛trít✐❝♦ ❡ q✉❡ ♦❜❡❞❡❝❡♠ ❛♦s ❝r✐tér✐♦s ❞❡ r♦t✉r❛ ❞❡ ▼♦❤r✲❈♦✉❧♦♠❜✳ ❆♣r❡s❡♥t❛✲ s❡✱ ✐❣✉❛❧♠❡♥t❡✱ ❛ ❢♦r♠❛ ❝♦♠♦ ❡st❛s t❡♦r✐❛s ❝❧áss✐❝❛s sã♦ ❡♠♣r❡❣✉❡s ♥♦ ❝á❧❝✉❧♦ ❞♦s ✐♠♣✉❧s♦s s♦❜r❡ ❡str✉t✉r❛s ❡ ❛❜♦r❞❛✲s❡✱ ❡♠ ❡s♣❡❝✐❛❧✱ ♦s ♠✉r♦s ❞❡ s✉♣♦rt❡ ❡♠ ❝♦♥s♦❧❛✳

  ✷✳✷ ▼ét♦❞♦s ❝❧áss✐❝♦s ❞❡ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ✐♠♣✉❧s♦s ❛❝t✐✈♦s ✷✳✷✳✶ ❆ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡

  ❆ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡ é ♣❛ssí✈❡❧ ❞❡ s❡r ❝♦♥s✐❞❡r❛❞❛ q✉❛♥❞♦ ✉♠❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡ s❡ ♠♦✈✐♠❡♥t❛ ❡♠ ❞✐r❡❝çã♦ ♦♣♦st❛ à ❞♦ t❡rr❡♥♦✱ ❞❡ ❢♦r♠❛ s✉✜❝✐❡♥t❡ ♣❛r❛ q✉❡ ♦ ❡st❛❞♦ ❞❡ t❡♥sã♦ ❛❝t✐✈♦ s❡❥❛ ♠♦❜✐❧✐③❛❞♦✳ ❘❛♥❦✐♥❡ ✭✶✽✺✼✮ ❛♣♦♥t❛ ❛❧❣✉♠❛s ❤✐♣ót❡s❡s ❞❡ ✈❛❧✐❞❛❞❡ q✉❡ ❞❡✈❡rã♦ s❡r t✐❞❛s ❡♠ ❝♦♥s✐❞❡r❛çã♦ ♣❛r❛ q✉❡ ♦ s❡✉ ♠ét♦❞♦ ♣♦ss❛ s❡r ❛♣❧✐❝❛❞♦ ✭❈❡r♥✐❝❛✱ ✶✾✾✹✮✳ ❙ã♦ ❡❧❛s✿

  ❼ ❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦ s❡r ❤♦r✐③♦♥t❛❧❀ ❼ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝♦♥t❛❝t♦ ❡♥tr❡ ♦ s♦❧♦ ❡ ❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡ s❡r ✈❡rt✐❝❛❧❀ ❼ ♥ã♦ ❡①✐st✐r ❛tr✐t♦ ♥❡♠ ❝♦❡sã♦ ♥♦ ❝♦♥t❛❝t♦ s♦❧♦✲❡str✉t✉r❛ ❞❡ s✉♣♦rt❡❀ ❼ ♦ s♦❧♦ s❡r ❤♦♠♦❣é♥❡♦✱ ✐s♦tró♣✐❝♦ ❡ s❡❝♦✳

  ✹ ❈❆P❮❚❯▲❖ ✷✳ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆

  a

  ❉❡✜♥✐♥❞♦ K ❝♦♠♦ ♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✐♠♣✉❧s♦ ❛❝t✐✈♦✱ q✉❡ r❡❧❛❝✐♦♥❛ ❛ t❡♥sã♦ ❡❢❡❝t✐✈❛ ✈❡rt✐❝❛❧ ❝♦♠ ❛ t❡♥sã♦ ❡❢❡❝t✐✈❛ ❤♦r✐③♦♥t❛❧ ♥✉♠ ❞❛❞♦ ❡❧❡♠❡♥t♦ ❞❡ s♦❧♦✱ t❡♠✲s❡✿

  ′

  σ

  h,a

  K a = ✭✷✳✷✮

  ′

  σ

  v

  ❆ss✐♠✱ ❛ t❡♥sã♦ ❡❢❡❝t✐✈❛ ❤♦r✐③♦♥t❛❧ ❛❝t✐✈❛ é ❞❛❞❛ ♣❡❧❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦✿

  ′

  σ = K γz

  a ✭✷✳✸✮ h,a

  ❆ ❡♥✈♦❧✈❡♥t❡ ❞❡ r♦t✉r❛ é ❞❡t❡r♠✐♥❛❞❛ ❛tr❛✈és ❞❛ ❡①♣r❡ssã♦ ❛♣r❡s❡♥t❛❞❛ ❞❡ s❡❣✉✐❞❛✱ q✉❡ r❡tr❛t❛ ♦ ♣r♦❜❧❡♠❛ s✐♠♣❧❡s✱ ❡♠ q✉❡ ♦ t❡rr❡♥♦ r❡s♣♦♥❞❡ ❡♠ ❝♦♥❞✐çõ❡s ❞r❡♥❛❞❛s ✭❚❡r③❛❣❤✐ ❡t ❛❧✳✱ ✶✾✹✽✮✳

  ′ ′

  τ = σ tan φ ✭✷✳✹✮

  ′

  ❡♠ q✉❡ φ r❡♣r❡s❡♥t❛ ♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦✳ ■❧✉str❛✲s❡✱ ♥❛ ❋✐❣✉r❛ ✷✳✶✱ ♦ ❝❛s♦ s✐♠♣❧❡s ❛❝✐♠❛ r❡❢❡r✐❞♦✳ ❙❡♥❞♦ ❛ t❡♥sã♦ ❡❢❡❝t✐✈❛ ✈❡rt✐❝❛❧ ❞❛❞❛

  ♣❡❧♦ ♣r♦❞✉t♦ ❛♣r❡s❡♥t❛❞♦ ♥❛ ❡①♣r❡ssã♦ ✷✳✶ ♣❡r❝❡❜❡✲s❡ q✉❡✱ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ ♣r♦❢✉♥❞✐❞❛❞❡✱ ♦ ✈❛❧♦r ❞❛q✉❡❧❛ t❡♥sã♦ ❛✉♠❡♥t❛ ❞❡ ❢♦r♠❛ ♣r♦♣♦r❝✐♦♥❛❧✳

  ❋✐❣✉r❛ ✷✳✶✿ ■♠♣✉❧s♦ ❞❡ t❡rr❛s✿ ❆ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡✳ ❉❡ ♠♦❞♦ ❛ ❝❛r❛❝t❡r✐③❛r ♦ ❡st❛❞♦ ❞❡ t❡♥sã♦ ❞♦ ❡❧❡♠❡♥t♦ ❞❡ s♦❧♦✱ ❛♣r❡s❡♥t❛✲s❡✱ ♥❛ ❋✐❣✉r❛ ✷✳✷✱ ♦

  ❝ír❝✉❧♦ ❞❡ ▼♦❤r ❝♦♠ ❛ ❡♥✈♦❧✈❡♥t❡ ❞❡ r♦t✉r❛ ❞♦ s♦❧♦✱ ❞❛❞❛ ♣❡❧❛ ❡①♣r❡ssã♦ ✷✳✹✳ ❆♦ s❡r ❛❞♠✐t✐❞❛ ❛ ✐♥❡①✐stê♥❝✐❛ ❞❡ ❛tr✐t♦ ♥♦ ❝♦♥t❛❝t♦ s♦❧♦✲❡str✉t✉r❛✱ ♥♦ ❝❛s♦ ❞❡ ♦❝♦rr❡r ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ❡str✉t✉r❛ ♥❛ ❞✐r❡❝çã♦ ♦♣♦st❛ ❛♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦✱ ❡①✐st✐rá ✉♠❛ ❞✐♠✐♥✉✐çã♦ ❞❛ t❡♥sã♦ ❤♦r✐③♦♥t❛❧ ♥❛q✉❡❧❡ ❡❧❡♠❡♥t♦✱ ♣♦❞❡♥❞♦ ❛t✐♥❣✐r ❛ r♦t✉r❛ ❡✱ ♣♦r ❝♦♥s❡❣✉✐♥t❡✱ ♠♦❜✐❧✐③❛r ♦ ❡st❛❞♦ ❛❝t✐✈♦✳

  ✷✳✷✳ ▼➱❚❖❉❖❙ ❈▲➪❙❙■❈❖❙ ❉❊ ❉❊❚❊❘▼■◆❆➬➹❖ ❉❊ ■▼P❯▲❙❖❙ ❆❈❚■❱❖❙ ✺

  ′ ′ σ v −σ h,a ′ ′

  ′ ′ ′

  − σ σ −

  v σ σ K 1 − K 1 − sin φ h,a a a , 2 v v

  sin φ = = = = =⇒ K a =

  ′ ′

  ✭✷✳✺✮

  σ +σ ′ ′ ′ ′ ′ v h,a

  σ + σ σ + σ K a 1 + K a 1 + sin φ

  v v v h,a

  2

  ❆❞♠✐t✐♥❞♦ ✉♠ s♦❧♦ ❤♦♠♦❣é♥❡♦✱ ❡♠ q✉❡ ♦ ♣❡s♦ ✈♦❧ú♠✐❝♦ γ ❡ ♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡

  ′

  ❞♦ s♦❧♦ φ sã♦ ❝♦♥st❛♥t❡s✱ ♦ ❞✐❛❣r❛♠❛ ❞❡ t❡♥sõ❡s r❡s✉❧t❛ tr✐❛♥❣✉❧❛r✱ ❛✉♠❡♥t❛♥❞♦ ❧✐♥❡❛r♠❡♥t❡ ❝♦♠ ❛ ♣r♦❢✉♥❞✐❞❛❞❡✳

  ❆ r❡s✉❧t❛♥t❡ ♣♦❞❡ s❡r ❡♥tã♦ ♦❜t✐❞❛ ❛tr❛✈és ❞❛ ár❡❛ ❞♦ r❡❢❡r✐❞♦ ❞✐❛❣r❛♠❛✱ ❡♥tr❡ ❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦ ❡ ❛ ♣r♦❢✉♥❞✐❞❛❞❡ H✳ ❆ss✐♠✱ ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ é ❝❛❧❝✉❧❛❞♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❡①♣r❡ssã♦ ✭❚❡r③❛❣❤✐ ❡t ❛❧✳✱ ✶✾✹✽✮✿ ˆ H ˆ H

  1

  ′

  2 I = K σ dz = K γzdz = K γH a a a a ✭✷✳✻✮ v

  2 s❡♥❞♦✿ K

  a ✲ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✐♠♣✉❧s♦ ❛❝t✐✈♦❀

  γ ✲ ♣❡s♦ ✈♦❧ú♠✐❝♦ ❞♦ s♦❧♦❀

  H ✲ ❛❧t✉r❛ ❞❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡✳

  P❛r❛ ❛❧é♠ ❞♦ r❡❢❡r✐❞♦✱ ❛ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡✱ ♥ã♦ ♦❜st❛♥t❡ ❛s ❤✐♣ót❡s❡s ♣♦r s✐ ♣r❡❝♦♥✐③❛❞❛s✱ ❛♥t❡r✐✲ ♦r♠❡♥t❡ ♠❡♥❝✐♦♥❛❞❛s✱ ♣♦❞❡ s❡r ❡st❡♥❞✐❞❛ ❛♦ ❝❛s♦ ❞❛ ❡①✐stê♥❝✐❛ ❞❡ ✐♥❝❧✐♥❛çã♦ ♥❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦ ♣❡❧❛ ❡str✉t✉r❛✳ ❆ r❡s✉❧t❛♥t❡ ❞♦ ✐♠♣✉❧s♦ ❣❡r❛❞♦ ♥♦ t❛r❞♦③ t❡rá ❛ ♠❡s♠❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉✲ ♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦✱ ❛❞♠✐t✐♥❞♦ q✉❡ ❡st❛ ❝♦♥s✐❞❡r❛çã♦ ♥ã♦ ♣r♦❞✉③ ❛❧t❡r❛çõ❡s ♥♦ ❞✐❛❣r❛♠❛ ❞❡ t❡♥sõ❡s ❛❝t✉❛♥t❡s✳ ●❡♥❡r✐❝❛♠❡♥t❡✱ ❛♣r❡s❡♥t❛✲s❡✱ ♥❛ ❋✐❣✉r❛ ✷✳✸✱ ♦ ♣r♦❜❧❡♠❛ ❡♠ q✉❡stã♦✳ ❋✐❣✉r❛ ✷✳✸✿ ■♠♣✉❧s♦ ❞❡ t❡rr❛s✿ ❛ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡ ❛♣❧✐❝❛❞❛ ❛ t❡rr❡♥♦ ❝♦♠ ✐♥❝❧✐♥❛çã♦ ✭❛❞❛♣t❛❞♦ ❞❡ ❈❡r♥✐❝❛✱ ✶✾✾✹✮✳

  ❖ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✐♠♣✉❧s♦ K a s❡rá ✐♥✢✉❡♥❝✐❛❞♦ ♣❡❧❛ ❛❧t❡r❛çã♦ ❞❛ ✐♥❝❧✐♥❛çã♦ ❡ ❝❛❧❝✉❧❛❞♦ ❛tr❛✈és ❞❛ ❡①♣r❡ssã♦ ✭❈❡r♥✐❝❛✱ ✶✾✾✹✮✿ q 2

  ′ cos φ 2

  1 − 1 −

  cos i

  K = cos i ×

  a q ✭✷✳✼✮ 2 ′ cos φ 2

  1 + 1 −

  cos i

  ❡♠ q✉❡✿ i ✲ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦❀

  ∂ ∂α

  ) = 0

  a

  ∂α = 0 ⇐⇒

  ✻ ❈❆P❮❚❯▲❖ ✷✳ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆

  W sin (α − φ

  ′

  ) sin (180 − ω − α + φ

  ′

  ✭✷✳✾✮ ▼✉❧❧❡r ❡ ❇r❡s❧❛✉ ❝♦♥❝❧✉✐r❛♠✱ ❡♠ ✶✾✵✻✱ q✉❡ ❛ s♦❧✉çã♦ ❞❛ ❡①♣r❡ssã♦ q✉❡ ❝❛r❛❝t❡r✐③❛ ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦

  ❆ ❝✉♥❤❛ ❞❡ r♦t✉r❛ é ❝❛r❛❝t❡r✐③❛❞❛ ♣❡❧❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ r♦t✉r❛✱ α✱ ♣❡❧♦ q✉❡✱ ❞❡ ♠♦❞♦ ❛ ♦❜t❡r✲s❡ ♦ ♠á①✐♠♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛ ♣❛rt✐r ❞❛ ❡q✉❛çã♦ ✷✳✽✱ ✐❣✉❛❧❛✲s❡ ❛ ❞❡r✐✈❛❞❛ ❡♠ ♦r❞❡♠ ❛ α ❛ ③❡r♦✿

  é ❞❛❞❛ ♣♦r ✭▼✐♥❡✐r♦✱ ✶✾✼✽✮✿

  I

  a

  =

  1

  a

  γH

  ∂I

  ) ✭✷✳✽✮

  ✭✷✳✶✵✮ ❡♠ q✉❡ ♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✐♠♣✉❧s♦ ❛❝t✐✈♦ K a é ❝❛❧❝✉❧❛❞♦ ❛tr❛✈és ❞❛ ❡①♣r❡ssã♦✿

  sin (α − φ

  ❖ ♠✉r♦✱ ❛♦ ❞❡s❧♦❝❛r✲s❡✱ é ❛❝♦♠♣❛♥❤❛❞♦ ♣♦r ✉♠❛ ❝✉♥❤❛ ❞❡ s♦❧♦✱ q✉❡ ❞♦ r❡st❛♥t❡ s♦❧♦ s❡ ❞❡st❛❝❛✳ ❊st❛ ❝✉♥❤❛ ❞❡ s♦❧♦ é ❞❡✜♥✐❞❛ ♣♦r ✉♠❛ s✉♣❡r❢í❝✐❡ ♣❧❛♥❛r✱ ✐❧✉str❛❞❛ ♥❛ ❋✐❣✉r❛ ✷✳✹✳ ◆❛ ✈❡r❞❛❞❡✱ ❛ ❛❞♠✐ssã♦ ❞❡ ✉♠❛ s✉♣❡r❢í❝✐❡ ❞❡ r♦t✉r❛ ♣❧❛♥❛ ❧❡✈❛ ❛ s♦❧✉çõ❡s ✐♥❢❡r✐♦r❡s às r❡❛✐s✱ ✉♠❛ ✈❡③ q✉❡✱ ❞❡ ❢❛❝t♦✱ ❛q✉❡❧❛ s❡ ❞á ❛♦ ❧♦♥❣♦ ❞❡ ✉♠❛ s✉♣❡r❢í❝✐❡ ❝✉r✈✐❧í♥❡❛✳ ◆♦ ❡♥t❛♥t♦✱ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣♦❞❡♠ s❡r ❝♦♥s✐❞❡r❛❞♦s ❛❝❡✐tá✈❡✐s✳ ❆♦ ❝♦♥trár✐♦ ❞♦ ❝♦♥s✐❞❡r❛❞♦ ♥❛ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡✱ ♥♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜ ❝♦♥s✐❞❡r❛✲s❡ ❛ ❡①✐stê♥❝✐❛ ❞❡ ❛tr✐t♦ ♥♦ ❝♦♥t❛❝t♦ s♦❧♦✲❡str✉t✉r❛✳

  ❚♦❞❛s ❛s ❝♦♥s✐❞❡r❛çõ❡s ❢❡✐t❛s sã♦ ✈á❧✐❞❛s✱ s❡❣✉♥❞♦ ♦ ❛✉t♦r✱ ♣❛r❛ s♦❧♦s ♥ã♦ ❝♦❡s✐✈♦s✱ s❡❝♦s ❡ ❤♦♠♦✲ ❣é♥❡♦s✳

  

✭❛✮ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❝✉♥❤❛ ❞❡ s♦❧♦✳ ✭❜✮ P♦❧í❣♦♥♦ ❞❡ ❢♦rç❛s✳

  ❋✐❣✉r❛ ✷✳✹✿ ❈✉♥❤❛ ❞❡ s♦❧♦ ❛❝t✐✈❛ ❛tr❛✈és ❞❛ t❡♦r✐❛ ❞❡ ❈♦✉❧♦♠❜ ✭❛❞❛♣t❛❞♦ ❞❡ ❈❡r♥✐❝❛✱ ✶✾✾✹✮✳ Pr♦❝✉r❛♥❞♦✲s❡ ❝♦♥❤❡❝❡r ❛ ❡①♣r❡ssã♦ q✉❡ ❝♦♥❞✉③ ❛♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✱ é ♣♦ssí✈❡❧✱ ❛tr❛✈és ❞♦ ♣♦❧í❣♦♥♦

  ❞❡ ❢♦rç❛s ♣r❡s❡♥t❡ ♥❛ ❋✐❣✉r❛ ✷✳✹❜ ❝❤❡❣❛r à s❡❣✉✐♥t❡ ✐❣✉❛❧❞❛❞❡✱ ❛tr❛✈és ❞❛ ❧❡✐ ❞♦s s❡♥♦s✿

  I

  a

  ′

  ′

  ) =

  W sin (180 − ω − α + φ

  

  ) =⇒ I

  a

  = W sin (α − φ

  ′

  ) sin (180 − ω − α + φ

  2

2 K

  K a =

  1 sin β

  × sin (β − φ

  ′

  ) psin (β + δ) + q

  sin(φ ′

  ′ −i) sin(β−i)

  2

  ✭✷✳✶✶✮

  • δ) sin(φ

  ✷✳✸✳ ❚■P❖❙ ❉❊ ▼❯❘❖❙ ❉❊ ❙❯P❖❘❚❊ ✼

  ✷✳✸ ❚✐♣♦s ❞❡ ♠✉r♦s ❞❡ s✉♣♦rt❡

  ❖s t✐♣♦s ❞❡ ♠✉r♦s ❞❡ s✉♣♦rt❡ ♠❛✐s ❝♦♠✉♥s sã♦ ♦s ♠✉r♦s ❞❡ ❣r❛✈✐❞❛❞❡ ❡ ❡♠ ❝♦♥s♦❧❛ ✭❡♠ L ♦✉ T ✐♥✈❡rt✐❞♦✱ ❝♦♠ ♦✉ s❡♠ ❝♦♥tr❛❢♦rt❡✮✱ ❝♦♠ ♦✉ s❡♠ t✐r❛♥t❡s ✭❊▼ ✶✶✶✵✲✷✲✷✺✵✷✮✳ ❆ss✐♠✱ ❛♣r❡s❡♥t❛♠✲s❡✱ ♥❛ ♣r❡s❡♥t❡ s❡❝çã♦✱ ❛❧❣✉♠❛s ❝♦♥s✐❞❡r❛çõ❡s ❛❝❡r❝❛ ❞❛s r❡❢❡r✐❞❛s ❡str✉t✉r❛s✳

  ✷✳✸✳✶ ▼✉r♦s ❞❡ ❣r❛✈✐❞❛❞❡

  ❖s ♠✉r♦s ❞❡ ❣r❛✈✐❞❛❞❡ sã♦ ❡str✉t✉r❛s ❞❡ s✉♣♦rt❡ ❞❡ t❡rr❛s ❡♠ q✉❡ ♦ s❡✉ ♣❡s♦ ♣ró♣r✐♦ s❡ r❡✈❡❧❛ ♥♦ ♣r✐♥❝✐♣❛❧ ❡❧❡♠❡♥t♦ r❡s♣♦♥sá✈❡❧ ♣❡❧❛ s✉❛ ❡st❛❜✐❧✐❞❛❞❡✳ ❙ã♦✱ ❣❡r❛❧♠❡♥t❡✱ ✉t✐❧✐③❛❞♦s ❡♠ ❧♦❝❛✐s ♦♥❞❡ ♦ s♦❧♦ ❛♣r❡s❡♥t❛ ❜♦❛s ❝❛♣❛❝✐❞❛❞❡s r❡s✐st❡♥t❡s ✭❉♦♠✐♥❣✉❡s✱ ✶✾✾✼✮✳ ❊st❡ t✐♣♦ ❞❡ ♠✉r♦s ♣♦❞❡ s❡r ❝♦♥str✉í❞♦ ❡♠ ❛❧✈❡♥❛r✐❛ ♦✉ ❜❡tã♦ ✭s✐♠♣❧❡s ♦✉ ❛r♠❛❞♦✮✱ ❝♦♠ ❣❛❜✐õ❡s ♦✉ ♣♥❡✉s ✉s❛❞♦s✳ ❆♣r❡s❡♥t❛♠✲s❡ ❛❧❣✉♥s ❡①❡♠♣❧♦s ✭❞❡ ✉♠❛ ✈❛st❛ ❣❛♠❛✮ ❞❡st❡ t✐♣♦ ❞❡ ♠✉r♦s✱ s❡✉ t✐♣♦ ❞❡ s❡❝çã♦ ❡ ❞✐♠❡♥sõ❡s ✈✉❧❣❛r♠❡♥t❡ ✉t✐❧✐③❛❞❛s✳

  ❉❡ ❛❝♦r❞♦ ❝♦♠ ❈❡r♥✐❝❛ ✭✶✾✾✹✮✱ ❛ ❣❡♦♠❡tr✐❛ ❝♦rr❡♥t❡ ♣❛r❛ ❡st❡ t✐♣♦ ❞❡ ♠✉r♦ é ❞♦ t✐♣♦ ❞❛ ✐❧✉str❛❞❛ ♥❛ ❋✐❣✉r❛ ✷✳✺✳

  ❋✐❣✉r❛ ✷✳✺✿ ●❡♦♠❡tr✐❛ ❞❡ ♠✉r♦s ❞❡ ❣r❛✈✐❞❛❞❡ ✭❈❡r♥✐❝❛✱ ✶✾✾✹✮✳ ◆♦ ❡♥t❛♥t♦✱ ❉♦♠✐♥❣✉❡s ✭✶✾✾✼✮ ❛♣r❡s❡♥t❛ três ♣❡r✜s ❜ás✐❝♦s ♣❛r❛ ♦ ♣r♦❥❡❝t♦ ❞❡ ♠✉r♦s ❞❡ ❣r❛✈✐❞❛❞❡✿ r❡❝t❛♥❣✉❧❛r✱ tr❛♣❡③♦✐❞❛❧ ❡ ❡♠ ❡s❝❛❞❛✳ ❉♦♠✐♥❣✉❡s r❡❢❡r❡ q✉❡ ♦ ♠✉r♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❝♦♠ ♣❡r✜❧ r❡❝t❛♥❣✉❧❛r é ❡❝♦♥ó♠✐❝♦ ♣❛r❛ ❛❧t✉r❛s ❛té ✷

  ♠❡tr♦s ❡ ❣❡r❛❧♠❡♥t❡ ❝♦♥❝❡❜✐❞♦ ❡♠ ❜❡tã♦ ❝✐❝❧ó♣✐❝♦✳ ◆❛ ❋✐❣✉r❛ ✷✳✻ ❡♥❝♦♥tr❛✲s❡ ✉♠❛ ✐❧✉str❛çã♦ ❞❡st❡ t✐♣♦ ❞❡ ♠✉r♦✳

  ✽ ❈❆P❮❚❯▲❖ ✷✳ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆

  ❖♥❞❡✿ H

  ✲ ❛❧t✉r❛ t♦t❛❧ ❞♦ ♠✉r♦❀ B

  ✲ ❧❛r❣✉r❛ ❞❛ ❜❛s❡❀ W

  ✲ ♣❡s♦ ♣ró♣r✐♦ ❞♦ ♠✉r♦✳ ❙❡❣✉♥❞♦ ▼♦❧✐t❡r♥♦ ✭✶✾✽✵✮ ✭❝✐t❛❞♦ ♣♦r ❉♦♠✐♥❣✉❡s ✭✶✾✾✼✮✮✱ ♣♦❞❡♠ s❡r ❛❞♦♣t❛❞❛s✱ ♣❛r❛ ♦ ♣ré✲

  ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞♦s ♠✉r♦s ❞❡ ❣r❛✈✐❞❛❞❡ ❝♦♠ s❡❝çã♦ r❡❝t❛♥❣✉❧❛r✱ ❛s ❞✐♠❡♥sõ❡s ♣r❡s❡♥t❡s ♥❛ ❚❛❜❡❧❛ ✷✳✶✳

  ❚❛❜❡❧❛ ✷✳✶✿ ❉✐♠❡♥sõ❡s ♣❛r❛ ♦ ♣ré✲❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ✭▼♦❧✐t❡r♥♦✱ ✶✾✽✵✮✳ ❚✐♣♦ ❞❡ ❡str✉t✉r❛ ❉✐♠❡♥sã♦

  ▼✉r♦ ❡♠ ❛❧✈❡♥❛r✐❛ ❞❡ t✐❥♦❧♦ B = 0,4H B = 0,3H

  ▼✉r♦ ❞❡ ❜❡tã♦ ❝✐❝❧ó♣✐❝♦ ❉♦♠✐♥❣✉❡s ❛♣r❡s❡♥t❛ ♦s ♠✉r♦s ❞❡ ❣r❛✈✐❞❛❞❡ ❝♦♠ ♣❡r✜❧ tr❛♣❡③♦✐❞❛❧ ❝♦♠♦ s❡♥❞♦ ♠❛✐s ❡❝♦♥ó♠✐❝♦s

  ❢❛❝❡ ❛♦s ❞❡ ♣❡r✜❧ r❡❝t❛♥❣✉❧❛r ❡ ❛♣❧✐❝á✈❡✐s ♣❛r❛ ❛❧t✉r❛s s✉♣❡r✐♦r❡s ✭❛té ✹ ♠❡tr♦s✮✳ ❙ã♦ ❝♦♥str✉í❞♦s ♠❡❞✐❛♥t❡ ♦ ♣r❡❡♥❝❤✐♠❡♥t♦ ❞❡ ✉♠❛ ❢♦r♠❛ ♣ré✲❞❡✜♥✐❞❛ ❝♦♠ ❜❡tã♦ ❡ r♦❝❤❛s ❞❡ ❞✐♠❡♥sõ❡s ✈❛r✐❛❞❛s✳ ❆ss✐♠✱ ❛♣r❡s❡♥t❛✲s❡✱ ♥❛ ❋✐❣✉r❛ ✷✳✼✱ ❛ ❣❡♦♠❡tr✐❛ ♣r♦♣♦st❛ ♣♦r ▼♦❧✐t❡r♥♦ ✭✶✾✽✵✮✱ ❞❡st❛❝❛♥❞♦✲s❡ ❛ ❢❛❝❡ ❡①t❡r♥❛ ❞❛ ♣❛r❡❞❡ ❞♦ ♠✉r♦ ✐♥❝❧✐♥❛❞❛✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ♦ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡ s❡ s✐t✉❡ ❞♦ ❧❛❞♦ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦✳

  ❋✐❣✉r❛ ✷✳✼✿ ▼✉r♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❝♦♠ ♣❡r✜❧ tr❛♣❡③♦✐❞❛❧ ✭❛❞❛♣t❛❞♦ ❞❡ ❉♦♠✐♥❣✉❡s ✭✶✾✾✼✮✮✳ ▼♦❧✐t❡r♥♦ ✭✶✾✽✵✮ ❛♣r❡s❡♥t❛ ❛s s❡❣✉✐♥t❡s ❞✐♠❡♥sõ❡s ❛ ❝♦♥s✐❞❡r❛r ♣❛r❛ ♦ ♣ré✲❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡

  ♠✉r♦s ❝♦♠ ♣❡r✜❧ tr❛♣❡③♦✐❞❛❧✿ b = 0,14H ✭✷✳✶✷✮

  ✷✳✸✳ ❚■P❖❙ ❉❊ ▼❯❘❖❙ ❉❊ ❙❯P❖❘❚❊ ✾

  ❋✐❣✉r❛ ✷✳✽✿ ▼✉r♦ ❞❡ ❣r❛✈✐❞❛❞❡ ❝♦♠ ♣❡r✜❧ ❡♠ ❡s❝❛❞❛ ✭❛❞❛♣t❛❞♦ ❞❡ ❉♦♠✐♥❣✉❡s ✭✶✾✾✼✮✮✳ ❖s ♠✉r♦s ❞❡ ❣❛❜✐õ❡s ❝♦♥s✐st❡♠ ♥✉♠ ❡❧❡♠❡♥t♦ ❡str✉t✉r❛❧ q✉❡ t❛♠❜é♠ ❢✉♥❝✐♦♥❛ ♣♦r ❣r❛✈✐❞❛❞❡✳ ❙ã♦ ❝♦♥st✐t✉í❞♦s ♣♦r ❝❛✐①❛s ♠❡tá❧✐❝❛s✱ ❝♦♠ ❢♦r♠❛ ♣❛r❛❧❡❧✐♣✐♣é❞✐❝❛✱ ❡①❡❝✉t❛❞❛s ❝♦♠ ✜♦s ❡♠ ❛ç♦

  ❣❛❧✈❛♥✐③❛❞♦ ❡♠ ❢♦r♠❛ ❤❡①❛❣♦♥❛❧✱ ❝♦♠♦ ✐❧✉str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✾ ✭❛❜❡rt✉r❛s ❝♦♠ ❞✐♠❡♥sõ❡s ✐♥❢❡r✐♦r❡s ❛♦ ❞✐â♠❡tr♦ ❞❛s ♣❡❞r❛s ♠❡♥♦r❡s✮✱ r❡✈❡st✐❞♦s ❝♦♠ ✉♠❛ ❝❛♠❛❞❛ ❞❡ P❱❈ q✉❡ ♣r♦♣♦r❝✐♦♥❛ ✉♠❛ ❡❧❡✈❛❞❛ ❡✜❝✐ê♥❝✐❛ ❝♦♥tr❛ ❛ ❛❝çã♦ ❞❡ ✐♥t❡♠♣ér✐❡s✱ á❣✉❛s ❡ s♦❧♦s ❛❣r❡ss✐✈♦s ✭❇❙ ✽✵✵✷✿✶✾✾✹ ✭✷✵✵✷✮✮✳ P♦st❡r✐♦r✲ ♠❡♥t❡✱ sã♦ ♣r❡❡♥❝❤✐❞❛s ♠❛♥✉❛❧♠❡♥t❡ ✭❞❡ ♠♦❞♦ ❛ ❝r✐❛r ♦ ♠❡♥♦r ✈♦❧✉♠❡ ❞❡ ✈❛③✐♦s ♣♦ssí✈❡❧✮ ❝♦♠ ♣❡❞r❛s ❞❡ ❞✐♠❡♥sõ❡s r❡❞✉③✐❞❛s✱ ❛té ✷✵ ❝♠ ✭❇❙ ✽✵✵✷✿✶✾✾✹ ✭✷✵✵✷✮✮✳

  ◆❡st❡ t✐♣♦ ❞❡ ❡str✉t✉r❛s ❞❡✈❡rã♦ s❡r✱ s❡❣✉♥❞♦ ▼❛s❝❛r❡♥❤❛s ✭✷✵✵✷✮✱ ✉t✐❧✐③❛❞❛s ♣❡❞r❛s ❞❡ ❣r❛♥✐t♦ ❡♠ ❞❡tr✐♠❡♥t♦ ❞❛s ❞❡ ❝❛❧❝ár✐♦✱ ❞❡✈✐❞♦ à ❡①♣❛♥sã♦ ❞❡st❛s ú❧t✐♠❛s q✉❛♥❞♦ ❤ú♠✐❞❛s✱ ♣r♦✈♦❝❛♥❞♦ ❞❡❢♦r✲ ♠❛çõ❡s ♥❛s ❣❛✐♦❧❛s ❞❡ r❡❞❡ ✭❆❣✉✐❛r ❡ ▼❛rt✐♥s ✭✷✵✵✺✮✮✳

  ❋✐❣✉r❛ ✷✳✾✿ ❚✐♣♦❧♦❣✐❛ ❞❛s ❣❛✐♦❧❛s ❡ ❣❡♦♠❡tr✐❛ ❞❛ ♠❛❧❤❛ ✭❇❙ ✽✵✵✷✿✶✾✾✹ ✭✷✵✵✷✮✮✳

  ✶✵ ❈❆P❮❚❯▲❖ ✷✳ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆

  ❋✐❣✉r❛ ✷✳✶✵✿ ▼✉r♦ ❞❡ ❣❛❜✐õ❡s ✭❆❣✉✐❛r ❡ ▼❛rt✐♥s✱ ✷✵✵✺✮✳ ❆ s✉❛ ♣r✐♥❝✐♣❛❧ ✈❛♥t❛❣❡♠ s♦❜r❡ ♦✉tr♦s r❡s✐❞❡ ♥❛ s✉❛ ❡❧❡✈❛❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✱ ❛❧t❛♠❡♥t❡ ❞r❡♥❛♥t❡ ❡

  ✢❡①✐❜✐❧✐❞❛❞❡ q✉❡ ✐♥❞✉③ ♥✉♠❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ s♦❢r❡r❡♠ ❞❡s❧♦❝❛♠❡♥t♦s ❡ ❞❡❢♦r♠❛çõ❡s s❡♠ s❡ r♦♠♣❡r❡♠✳ ❖ s❡✉ ✉s♦ é ❡ss❡♥❝✐❛❧♠❡♥t❡ ✐♠♣❧❡♠❡♥t❛❞♦ ❡♠ ✈✐❛s r♦❞♦✈✐ár✐❛s ❞❡✈✐❞♦ ❛♦ s❡✉ ❜♦♠ ❡♥q✉❛❞r❛♠❡♥t♦

  ♣❛✐s❛❣íst✐❝♦ ✭▼❛❝❝❛❢❡rr✐✱ ✷✵✵✸✮✳ ❖s ♠✉r♦s ❞❡ ♣♥❡✉s sã♦ ❡str✉t✉r❛s r❡❧❛t✐✈❛♠❡♥t❡ ♣♦✉❝♦ ✉s✉❛✐s✳ ◆♦ ❡♥t❛♥t♦✱ r❡✈❡❧❛✲s❡ ✐♥t❡r❡ss❛♥t❡ ❛ s✉❛ ♦❜s❡r✈❛çã♦✱ ✉♠❛ ✈❡③ q✉❡ r❡✈❡❧❛♠ ✉♠ ❜❛✐①♦ ❝✉st♦ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦s ♠❛t❡r✐❛✐s ❝♦♥✈❡♥❝✐✲

  ♦♥❛✐s✳ ❆♣r❡s❡♥t❛♠✲s❡ ❝♦♠♦ ♠✉r♦s ❞❡ ❣r❛✈✐❞❛❞❡ ❡ sã♦ ❝♦♥str✉í❞♦s ❛tr❛✈és ❞❡ ♣♥❡✉s ✉s❛❞♦s✱ ❞✐s♣♦st♦s ❤♦r✐③♦♥t❛❧♠❡♥t❡✱ ❛♠❛rr❛❞♦s ❡♥tr❡ s✐ ❝♦♠ ❝♦r❞❛ ♦✉ ❛r❛♠❡ ❡ ♣r❡❡♥❝❤✐❞♦s ❝♦♠ s♦❧♦ ❝♦♠♣❛❝t❛❞♦✳ ❉❡✈✐❞♦ à ❡❧❡✈❛❞❛ ✢❡①✐❜✐❧✐❞❛❞❡ ❞♦ ♠❛t❡r✐❛❧✱ ❡st❡ t✐♣♦ ❞❡ ♠✉r♦s ♣❡r♠✐t❡ ❞❡s❧♦❝❛♠❡♥t♦s ❤♦r✐③♦♥t❛✐s ❡ ✈❡rt✐❝❛✐s s✉♣❡r✐♦r❡s ❛♦s ❝♦♥str✉í❞♦s ❡♠ ❜❡tã♦ ♦✉ ❛❧✈❡♥❛r✐❛✳ ◆♦ ❡♥t❛♥t♦✱ ❡ ♣♦r ❡ss❡ ❢❛❝t♦✱ ♥ã♦ ❞❡✈❡rã♦ s❡r ❛♣❧✐✲ ❝á✈❡✐s ❡♠ ❝♦♥t❡♥çõ❡s q✉❡ s✐r✈❛♠ ❞❡ s✉♣♦rt❡ ❛ ❡str✉t✉r❛s ♣♦✉❝♦ ❞❡❢♦r♠á✈❡✐s✱ ❝♦♠♦ ❢✉♥❞❛çõ❡s ♦✉ ✈✐❛s ❢❡rr♦✈✐ár✐❛s✳

  ❙❡❣✉♥❞♦ ●❡rs❝♦✈✐❝❤ ✭✷✵✵✻✮✱ ❡st❡ t✐♣♦ ❞❡ ♠✉r♦ ❡stá ❧✐♠✐t❛❞♦ ❛ ❛❧t✉r❛s ✐♥❢❡r✐♦r❡s ❛ ✺ ♠❡tr♦s ❡ ❛ ❜❛s❡ ❞❡✈❡rá s❡r ♥❛ ♦r❞❡♠ ❞♦s ✹✵ ❛ ✻✵✪ ❞❛ ❛❧t✉r❛ ❞♦ ♠❡s♠♦✳

  ✷✳✸✳✷ ▼✉r♦s ❡♠ ❝♦♥s♦❧❛

  ❖s ♠✉r♦s ❡♠ ❝♦♥s♦❧❛ sã♦ ❡str✉t✉r❛s ❡s❜❡❧t❛s✱ r❡❣✉❧❛r♠❡♥t❡ ❝♦♠ s❡❝çã♦ tr❛♥s✈❡rs❛❧ ❡♠ L ♦✉ ❡♠ T

  ✷✳✹✳ ■▼P❯▲❙❖❙ ❆❈❚■❱❖❙ ❙❖❇❘❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ L ❖❯ T ■◆❱❊❘❚■❉❖ ✶✶ ❋✐❣✉r❛ ✷✳✶✶✿ ●❡♦♠❡tr✐❛ ❞❡ ♠✉r♦s ❡♠ ❝♦♥s♦❧❛ ✭❈❡r♥✐❝❛✱ ✶✾✾✹✮✳

  ❆ ❡st❡s ♠✉r♦s ♣♦❞❡♠ s❡r ❛❞✐❝✐♦♥❛❞❛s ❛♥❝♦r❛❣❡♥s✱ ♣♦r ❢♦r♠❛ ❛ ❛✉♠❡♥t❛r ❛ s✉❛ r❡s✐stê♥❝✐❛ ❛♦ ❞❡s❧✐③❛♠❡♥t♦✳ ❊st❛ s♦❧✉çã♦ ♣♦❞❡ s❡r ❛♣❧✐❝❛❞❛ q✉❛♥❞♦ ❡①✐st❡♠ ❧✐♠✐t❛çõ❡s ❞❡ ❡s♣❛ç♦ ❞✐s♣♦♥í✈❡❧ ❡ ❡①✐st❡ ✉♠ t❡rr❡♥♦ ❝♦♠ ❡❧❡✈❛❞❛s ❝❛r❛❝t❡ríst✐❝❛s r❡s✐st❡♥t❡s ♥❛ ❢✉♥❞❛çã♦✳ ❆s ❛♥❝♦r❛❣❡♥s ♣♦❞❡♠ ❧♦❝❛❧✐③❛r✲s❡ ♥❛ ❜❛s❡ ✭❋✐❣✉r❛ ✷✳✶✷❛✮ ♦✉ ♥♦ t♦♣♦ ❞♦ ♠✉r♦ ✭❋✐❣✉r❛ ✷✳✶✷❜✮✱ ❡st❛♥❞♦✱ ♥❡st❡ ú❧t✐♠♦ ❝❛s♦✱ ✜①❛❞❛s ❛ ✉♠❛ ♣❧❛❝❛ ❞❡ ❛♥❝♦r❛❣❡♠ ✭❉♦♠✐♥❣✉❡s✱ ✶✾✾✼✮✳

  

✭❛✮ ❆♥❝♦r❛❣❡♠ ♥❛ ❜❛s❡ ✭❛❞❛♣t❛❞♦ ❞❡ ✭❜✮ ❆♥❝♦r❛❣❡♠ ♥♦ t♦♣♦ ✭❛❞❛♣t❛❞♦ ❞❡ ❘♦❝❤❛✱

●❡rs❝♦✈✐❝❤✱ ✷✵✵✻✮✳ ✶✾✼✹ ✭❉♦♠✐♥❣✉❡s✱ ✶✾✾✼✮✮✳

  ❋✐❣✉r❛ ✷✳✶✷✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ♠✉r♦ ❝♦♠ ❛♥❝♦r❛❣❡♥s✳ ❙❛❧✐❡♥t❛✲s❡ q✉❡✱ ♥♦ ❞❡❝♦rr❡r ❞❛ ♣r❡s❡♥t❡ ❞✐ss❡rt❛çã♦✱ ❛❜♦r❞❛r✲s❡✲ã♦ ♦s ✐♠♣✉❧s♦s s♦❜r❡ ♠✉r♦s ❞❡ s✉♣♦rt❡ ❡♠ ❝♦♥s♦❧❛ ✭❡♠ L ♦✉ T ✐♥✈❡rt✐❞♦✮✳

  ✶✷ ❈❆P❮❚❯▲❖ ✷✳ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆ t❛♠❜é♠ ❛ ❧♦❝❛❧✐③❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧✱ ✐st♦ é✱ ❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ♣❧❛♥♦ ❡♠ q✉❡ s❡ ❡♥❝♦♥tr❛♠ ❛♣❧✐❝❛❞♦s ♦s ✐♠♣✉❧s♦s✳

  

✷✳✹✳✶ ▼ét♦❞♦ ❜❛s❡❛❞♦ ♥❛ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡ ✭▼ét♦❞♦ R✮ ✭❚❡r③❛❣❤✐ ❡t ❛❧✳✱

✶✾✹✽✮

  ❖ ♠ét♦❞♦ R ❝♦♥s✐❞❡r❛ q✉❡ ❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ é ✈❡rt✐❝❛❧ ✭❋✐❣✉r❛ ✷✳✶✸✮ ❡ q✉❡ ❛ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡ é ❛ ✉s❛❞❛ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s ❛❝t✉❛♥t❡s✳

  ❋✐❣✉r❛ ✷✳✶✸✿ ❙✉♣❡r❢í❝✐❡ ❞❡ r♦t✉r❛✿ ❊st❛❞♦ ❛❝t✐✈♦ ✭❚❡r③❛❣❤✐ ❡t ❛❧✳✱ ✶✾✹✽✮✳ ❖ ✐♠♣✉❧s♦ ❛❝t✉❛♥t❡ ♥❛ ❡str✉t✉r❛ é r❡♣r❡s❡♥t❛❞♦ ♣♦r ✉♠ ❞✐❛❣r❛♠❛ ❞❡ t❡♥sõ❡s tr✐❛♥❣✉❧❛r ✭❛s t❡♥sõ❡s

  ✈❛r✐❛♠ ❧✐♥❡❛r♠❡♥t❡ ❝♦♠ ❛ ♣r♦❢✉♥❞✐❞❛❞❡✮✱ ❡st❛♥❞♦ ♦ ♣♦♥t♦ ❞❡ ❛♣❧✐❝❛çã♦ ❞❛ s✉❛ r❡s✉❧t❛♥t❡ ❧♦❝❛❧✐③❛❞♦ ❛

  1 ′

  ❞❛ ♣r♦❢✉♥❞✐❞❛❞❡ H ✭❚❡r③❛❣❤✐ ❡t ❛❧✳✱ ✶✾✹✽✮✱ ❛♦ s❡r ❝♦♥s✐❞❡r❛❞❛ ❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦

  3

  s✉♣♦rt❛❞♦ ✭❋✐❣✉r❛ ✷✳✶✹✮✳ ❋✐❣✉r❛ ✷✳✶✹✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♠ét♦❞♦ ❜❛s❡❛❞♦ ♥❛ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡ ✲ ♠ét♦❞♦ R ✭❛❞❛♣✲ t❛❞♦ ❞❡ ❚❡r③❛❣❤✐ ❡t ❛❧✳✱ ✶✾✹✽✮✳

  ✷✳✹✳ ■▼P❯▲❙❖❙ ❆❈❚■❱❖❙ ❙❖❇❘❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ L ❖❯ T ■◆❱❊❘❚■❉❖ ✶✸

  1

✷✳✹✳✷ ▼ét♦❞♦ ❜❛s❡❛❞♦ ♥♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜ ✭▼ét♦❞♦ C ✮ ✭▼✐♥❡✐r♦✱

✶✾✼✽✮

  ❖ ♠ét♦❞♦ C

  1 ❛❞♦♣t❛ ✉♠ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❝♦♠ ✉♠❛ ✐♥❝❧✐♥❛çã♦ β C1 ✱ ❢✉♥çã♦ ❞❛ ❛❧t✉r❛ H ❡ ❞♦ ❝♦♠✲

  ♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ B ❞❛ ❡str✉t✉r❛ ✭❋✐❣✉r❛ ✷✳✶✺✮✳ P❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s ❛❝t✉❛♥t❡s✱ ♥♦ ♠ét♦❞♦ C

  1 é ✉t✐❧✐③❛❞❛ ❛ ❢♦r♠✉❧❛çã♦ ❞♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜✳

  ❖ ♣❡s♦ ❞♦ ♠✉r♦✱ ❛❧✐❛❞♦ ❛♦ s♦❧♦ ❝♦♥t✐❞♦ ♥♦ ✈✉❧❣❛r♠❡♥t❡ ❞❡♥♦♠✐♥❛❞♦ ✏♠✉r♦ ✈✐rt✉❛❧✑✱ ❧✐♠✐t❛❞♦ ♣❡❧❛ ♣❛r❡❞❡ ❡ ❜❛s❡ ❞❛ ❡str✉t✉r❛ ❡ ♣❡❧❛ s✉♣❡r❢í❝✐❡ ❞❡ r♦t✉r❛✱ ❝♦♥st✐t✉❡♠ ♦ ♣❡s♦ t♦t❛❧ W ✳ ❏✉♥t❛♠❡♥t❡ ❝♦♠ ❛ ❝♦♠♣♦♥❡♥t❡ ✈❡rt✐❝❛❧ ❞♦ ✐♠♣✉❧s♦ ❛❝t✉❛♥t❡✱ r❡♣r❡s❡♥t❛♠ ❛s ❝❛r❣❛s ✈❡rt✐❝❛✐s✳

  ❋✐❣✉r❛ ✷✳✶✺✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♠ét♦❞♦ ❜❛s❡❛❞♦ ♥♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜ ✲ ♠ét♦❞♦ C

  1 ✳

  ◆❛ ❋✐❣✉r❛ ✷✳✶✺✱ ✐❧✉str❛✲s❡ ♦ ♠ét♦❞♦ C

  1 ✱ ❞❡st❛❝❛♥❞♦✲s❡ ❛ ❧♦❝❛❧✐③❛çã♦ ❞♦ ♣♦♥t♦ ❞❡ ❛♣❧✐❝❛çã♦ ❞♦

  1

  ✐♠♣✉❧s♦ ❛ ❞❛ ❛❧t✉r❛ ❞♦ ❞✐❛❣r❛♠❛ ❞❡ t❡♥sõ❡s✱ ❛❞♠✐t✐❞♦ tr✐❛♥❣✉❧❛r✱ ❞❛❞♦ q✉❡ ❛s t❡♥sõ❡s ♣r❡s❡♥t❡s

  3

  ✈❛r✐❛♠ ❧✐♥❡❛r♠❡♥t❡ ❝♦♠ ❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❞♦ t❡rr❡♥♦✳ ❆ r❡s✉❧t❛♥t❡ q✉❡ ❛❝t✉❛ ♥♦ t❛r❞♦③ ❞❛ ♣❛r❡❞❡ ❞❛ ❡str✉t✉r❛ ❢❛③ ✉♠ â♥❣✉❧♦ δ s ❝♦♠ ❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ✭❋✐❣✉r❛ ✷✳✶✺✮✳ ❊ss❡ â♥❣✉❧♦✱ q✉❡ r❡♣r❡s❡♥t❛ ♦ ❛tr✐t♦ ♣r❡s❡♥t❡ ♥❛ ✐♥t❡r❢❛❝❡ s♦❧♦✲❡str✉t✉r❛✱ é ✐❣✉❛❧ ❛♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡

  ′

  ❞♦ s♦❧♦ φ ✱ ♣♦✐s✱ ♥❛ ✈❡r❞❛❞❡✱ ♦ ❝♦♥t❛❝t♦ ❞á✲s❡ ❡♥tr❡ s♦❧♦ ❡ s♦❧♦✳ ❆ ❡①♣r❡ssã♦ ✷✳✶✵✱ ♣r❡s❡♥t❡ ♥❛ s❡❝çã♦ ✷✳✷✳✷✱ ❝❛r❛❝t❡r✐③❛ ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✳

  ✶✹ ❈❆P❮❚❯▲❖ ✷✳ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆

  2

✷✳✹✳✸ ▼ét♦❞♦ ❜❛s❡❛❞♦ ♥♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜ ✭▼ét♦❞♦ C ✮ ✭▼❛t♦s ❋❡r✲

♥❛♥❞❡s ❡t ❛❧✳✱ ✶✾✾✼✮

  ❖ ❛ss✉♥t♦ ❞♦ ❝á❧❝✉❧♦ r✐❣♦r♦s♦ ❞♦s ✐♠♣✉❧s♦s s♦❜r❡ ♠✉r♦s ❞❡ s✉♣♦rt❡ ❡♠ ❝♦♥s♦❧❛ t❡♠ s✐❞♦ ❛❜♦r❞❛❞♦ ♣♦r ❞✐✈❡rs♦s ❛✉t♦r❡s ❝♦♠♦ ❇❛r❣❤♦✉t❤✐ ✭✶✾✾✵✮✱ ●r❡❝♦ ✭✶✾✾✷❀ ✶✾✾✾❀ ✷✵✵✶✮✱ ▼❛t♦s ❋❡r♥❛♥❞❡s ❡t ❛❧✳ ✭✶✾✾✼✮ ❡ ▼❛t♦s ❋❡r♥❛♥❞❡s ✭✷✵✶✶✮✳

  P❛r❛ ♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✱ ❝♦♥s✐❞❡r❛✲s❡ ❝♦♠♦ ♠ét♦❞♦ C

  2 ✱ ♦ ❞❡s❝r✐t♦ ♣♦r ▼❛t♦s ❋❡r♥❛♥❞❡s ❡t ❛❧✳

  ✭✶✾✾✼✮✱ ♣♦r s❡ ❥✉❧❣❛r q✉❡ ♦ ♣r♦❜❧❡♠❛ ✭❡ ❛ ♠❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ♦ r❡s♦❧✈❡r✮ é ❝♦❧♦❝❛❞♦ ♣♦r ❡st❡s ❛✉t♦r❡s ♥❛ ❢♦r♠❛ ♠❛✐s ❞✐r❡❝t❛✳ ❈♦♠♦ s❡ ✈❡rá✱ ♦s r❡st❛♥t❡s tr❛❜❛❧❤♦s ✐♥tr♦❞✉③❡♠ ❛❧❣✉♥s ❡s❝❧❛r❡❝✐♠❡♥t♦s ❛❞✐❝✐♦♥❛✐s✱ ♣❡❧♦ q✉❡ t❛♠❜é♠ sã♦ ❛❜♦r❞❛❞♦s✳

  ❖ ♠ét♦❞♦ ♣r♦♣♦st♦ ♣♦r ▼❛t♦s ❋❡r♥❛♥❞❡s ❡t ❛❧✳ ✭✶✾✾✼✮ ♣r♦❝✉r❛ t❡st❛r t♦❞❛s ❛s s✉♣❡r❢í❝✐❡s ♣❧❛♥❛s✱ ❝♦♠♣♦st❛s ♦✉ ♥ã♦✱ ❞❡ s❡♣❛r❛çã♦ ❡♥tr❡ ❛ ❝✉♥❤❛ ❞❡ t❡rr❡♥♦ q✉❡ ❛❝t✉❛ s♦❧✐❞❛r✐❛♠❡♥t❡ ❝♦♠ ♦ ♠✉r♦ ❡ ♦ ♠❛❝✐ç♦ s✉♣♦rt❛❞♦✱ ✉t✐❧✐③❛♥❞♦✱ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s✱ ❛s ❡①♣r❡ssõ❡s ❞❡ ❈♦✉❧♦♠❜✳

  ◆❛ ❋✐❣✉r❛ ✷✳✶✻ ✐♥❞✐❝❛✲s❡ ❛ ✐♥❝❧✐♥❛çã♦ ❛❞♠✐t✐❞❛ ♣❛r❛ ❛ r❡s✉❧t❛♥t❡ ❞♦ ✐♠♣✉❧s♦ ❡♠ ❝❛❞❛ ✉♠ ❞♦s tr♦ç♦s ❞❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❞♦ ♠✉r♦✳ ❋✐❣✉r❛ ✷✳✶✻✿ ▼ét♦❞♦ ❞❡ ❛✈❛❧✐❛çã♦ ❞♦s ✐♠♣✉❧s♦s ❡♠ ♠✉r♦s ❞❡ ❜❡tã♦ ❛r♠❛❞♦ ✭▼❛t♦s ❋❡r♥❛♥❞❡s ❡t ❛❧✳ ✭✶✾✾✼✮✮✳

  2

  ◆♦ ♠ét♦❞♦ C ❝♦♥s✐❞❡r❛✲s❡✱ ❛ss✐♠✱ q✉❡ ❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ é ✉♠❛ s✉♣❡r❢í❝✐❡

  C2

  q✉❡❜r❛❞❛✱ ❡♠ ✷ ♦✉ ✸ tr♦ç♦s✱ ❝♦♥s♦❛♥t❡ ♦ ✈❛❧♦r ❞♦ â♥❣✉❧♦ β ✭❋✐❣✉r❛ ✷✳✶✼❜✮✳ ❈♦♠ ❡❢❡✐t♦✱ ❝❛s♦ ♦ â♥❣✉❧♦

  ∗ ∗

  C2 C2 ∗ C2

  β C2 s❡❥❛ ✐♥❢❡r✐♦r ❛♦ â♥❣✉❧♦ β ✭β ✐❧✉str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✶✼❛✮✱ ♦ ♣❛r❛♠❡♥t♦ ❞♦ ♠✉r♦ é ❝♦♠♣♦st♦ ♣♦r

  ✷ tr♦ç♦s ✭❋✐❣✉r❛ ✷✳✶✽❛✮✳ ◆♦ ❝❛s♦ ❞❡ β s❡r s✉♣❡r✐♦r ❛ β C2 ✱ ♦ ♣❛r❛♠❡♥t♦ t❡♠ ✸ tr♦ç♦s ✭❋✐❣✉r❛ ✷✳✶✽❜✮✳ ❊♠ q✉❛❧q✉❡r ❞♦s ❝❛s♦s✱ ✉t✐❧✐③❛✲s❡ ❛ t❡♦r✐❛ ❞❡ ❈♦✉❧♦♠❜ ♣❛r❛ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s✳ ❖ ❝♦♥t❛❝t♦ ❡♥tr❡ ❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ♦ ♣❛r❛♠❡♥t♦ ❞♦ ♠✉r♦ ✏✈✐rt✉❛❧✑ ❡ ♦ s♦❧♦ é ❝❛r❛❝t❡r✐③❛❞♦ ♣❡❧♦

  ′

  â♥❣✉❧♦ ❞❡ ❛tr✐t♦ s♦❧♦✲s♦❧♦✱ ♦✉ s❡❥❛✱ φ ✳

  ✷✳✹✳ ■▼P❯▲❙❖❙ ❆❈❚■❱❖❙ ❙❖❇❘❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ L ❖❯ T ■◆❱❊❘❚■❉❖ ✶✺

  C2 ✭❛✮ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ✐♥❝❧✐♥❛çã♦ ✜①❛ ❞♦ ♣❛r❛✲ ✭❜✮ ❱❛r✐❛çã♦ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞♦ ♣❛r❛♠❡♥t♦✱ β ✳

  ∗ ♠❡♥t♦✱ β ✳

  C2

  ❋✐❣✉r❛ ✷✳✶✼✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♠ét♦❞♦ C

  2 ✿ ✐♥❝❧✐♥❛çã♦ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❞♦ ♠✉r♦✳

  ❆ ♣❛rt✐r ❞♦s ✐♠♣✉❧s♦s r❡s✉❧t❛♥t❡s ❞♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜✱ ♣♦❞❡ ✐♥❢❡r✐r✲s❡ ♦ ❞✐❛❣r❛♠❛ ❞❡ t❡♥sõ❡s s♦❜r❡ ❛ ❡str✉t✉r❛ q✉❡ ❛✉♠❡♥t❛ ❧✐♥❡❛r♠❡♥t❡ ❝♦♠ ❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❡♠ ❝❛❞❛ tr♦ç♦✱ ❝♦♥❢♦r♠❡ ✐❧✉str❛❞♦

  C2

  ♥❛ ❋✐❣✉r❛ ✷✳✶✽✳ ❆ ❡s❝♦❧❤❛ ❞❡ β é ❢❡✐t❛ ♣♦r ❢♦r♠❛ ❛ ♠❛①✐♠✐③❛r ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ✭♦✉ ❛ s✉❛ ❝♦♠♣♦✲ ♥❡♥t❡ ❤♦r✐③♦♥t❛❧ ♦✉ ❛ ♦❜t❡♥çã♦ ❞❛ s✐t✉❛çã♦ ♠❡♥♦s ❡stá✈❡❧ ❞❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡✱ ♥♦♠❡❛❞❛♠❡♥t❡✱ ♦ ❞❡s❧✐③❛♠❡♥t♦✱ ♦ ❞❡rr✉❜❛♠❡♥t♦✱ ❛ r♦t✉r❛ ❞❛ ❢✉♥❞❛çã♦✱ ❡t❝✳✮✳

  ∗ ∗

  ✭❛✮ ❈❛s♦ β C2 ≤ β ✳ ✭❜✮ ❈❛s♦ β C2 > β ✳ C2

  C2

  ✶✻ ❈❆P❮❚❯▲❖ ✷✳ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆

  2

  ❞✉③ ❡s❝❧❛r❡❝✐♠❡♥t♦s ❛❞✐❝✐♦♥❛✐s à s♦❧✉çã♦ ♦❜t✐❞❛ ❞♦ ♠ét♦❞♦ C ❀ ❼ ✐❣♥♦r❛ ❛ ♣❛rt❡ ❤❛❜✐t✉❛❧♠❡♥t❡ ✈❡rt✐❝❛❧ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦✱ ✐st♦ é✱ ❛❞♠✐t❡ q✉❡ ❛s s✉♣❡r❢í❝✐❡s ❛ ❛♥❛❧✐s❛r

  ♣❛rt❡♠ ❞♦ ♣♦♥t♦ ❆ ❡ ♥ã♦ ❞♦ ♣♦♥t♦ ❆✬✱ ✐♥❞✐❝❛❞♦s ♥❛ ❋✐❣✉r❛ ✷✳✶✾✳ ❆ ❛♥á❧✐s❡ ❞♦ ♣r♦❜❧❡♠❛✱ t❛❧ ❝♦♠♦ ❢♦✐ ❝♦❧♦❝❛❞♦ ♣♦r ❡st❡s ❛✉t♦r❡s✱ ❢♦✐ r❡s✉♠✐❞❛ ♣♦r ▼❛t♦s ❋❡r♥❛♥❞❡s

  ′ ′ ∗

  < β ✭✷✵✶✶✮✿ ◆♦s ❝❛s♦s ❡♠ q✉❡ β ✱ ♦ ♠✉r♦ ❛♦ ❞❡s❧♦❝❛r✲s❡✱ ♠♦❜✐❧✐③❛ ♦ ❡st❛❞♦ ❛❝t✐✈♦ ♥❛s ❝✉♥❤❛s ❆❇❈

  B B ′

  ❡ ❆❈❉ ✭❋✐❣✉r❛ ✷✳✶✾✮✳ ❖s â♥❣✉❧♦s β ❡ β B sã♦ ❞❡✜♥✐❞♦s ♣❡❧❛s ❡①♣r❡ssõ❡s ❛♣r❡s❡♥t❛❞❛s ♣♦r ❇❛r❣❤♦✉t❤✐

  B

  ✭✶✾✾✵✮✿

  ′ ′

  φ ε − i

  o o

  45 + β = 180 − ✭✷✳✶✹✮

  • B

  2

  2

  ′

  φ ε − i

  o

  β = 45

  B

  ✭✷✳✶✺✮

  2

  2 ❡♠ q✉❡ ε é ❞❛❞♦ ♣❡❧❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦✿ sin i

  ε = arcsin ✭✷✳✶✻✮

  ′

  sin φ ❋✐❣✉r❛ ✷✳✶✾✿ ▼✉r♦ ❡♠ ❝♦♥s♦❧❛ ❡ ❝✉♥❤❛s ❞❡ t❡rr❛s ❡♠ ❡st❛❞♦ ❛❝t✐✈♦ ✭❛❞❛♣t❛❞♦ ❞❡ ▼❛t♦s ❋❡r♥❛♥❞❡s✱ ✷✵✶✶✮✳

  B

  ◗✉❛♥❞♦ ❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦ é ♥✉❧❛✱ ♦s ❞♦✐s â♥❣✉❧♦s ❛♣r❡s❡♥t❛❞♦s✱ β

  ′ ′

  4

  2

  / / ❡ β ✱ sã♦ ✐❣✉❛✐s ❛ ✭❇❛r❣❤♦✉t❤✐✱ ✶✾✾✵✮✳

  • π φ

  B

  ✷✳✹✳ ■▼P❯▲❙❖❙ ❆❈❚■❱❖❙ ❙❖❇❘❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ L ❖❯ T ■◆❱❊❘❚■❉❖ ✶✼

  ✭❛✮ ■♠♣✉❧s♦ ❛♦ ❧♦♥❣♦ ❞❛ s✉♣❡r❢í❝✐❡ q✉❡ ❧✐♠✐t❛ ❛ ✭❜✮ ■♠♣✉❧s♦ ♥♦ ♣❧❛♥♦ ✈❡rt✐❝❛❧✳ ❝✉♥❤❛ s♦❧✐❞ár✐❛ ❝♦♠ ♦ ♠✉r♦✳

  ❋✐❣✉r❛ ✷✳✷✵✿ ❆✈❛❧✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❡♠ ♠✉r♦s ❡♠ ❝♦♥s♦❧❛✳ ❈❛s♦ ❡♠ q✉❡ ❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ♦ ♣❛r❛♠❡♥t♦ s❡ ❡♥❝♦♥tr❛ ❛❝✐♠❛ ❞♦ t♦♣♦ ❞♦ ♠✉r♦ ✭❛❞❛♣t❛❞♦ ❞❡ ▼❛t♦s ❋❡r♥❛♥❞❡s✱ ✷✵✶✶✮✳

  ′ ′ ∗

  > β ◆♦ ❝❛s♦ ❞❡ β ✱ ♦ ❝á❧❝✉❧♦ ❞♦ ✐♠♣✉❧s♦ t♦r♥❛✲s❡ ♠❛✐s ❝♦♠♣❧❡①♦ ♣♦rq✉❡ ❛ s✉♣❡r❢í❝✐❡ ❆❇ ✐♥t❡rs❡❝t❛

  B B

  ♦ ♣❛r❡❞❡ ❞♦ ♠✉r♦ ✭❋✐❣✉r❛ ✷✳✷✶❛✮✳ ❖ ♣r♦❝❡❞✐♠❡♥t♦ ❞❡ ❝á❧❝✉❧♦ s✉❣❡r✐❞♦ ♣♦r ▼❛t♦s ❋❡r♥❛♥❞❡s ✭✷✵✶✶✮

  ′

  ♣❛ss❛ ♣♦r ❛❞♦♣t❛r ✉♠ ✈❛❧♦r ♣❛r❛ ♦ â♥❣✉❧♦ β ✭β B ♠❛♥té♠ ❛ s✉❛ ❡①♣r❡ssã♦✮ ✜①❛♥❞♦ ❛ ♣♦s✐çã♦ ❞♦

  B

  ♣♦♥t♦ ❇ ❡ ❝❛❧❝✉❧❛♥❞♦✱ ❞❡ s❡❣✉✐❞❛✱ ♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s ♥♦s tr♦ç♦s ❆❇ ❡ ❇❋✱ ❛tr❛✈és ❞♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜✳ ❈♦♠ ♦s ✐♠♣✉❧s♦s ❡ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ♣❡s♦ ❞♦ s♦❧♦ ❞♦ ❜❧♦❝♦ ❆❇❋❈ ❡ s❡❣✉✐♥❞♦ ♦ ♣r♦❝❡ss♦ ❛♥t❡r✐♦r ✭❡q✉✐❧í❜r✐♦ ❞❡ ❢♦rç❛s✮✱ ❝❛❧❝✉❧❛✲s❡ ❛ ❢♦rç❛ ♥❛ s✉♣❡r❢í❝✐❡ ❆❈ ✭❋✐❣✉r❛ ✷✳✷✶❜✮✳ ❘❡♣❡t❡♠✲s❡ ♦s

  ′

  ♣❛ss♦s r❡❢❡r✐❞♦s✱ ❝♦♠ ♥♦✈♦s ✈❛❧♦r❡s ❞❡ β ❞❡ ♠♦❞♦ ❛ ❡♥❝♦♥tr❛r ♦ ✈❛❧♦r ♠á①✐♠♦ ❞❛ ❢♦rç❛ ♥❛ s✉♣❡r❢í❝✐❡

  B

  ❆❈✱ q✉❡✱ ♣❛r❛ ❡ss❡ ✈❛❧♦r ❞♦ â♥❣✉❧♦✱ s❡rá ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✳ ❈♦♠♦ s❡ ✈ê ❡ ❝♦♠♦ s❡ r❡❢❡r✐✉✱ ♦ ê♥❢❛s❡ ♥❡st❛ ❛❜♦r❞❛❣❡♠ ❡stá ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦s ✐♠♣✉❧s♦s ♥❛ s✉♣❡r❢í❝✐❡ ✈❡rt✐❝❛❧ ♦ q✉❡ é ❡q✉✐✈❛❧❡♥t❡ à ❛❜♦r❞❛❣❡♠

  2

  ❞♦ ♠ét♦❞♦ C ✳

  ✶✽ ❈❆P❮❚❯▲❖ ✷✳ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆

  ′ ′ AC

  ∗

  = β ❘❡❢❡r❡✲s❡ ❛✐♥❞❛ q✉❡ ♦ ✐♠♣✉❧s♦ I a ✱ é✱ ♥♦ ♠á①✐♠♦✱ ♦ ✐♠♣✉❧s♦ ❞❡ ❘❛♥❦✐♥❡ ✭❝❛s♦ β ✮ ❡ é✱ ♥♦

  B B

  ♠í♥✐♠♦✱ ♦ ✐♠♣✉❧s♦ ❞❡ ❈♦✉❧♦♠❜ ✭❝❛s♦ ❞❡ ❜❛s❡ ❝♦♠ ❝♦♠♣r✐♠❡♥t♦ ♣❡q✉❡♥♦✮✳ ❈♦♥❝❧✉✐✲s❡✱ ♣♦rt❛♥t♦✱ q✉❡✱

  AC

  s❡ δ ≥ i✱ ❛ ❛❞♦♣çã♦ ❞❡ I ✐❣✉❛❧ ❛♦ ✐♠♣✉❧s♦ ❞❡ ❘❛♥❦✐♥❡ ❡stá ❞♦ ❧❛❞♦ ❞❛ s❡❣✉r❛♥ç❛✳

  a

  ❘❡❢❡r❡✲s❡✱ ✜♥❛❧♠❡♥t❡✱ q✉❡ ▼❛t♦s ❋❡r♥❛♥❞❡s ✭✷✵✶✶✮ ❝♦♥s✐❞❡r❛✱ ♥❛ s✉❛ ❧❡✐t✉r❛ ❞♦s ♠ét♦❞♦s ❞❡

  ′

  ❇❛r❣❤♦✉t❤✐ ✭✶✾✾✵✮ ❡ ●r❡❝♦ ✭✶✾✾✷❀ ✶✾✾✾❀ ✷✵✵✶✮✱ q✉❡ ♦s â♥❣✉❧♦s β ❡ β B ♣❛rt❡♠ ❞♦ ♣♦♥t♦ ❆✬ ✭❋✐❣✉r❛s

  B

  ✷✳✶✾ ❛ ✷✳✷✶✮ ❡ ♥ã♦ ❞♦ ♣♦♥t♦ ❆✱ ❝♦♥❢♦r♠❡ ❝♦♥s✐❞❡r❛❞♦ ♥❛s ✜❣✉r❛s r❡❢❡r✐❞❛s ❡ ♣❡❧♦s ❛✉t♦r❡s ✐♥❞✐❝❛❞♦s✳

  ′

  ❊ss❛ ❧❡✐t✉r❛ ❛♣r♦①✐♠❛ ♦ s✐❣♥✐✜❝❛❞♦ ❞❡ β ❛♦ ❞❡ β C2 ❡ ❝♦♥st✐t✉✐ ❛ ♠❡❧❤♦r ♦♣çã♦✱ ♥❛ ♠❡❞✐❞❛ ❡♠ q✉❡

  B

  r❡❞✉③ ♦ ♣r♦❜❧❡♠❛ à ❞❡t❡r♠✐♥❛çã♦ ❞♦s ✐♠♣✉❧s♦s s♦❜r❡ ❛ ❡str✉t✉r❛ ❛❝✐♠❛ ❞❡ ❆✬✳ ❈♦♠ ❡❢❡✐t♦✱ ♦ ✐♠♣✉❧s♦ ❡♥tr❡ ❆✬ ❡ ❆ é ❝♦♥❤❡❝✐❞♦✱ ♣♦❞❡♥❞♦ s❡r ❞❡t❡r♠✐♥❛❞♦ ♣❡❧♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜✳

  ❈❛♣ít✉❧♦ ✸

❆♥á❧✐s❡ ❞❡ ❡str✉t✉r❛s ❞❡ s✉♣♦rt❡ ❡♠ ▲

✸✳✶ ■♥tr♦❞✉çã♦

  ◆♦ ❈❛♣ít✉❧♦ ✷ ❛♣r❡s❡♥t❛r❛♠✲s❡ ♠ét♦❞♦s ♣❛r❛ ❝❛❧❝✉❧❛r ♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s s♦❜r❡ ❡str✉t✉r❛s ❞❡ s✉✲ ♣♦rt❡ ❡♠ L ♦✉ T ✐♥✈❡rt✐❞♦✳ ◆♦ ♣r❡s❡♥t❡ ❝❛♣ít✉❧♦ ❛♣❧✐❝❛♠✲s❡ ♦s r❡❢❡r✐❞♦s ♠ét♦❞♦s✱ ❝♦♠♣❛r❛♥❞♦✲♦s ♣♦st❡r✐♦r♠❡♥t❡✳

  ❙❛❧✐❡♥t❛✲s❡ ♦ ❢❛❝t♦ ❞❡✱ ♥❛s ❛♣❧✐❝❛çõ❡s ❝♦♥s✐❞❡r❛❞❛s✱ ♥ã♦ s❡ ❡♥❝♦♥tr❛r ♣r❡s❡♥t❡ q✉❛❧q✉❡r t✐♣♦ ❞❡ s♦❜r❡❝❛r❣❛ ♥❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦✳ ❆ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡ ❝♦♥s✐❞❡r❛❞❛ é ✐❧✉str❛❞❛ ♥❛ ❋✐❣✉r❛ ✸✳✶✱ ♦♥❞❡ s❡ ❡①♣õ❡♠ ❛s ❞✐♠❡♥sõ❡s ♥❡❝❡s✲ sár✐❛s ♣❛r❛ ❛ ❞❡✜♥✐çã♦ ❞❛ s✉❛ ❣❡♦♠❡tr✐❛✳

  ❋✐❣✉r❛ ✸✳✶✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❛s ❞✐♠❡♥sõ❡s ❣❡r❛✐s ❞❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡✳

  ✷✵ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

  ✭❛✮ ❉✐♠❡♥sõ❡s ♣r✐♥❝✐♣❛✐s✳ ✭❜✮ ❉✐♠❡♥sõ❡s s❡❝✉♥❞ár✐❛s✳

  ❋✐❣✉r❛ ✸✳✷✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❛s ❞✐♠❡♥sõ❡s ❞♦ ♠♦❞❡❧♦ ❛❞♦♣t❛❞♦✳ ❆s ❞✐♠❡♥sõ❡s ❛♣r❡s❡♥t❛❞❛s ♥❛ ❋✐❣✉r❛ ✸✳✷❜ sã♦ ❢✉♥çã♦ ❞❛s ✐❧✉str❛❞❛s ♥❛ ❋✐❣✉r❛ ✸✳✷❛ ❛tr❛✈és ❞❛s s❡❣✉✐♥t❡s ❡①♣r❡ssõ❡s✿

  − B

  2 = B 1 (a + b 2 )

  ✭✸✳✶✮ a = (H − e) tan ξ ✭✸✳✷✮

  o

  ξ = α − 90 ✭✸✳✸✮

  − − B (B b )

  

2

  1

  1

  ϕ = arctan ✭✸✳✹✮

  H − e

  o

  ◆♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✱ ♦s â♥❣✉❧♦s ξ ❡ ϕ sã♦ ❝♦♥s✐❞❡r❛❞♦s ♥✉❧♦s✱ t♦♠❛♥❞♦ α ♦ ✈❛❧♦r ❞❡ 90 ✳ P♦r ❝♦♥s❡❣✉✐♥t❡✱ ❛s ❞✐♠❡♥sõ❡s b

  1 ❡ b 2 sã♦ ✐❣✉❛✐s✳ ❆ ❞✐♠❡♥sã♦ B 3 é ❝♦♥s✐❞❡r❛❞❛ ♥✉❧❛✱ ❛❧t❡r❛♥❞♦ ♦ ♠✉r♦

  ♣❛r❛ ✉♠❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡ ❡♠ L✳

  ✸✳✸ ❈á❧❝✉❧♦ ❞♦s ✐♠♣✉❧s♦s s♦❜r❡ ❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡ ✸✳✸✳✶ ▼ét♦❞♦ R

  ✸✳✸✳ ❈➪▲❈❯▲❖ ❉❖❙ ■▼P❯▲❙❖❙ ❙❖❇❘❊ ❆ ❊❙❚❘❯❚❯❘❆ ❉❊ ❙❯P❖❘❚❊ ✷✶ ❋✐❣✉r❛ ✸✳✸✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❛s ❝♦♥s✐❞❡r❛çõ❡s ❞♦ ♠ét♦❞♦ R✳

  ❈♦♠♦ s❡ ✈✐✉✱ ♦ ♠ét♦❞♦ R ❝♦♥s✐❞❡r❛ ❛ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡✱ ♣❡❧♦ q✉❡✱ ❞❛ ❡q✉❛çã♦ ✷✳✻✱ s❡ ♦❜té♠ ✉♠❛ ❝♦♠♣♦♥❡♥t❡ ❤♦r✐③♦♥t❛❧ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✱ ❞❛❞❛ ♣♦r✿

  1

  1 H

  2

  2 ′

  I = K γ (H ) cos i = K γ (H + B tan i) cos i

  a a 2 ✭✸✳✻✮ a

  2

  2 ❈♦♠ ♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✐♠♣✉❧s♦ ❛❝t✐✈♦ K a ❞❛❞♦ ♣❡❧❛ ❡q✉❛çã♦ ✷✳✼✳ ❉❡ ♠♦❞♦ ❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛r ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✱ ❡♠ ❢✉♥çã♦ ❞♦s ♣❛râ♠❡tr♦s ✐♥✐❝✐❛✐s ❞❛ ❡str✉t✉r❛ ❡

  ❞♦ t❡rr❡♥♦✱ r❡❡s❝r❡✈❡✲s❡ ❛ ❡q✉❛çã♦ ✸✳✻ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿

  2

  1

  

2

H

  K γ (H + B tan i) I a

  2 B

  2 a

  2

  = cos i = K a 1 + tan i cos i ✭✸✳✼✮

  1

  1

  2

  2 H

  γH γH

  2

  2

  1 ✸✳✸✳✷ ▼ét♦❞♦ C

  P❛r❛ ❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ C

  1 ✱ ♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❞♦ ♠✉r♦ é ❝♦♥s✐❞❡r❛❞♦ ❝♦♠ ✉♠❛ ✐♥❝❧✐♥❛çã♦ β C1

  ❢❛❝❡ à ❤♦r✐③♦♥t❛❧ ✭❋✐❣✉r❛ ✸✳✹✮✱ ❝✉❥❛ ❡①♣r❡ssã♦ é ❞❛❞❛ ♣♦r✿

2 K a γH

  cos (θ

  γH

  2

  1

  2

  γH

  2

  cos (θ

  C1

  ′

  ) = K

  a

  

C1

  1

  ′

  ) = K

  a

  cos arctan B

  2 H

  ′

  ✭✸✳✶✶✮ ❝♦♠ ♦ â♥❣✉❧♦ θ C1 ❞❛❞♦ ♣❡❧❛ ❡①♣r❡ssã♦ ✸✳✾ ❡ ❡♠ q✉❡ ♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✐♠♣✉❧s♦ ❛❝t✐✈♦ K a é ❞❛❞♦

  ♣❡❧❛ ❡①♣r❡ssã♦ ✷✳✶✶ ✭s❡❝çã♦ ✷✳✷✳✷✮✱ s❡♥❞♦ ♦ â♥❣✉❧♦ β C1 ♣r❡s❡♥t❡ ❞❛❞♦ ♣❡❧❛ ❡①♣r❡ssã♦ ✸✳✽✳ ❉❡st❡ ♠♦❞♦✱ ♣r♦❝✉r❛✲s❡ ❝♦♥❤❡❝❡r ❛ ✐♥✢✉ê♥❝✐❛ ❞♦ ❝r❡s❝✐♠❡♥t♦ ❞❛ r❡❧❛çã♦

  B 2 H

  ♥❛ ❡①♣r❡ssã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✳

  ✸✳✸✳✸ ▼ét♦❞♦ C

  2

  2 K a

  =

  ❖♥❞❡✿ K a

  ✲ ♣❡s♦ ✈♦❧ú♠✐❝♦ ❞♦ s♦❧♦❀ H

  a

  =

  1

  

2

  cos (θ C1 + φ

  ′

  ) ✭✸✳✶✵✮

  1 ❝♦♥s✐❞❡r❛ ♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s✳ ❆ss✐♠✱ ❛♣❧✐❝❛♥❞♦

  ✲ ❝♦❡✜❝✐❡♥t❡ ❞❡ ✐♠♣✉❧s♦ ❛❝t✐✈♦❀ γ

  ✲ ❛❧t✉r❛ t♦t❛❧ ❞♦ ♠✉r♦❀ θ

  ❛ ❡q✉❛çã♦ ✷✳✶✵ ❛♦ ❝❛s♦ ♣r❡s❡♥t❡ t❡♠✲s❡✱ ❡♠ ❢✉♥çã♦ ❞♦s ♣❛râ♠❡tr♦s ✐♥✐❝✐❛✐s✿

  C1 ✲ ✐♥❝❧✐♥❛çã♦ ❞♦ ♣❛r❛♠❡♥t♦ ❞♦ ♠✉r♦ ❢❛❝❡ à ✈❡rt✐❝❛❧❀

  φ

  ′

  ✲ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦✳ ❘❡♣r❡s❡♥t❛♥❞♦✲s❡ ❛ r❛③ã♦ ❛❞✐♠❡♥s✐♦♥❛❧ ❞❛ ❛❝çã♦✱ ❛ ❡q✉❛çã♦ ✸✳✶✵ é r❡❡s❝r✐t❛ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛ ✿

  I H

  a

  ❖ ♠ét♦❞♦ C

  1 ✳

  ✷✷ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲ ❋✐❣✉r❛ ✸✳✹✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❛s ❝♦♥s✐❞❡r❛çõ❡s ❞♦ ♠ét♦❞♦ C

  I H

  • φ
  • φ

  • φ

  2

  1

  2

  γH

  • arctan

  ❛♣r❡s❡♥t❛♠ ❛s s❡❣✉✐♥t❡s ❡①♣r❡ssõ❡s ✭❡♠ ❢✉♥çã♦ ❞❛s ❞✐♠❡♥sõ❡s ✐♥✐❝✐❛✐s✮✿ h

  = H − e − h

  2

  tan i ✭✸✳✶✻✮ h

  C2

  1 + tan θ

  3

  = h

  3

  ′

  ✭✸✳✶✺✮ h

  3 = H − e − [B 2 tan (90 − θ C2 )]

  = e ✭✸✳✶✹✮ h

  1

  3

  ✸✳✸✳ ❈➪▲❈❯▲❖ ❉❖❙ ■▼P❯▲❙❖❙ ❙❖❇❘❊ ❆ ❊❙❚❘❯❚❯❘❆ ❉❊ ❙❯P❖❘❚❊ ✷✸ β

  1 ✱ h 2 ❡ h 3 ❡ h ′

  ❆s ❞✐♠❡♥sõ❡s h

  2 ✳

  ✭✸✳✶✸✮ ❋✐❣✉r❛ ✸✳✺✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❛s ❝♦♥s✐❞❡r❛çõ❡s ❞♦ ♠ét♦❞♦ C

  2 H − e

  = arctan B

  ∗ C2

  ✭✸✳✶✷✮ θ

  2 H − e

  B

  o

  = 90

  ∗ C2

  3 ✭✸✳✶✼✮

  ✷✹ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲ ❋✐❣✉r❛ ✸✳✻✿ P♦r♠❡♥♦r ❞❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ ❣r❛♥❞❡③❛s✿ ▼ét♦❞♦ C

  2 ✳

  ❆ss✐♠✱ ❛s ❞✐♠❡♥sõ❡s ♣r❡s❡♥t❡s ♥❛ ❋✐❣✉r❛ ❡①♣♦st❛ ❛❝✐♠❛ ✭✸✳✻✮ tê♠ ❛s s❡❣✉✐♥t❡s ❡①♣r❡ssõ❡s✿ l tan θ C2 = =⇒ l = (H − e) tan θ C2

  ✭✸✳✶✽✮ H − e l = B − l

  2 2 ✭✸✳✶✾✮

  h h tan i = =⇒ l =

  3 ✭✸✳✷✵✮

  l

  3 tan i 2 3 l − tan 2 h l i −l h

  tan θ = ⇐⇒ tan θ = =⇒ h tan θ = l − =⇒

C2 C2 C2

  2 h h tan i

  1 l

  2

  • =⇒ h tan θ = l =⇒ h =

  C2 2 ✭✸✳✷✶✮

  1

  tan i

  • tan θ C2

  tan i

  ❉❡st❡ ♠♦❞♦✱ ❛ ❡①♣r❡ssã♦ q✉❡ ♦r✐❣✐♥❛ ❛ ❛❧t✉r❛ H

  1 é ❞❛❞❛ ♣♦r✿

  H = H + h

  1

  ✭✸✳✷✷✮

  • I
  • I
  • φ

  =

  tan i e + e

  2

  2 H − e + B

  a1 h

  K

  1 H 2 "

  ) 1 2 γH 2 =

  cos δ

  θ C2 +φ ′

  (

  

I a1 cos δ p +I a4 cos

  =

  I H a 1 2 γH 2

  ✭✸✳✷✺✮ ❆ss✐♠✱ é ♣♦ssí✈❡❧ r❡❡s❝r❡✈❡r ❛ ❡①♣r❡ssã♦ ✸✳✷✸✱ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛✱ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿

  2

  2 i

  p

  −

  = K a1 " 2 1 − e H

  ◆♦ ❝❛s♦ ❞❡ ♦ ♣❛r❛♠❡♥t♦ s❡ ❡♥❝♦♥tr❛r ❛❜❛✐①♦ ❞♦ t♦♣♦ ❞♦ ♠✉r♦ ✭❋✐❣✉r❛ ✸✳✼❜✮✱ ❛ r❡s✉❧t❛♥t❡ ❞♦ ✐♠♣✉❧s♦

  90 ✭✸✳✷✻✮

  ′ −

  − 90) + 1 tan i − e H # 2 cos β C2 + φ

  90) tan (β C2

  − 1 − e H tan (β C2 −

  ) # =

  a4 h

  ′

  C2

  cos(θ

  2

  − e i

  B 2 −(H−e) tan θ C2 tan θ C2 + 1 tan i

  H +

  e)

  1

  a4

  a

  cos δ

  a1

  = I

  H a4

  H a1

  = I

  I H

  γ (H

  ◆♦ ❝❛s♦ ❡♠ q✉❡ ♦ ♣❛r❛♠❡♥t♦ ❞♦ ♠✉r♦ s❡ ❡♥❝♦♥tr❛ ❛❝✐♠❛ ❞❛ ❛❧t✉r❛ H ✭❋✐❣✉r❛ ✸✳✼❛✮✱ ❛ r❡s✉❧t❛♥t❡ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ é ❞❛❞❛ ♣♦r ✭❝♦♥s✐❞❡r❛♥❞♦ ❛♣❡♥❛s ❛s ❝♦♠♣♦♥❡♥t❡s ❤♦r✐③♦♥t❛✐s✮✿

  2 ✳

  ❋✐❣✉r❛ ✸✳✼✿ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ✐♠♣✉❧s♦s ♣❛r❝✐❛✐s✿ ▼ét♦❞♦ C

  ✳

  C2 > β ∗ C2

  C2 ✳ ✭❜✮ ❈❛s♦ β

  p

  cos (θ

  ✸✳✸✳ ❈➪▲❈❯▲❖ ❉❖❙ ■▼P❯▲❙❖❙ ❙❖❇❘❊ ❆ ❊❙❚❘❯❚❯❘❆ ❉❊ ❙❯P❖❘❚❊ ✷✺

  2

  

a4

  1

  =

  a4

  I

  ✭✸✳✷✹✮

  2 K a1 γe

  C2

  1

  2 tan i) e +

  I a1 = K a1 γ (H − e + B

  ❙❡♥❞♦ ♦s ✐♠♣✉❧s♦s ♣❛r❝✐❛✐s ♣r❡s❡♥t❡s ♥❛ ❡①♣r❡ssã♦ ✸✳✷✸ ❝❛❧❝✉❧❛❞♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s s❡❣✉✐♥t❡s ❡①♣r❡ssõ❡s✿

  ) ✭✸✳✷✸✮

  ′

  ✭❛✮ ❈❛s♦ β C2 ≤ β ∗

2 K

  • K
  • φ
  • B
  • 2 H tan
  • e H
  • 2 # cos δ p + K a4 "

    1 +

    B 2 H

      ✷✻ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

      

      1

      2 I = K γh h

    • K γh

      a2 a2 2 a2

      ✭✸✳✷✽✮

      3

      2

      2

      1

      2 I = K γh a3 a3 ✭✸✳✷✾✮

      3

      2

      a1

      s❡♥❞♦ I ❝❛❧❝✉❧❛❞♦ ❛tr❛✈és ❞❛ ❡①♣r❡ssã♦ ✸✳✷✹✳ ❖s ✈❛❧♦r❡s r❡❧❛t✐✈♦s ❛♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ ✐♠♣✉❧s♦ ❛❝t✐✈♦✱ ♣r❡s❡♥t❡s ♥❛s ❡①♣r❡ssõ❡s ❛❝✐♠❛✱ K a1 ✱ K a2 ✱

      K

      

    a3 ❡ K a4 sã♦ ❞❛❞♦s ❛tr❛✈és ❞❛ ❡①♣r❡ssã♦ ✷✳✶✶✱ t❡♥❞♦ ❡♠ ❝♦♥s✐❞❡r❛çã♦ q✉❡✱ ♣❛r❛ K a1 ❡ K a3 ✱ ♦ â♥❣✉❧♦

    o

      β ✱ ♣r❡s❡♥t❡ ♥❛s s✉❛s ❡①♣r❡ssõ❡s✱ ❛ss✉♠❡ ♦ ✈❛❧♦r ❞❡ 90 ✱ ❞❛❞♦ q✉❡ ♦ ♣❛r❛♠❡♥t♦ ❞♦ ♠✉r♦ é ✈❡rt✐❝❛❧✱ t❡♥❞♦ K a2 ❡ K a4 ✈❛❧♦r❡s ✈❛r✐á✈❡✐s✱ ❝♦♥s♦❛♥t❡ ❛ ✐♥❝❧✐♥❛çã♦ ❞♦ ♣❧❛♥♦ q✉❡ ❞❡✜♥❡ ❛q✉❡❧❡ ♣❛r❛♠❡♥t♦✳

      ❆ss✐♠✱ ❛ ❡①♣r❡ssã♦ q✉❡ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛ ❛ ❛❝çã♦ é ❞❛❞❛ ♣♦r✿ H

      ′ I a1 cos δ p +I a2 cos θ C2 +φ +I a3 cos δ p 1 I a ( ) 2

    1

    2

      = = 1 2 γH γH 2

    2

    1 2 1 2 2 2 3

      K tan i)e+ K cos δ K γh h a1 a1 p a2 K a2 γh + + γe + 2 cos θ C2 +φ K a3 γh 3 cos δ p γ(H−e+B 2 2 2

      [( ) ] [( ) ( )] [( ) ] 1 2 = 1 2 2 γH 2 2 = 2 a1 2 a1 p a2 2 3 a2 C2 a3 p

      γ

      2K tan i)e+K e cos δ + +

      2K h h +K h 2 cos θ +φ K h 3 cos δ

      [[( (H−e+B ) ] [( ) ( )] [( ) ]] 1 2 1 = 2 2 γH 2 2 = 2 2 3

      = 2

      2K a1 (H − e + B tan i) e + K a1 e cos δ p + +

      2K a2 h h + K a2 h cos (θ C2 + φ ) K a3 h cos δ p = 2 3 H 1 " h i 2 2

    = +

    2 K a1 2 (H − e + B tan i) e + e cos δ p

    h H 2 i 2 2 2

    • +K a2 2 (B tan (90 − θ C2 ) (H − e − B tan (90 − θ C2 ))) + (B tan (90 − θ C2 )) cos (θ C2 + φ ) +

      h i
    • 2 2 # " # "

      +K a3 H − e − B tan (90 − θ C2 ) cos δ p =

      2 e e B 2 e B 2 e

        2 1 − tan i + a1 cos δ p + K a2 + = K 2 tan (180 − β C2 ) 1 − − H H H H H H

      2

      #

      B 2 ′ tan (180 − β C2 ) cos (β C2 + φ − 90) +

        H

      " #

      2 2 e B

      • K a3 1 − − tan (180 − β C2 ) cos δ p ✭✸✳✸✵✮ H H

        ✸✳✹ ❈♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦

        ◗✉❛♥❞♦ ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ é ♠♦❜✐❧✐③❛❞♦✱ ❞❡s❡♥✈♦❧✈❡✲s❡✱ ♥❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡✱ ✉♠❛ ❢♦rç❛ ❛trí✲

        a

        t✐❝❛ F ✳ ◆✉♠❛ s✐t✉❛çã♦ ❧✐♠✐t❡✱ ❡♠ q✉❡ ♦ ❝♦❧❛♣s♦ s❡ r❡✈❡❧❛ ✐♠✐♥❡♥t❡ r❡❧❛t✐✈❛♠❡♥t❡ ❛♦ ❞❡s❧✐③❛♠❡♥t♦✱ ❡ss❛

        ✸✳✹✳ ❈❖◆❉■➬➹❖ ❉❊ ❉❊❙▲■❩❆▼❊◆❚❖ ✷✼

        ♣❡s♦ ❞❛ ❝✉♥❤❛ ❞❡ s♦❧♦ ♣❛r❛ ❝❛❞❛ ♠ét♦❞♦ ❡♠ ♣❛rt✐❝✉❧❛r✱ ❞❛❞❛s ❛s ❞✐s❝r❡♣â♥❝✐❛s ♥❛ ❞❡✜♥✐çã♦ ❞♦ ♣❧❛♥♦ q✉❡ ❞❡✜♥❡ ♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❞♦ ♠✉r♦✳ ❋✐❣✉r❛ ✸✳✽✿ ■❧✉str❛çã♦ ❣❡♥ér✐❝❛ ❞❛s ♣r✐♥❝✐♣❛✐s ❣r❛♥❞❡③❛s ❡♥✈♦❧✈✐❞❛s ♥♦ ❡st✉❞♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛✲ ♠❡♥t♦✿ ❡①❡♠♣❧♦ ♠ét♦❞♦ R✳

        ❖ ♣❡s♦ t♦t❛❧ ❞♦ ♠✉r♦✱ ❞❛❞♦ ♣♦r W

        1 ❡ W 2 ✱ ❛❧✐❛❞♦ ❛♦ ♣❡s♦ ❞❛ ✏❝✉♥❤❛ ♠♦rt❛✑ W s ✱ q✉❡ ❝♦♠ ❛q✉❡❧❡ s❡

        V

        ♠♦✈❡✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛ ❝♦♠♣♦♥❡♥t❡ ✈❡rt✐❝❛❧ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✱ ❞❛❞❛ ♣♦r I a ✱ ❝♦♥st✐t✉❡♠ ❛ r❡s✉❧t❛♥t❡ ❞❛s ❝❛r❣❛s ✈❡rt✐❝❛✐s V ✳ 2

        ❖s ♣❡s♦s W

        1 ❡ W 2 sã♦ ❞❛❞♦s ♣♦r ✭r❡❧❡♠❜r❛♥❞♦✲s❡ q✉❡ s❡ ♣r❡t❡♥❞❡ ❝♦♥❤❡❝❡r ❛ ✐♥✢✉ê♥❝✐❛ ❞❛ r❡❧❛çã♦ B

        ♥♦ ❡st✉❞♦✮✿

        H

        W = b × (H − e) γ

        1 2 b ✭✸✳✸✶✮

        B

        2

        × × × × W = [(b

        e) + (B e)] γ = (b

        e) + H × e γ

        2

        1 2 b 1 b ✭✸✳✸✷✮

        H

        H

        V s

        ◆♦ ❞❡❝♦rr❡r ❞♦ ♣r❡s❡♥t❡ ❡st✉❞♦✱ ♣r♦❝✉r❛✲s❡ ❞❡✜♥✐r ❛s ❡①♣r❡ssõ❡s ❞❛s ❣r❛♥❞❡③❛s w ✱ I a ❡ I a ✳ ❊st❛s sã♦ ❡s♣❡❝í✜❝❛s ❛ ❝❛❞❛ ♠ét♦❞♦✱ ❞❡✈✐❞♦ à ❞ís♣❛r ❝♦♥s✐❞❡r❛çã♦ ❞❛ ❧♦❝❛❧✐③❛çã♦ ❡ ✐♥❝❧✐♥❛çã♦ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❞♦ ♠✉r♦✳ ❚♦❞❛✈✐❛✱ ❛ ❡①♣r❡ssã♦ ❣❡r❛❧ q✉❡ ♣❡r♠✐t❡ ❝❛❧❝✉❧❛r ❛ r❡s✉❧t❛♥t❡ ❞❛s ❝❛r❣❛s ✈❡rt✐❝❛✐s V é ❞❛❞❛ ♣♦r✿

        V V = W 1 + W 2 + W s + I a ✭✸✳✸✸✮

        ❆ ❢♦rç❛ ❛trít✐❝❛ r❡❧❛❝✐♦♥❛✲s❡ ❝♦♠ ❛ r❡s✉❧t❛♥t❡ ❞❛s ❝❛r❣❛s ✈❡rt✐❝❛✐s ✭♣♦r♠❡♥♦r✐③❛❞❛s ♥♦ ❞❡❝♦rr❡r ❞♦ ❡st✉❞♦✱ ❝♦♥s♦❛♥t❡ ❛ ❝♦♥s✐❞❡r❛çã♦ ❞❡ ❝❛❞❛ ♠ét♦❞♦✮ ❛tr❛✈és ❞❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦✿

        ✷✽ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲ ❆ ❡①♣r❡ssã♦ ❛❝✐♠❛ ♣♦❞❡ s❡r ♦r❞❡♥❛❞❛ ❡♠ ❢✉♥çã♦ ❞♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ δ✱ ♦ q✉❡ ♦r✐❣✐♥❛ ✉♠❛ r❡❧❛✲

        çã♦ ❢r❛❝❝✐♦♥❛❞❛ ❡♥tr❡ ❛ ❝♦♠♣♦♥❡♥t❡ ❤♦r✐③♦♥t❛❧ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❡ ❛s ❝❛r❣❛s ✈❡rt✐❝❛✐s ♣r❡s❡♥t❡s ♥♦ ♣r♦❜❧❡♠❛ ❡♠ ❛♥á❧✐s❡✳ P♦r ❝♦♥s❡❣✉✐♥t❡✱ r❡tr❛t❛✲s❡ ❛ r❛③ã♦ ❛❞✐♠❡♥s✐♦♥❛❧ ❞❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦ ♠✉r♦ ❛♦ ❞❡s❧✐③❛♠❡♥t♦ ✭❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦✮✿

        H

        I

        a

        tan δ = ✭✸✳✸✻✮

        V

        ✸✳✹✳✶ ▼ét♦❞♦ R

        ❚❡♥❞♦ ♣♦r ❜❛s❡ ♦ ♠ét♦❞♦ ❡♠ q✉❡stã♦✱ ♥❛ ❋✐❣✉r❛ ✸✳✾ ♣♦❞❡♠✲s❡ ♦❜s❡r✈❛r t♦❞❛s ❛s ❝♦♥s✐❞❡r❛çõ❡s ❡ ❣r❛♥✲ ❞❡③❛s ♥❡❝❡ssár✐❛s ♣❛r❛ ❛ ❞❡✜♥✐çã♦ ❞♦ ❡st✉❞♦ ❞❛s ❣r❛♥❞❡③❛s ❡♥✈♦❧✈✐❞❛s ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛ r❡s✉❧t❛♥t❡

        H

        ❞❛s ❝❛r❣❛s ✈❡rt✐❝❛✐s ❡ ❞❛ ❝♦♠♣♦♥❡♥t❡ ❤♦r✐③♦♥t❛❧ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✱ V ❡ I a r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❋✐❣✉r❛ ✸✳✾✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ❣r❛♥❞❡③❛s✿ ♠ét♦❞♦ R✳

        ❖ ♣❡s♦ ❞❛ ❝✉♥❤❛ ❞❡ s♦❧♦✱ ❞❛❞❛ ♣♦r W s ✱ é ❝❛❧❝✉❧❛❞♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦ ✭r❡❧❡♠❜r❛♥❞♦ 2 B q✉❡ s❡ ♣r❡t❡♥❞❡ ❝♦♥❤❡❝❡r ❛ ✐♥✢✉ê♥❝✐❛ ❞❛ r❡❧❛çã♦ ♥♦ ❡st✉❞♦✮✿

        

      H

        

      1

        × W = B (H − e) γ + B B tan i × γ =⇒

        s

        2

        2

        2 2

        

      2

      2 2 B B B

        1

        =⇒ W = H (H − e) γ + H × H tan i γ

        s H

        2 H H !

        2 B

        1 B

        2

        2

        2

        =⇒ W = H (H − e) γ + H tan i γ

        s

        ✭✸✳✸✼✮ H

        2 H ❆ ❝♦♠♣♦♥❡♥t❡ ✈❡rt✐❝❛❧ ❞♦ ✐♠♣✉❧s♦ é ❞❛❞❛ ♣❡❧❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦ ✭❡♠ ❢✉♥çã♦ ❞♦s ♣❛râ♠❡tr♦s

        ✐♥✐❝✐❛✐s✮✿

        2

        ✸✳✹✳ ❈❖◆❉■➬➹❖ ❉❊ ❉❊❙▲■❩❆▼❊◆❚❖ ✷✾

        2

        1 B

        2

        2 V = W + W + W γK H tan i + 1 sin i

      • 1

        2 s a ✭✸✳✸✾✮

        2 H ◆♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ à ❝♦♠♣♦♥❡♥t❡ ❤♦r✐③♦♥t❛❧ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✱ ❡st❛ é ❞❛❞❛ ♣❡❧❛ ❡①♣r❡ssã♦ ✸✳✻✱

        ♣r❡s❡♥t❡ ♥❛ s❡❝çã♦ ✸✳✸✳✶✳ ❆ss✐♠✱ ❡♥❝♦♥tr❛♠✲s❡ ❞❡✜♥✐❞❛s ❛s ❣r❛♥❞❡③❛s ♣r❡s❡♥t❡s ♥❛ ❡①♣r❡ssã♦ ✸✳✸✻✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ♠ét♦❞♦

        R ✳

        1 ✸✳✹✳✷ ▼ét♦❞♦ C

        ❆❞♦♣t❛♥❞♦ ♦ ♠ét♦❞♦ ❡♠ q✉❡stã♦✱ ♥❛ ❋✐❣✉r❛ ✸✳✶✵✱ ✐❧✉str❛✲s❡ ❛ ❢♦rç❛ ❞❡ ❛tr✐t♦✱ ❛ ❞❡❝♦♠♣♦s✐çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ♥❛s s✉❛s ❝♦♠♣♦♥❡♥t❡s ❤♦r✐③♦♥t❛❧ ❡ ✈❡rt✐❝❛❧ ❡ ❛ ❞✐✈✐sã♦ ❞♦ ♠✉r♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ s✉❛ ❣❡♦♠❡tr✐❛ ❝♦♠ ♦s s❡✉s r❡s♣❡❝t✐✈♦s ♣❡s♦s✱ ❜❡♠ ❝♦♠♦ ❞❛ ❝✉♥❤❛ ❞❡ s♦❧♦ q✉❡ ❝♦♠ ♦ ♠✉r♦ s❡ ♠♦✈❡✱ ❝♦♠ ♦ ♦❜❥❡❝t✐✈♦ ❞❡ tr❛♥s♠✐t✐r t♦❞❛s ❛s ❣r❛♥❞❡③❛s ❡♥✈♦❧✈✐❞❛s ♥♦ ❞❡❝♦rr❡r ❞♦ ❡st✉❞♦✳

        ❋✐❣✉r❛ ✸✳✶✵✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ❣r❛♥❞❡③❛s✿ ♠ét♦❞♦ C

        1 ✳

        1

        2

        ❖s ♣❡s♦s W ❡ W sã♦ ❞❛❞♦s ❛tr❛✈és ❞❛s ❡①♣r❡ssõ❡s ✸✳✸✶ ❡ ✸✳✸✷✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ s❡♥❞♦ ♦ ♣❡s♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛♦ s♦❧♦ ♥❛ ❝✉♥❤❛ ❧✐♠✐t❛❞❛ ♣❡❧❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❞♦ ♠✉r♦✿

        B

        2

        × − W s = B

        2 e tan θ C1 (H − e) γ

        ✭✸✳✹✵✮ H

        ❆ ❝♦♠♣♦♥❡♥t❡ ✈❡rt✐❝❛❧ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ é ❞❛❞❛ ♣❡❧❛ ❡①♣r❡ssã♦✿

      1 V

        

      2

        I = K γH sin (θ + φ )

        a C1 ✭✸✳✹✶✮ a

        2

        ✸✵ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

        1

        ❊♥❝♦♥tr❛♠✲s❡✱ ❛ss✐♠✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ♠ét♦❞♦ C ✱ ❞❡✜♥✐❞❛s t♦❞❛s ❛s ❣r❛♥❞❡③❛s ✐♥❞✐s♣❡♥sá✈❡✐s à ❡①♣r❡ssã♦ ✸✳✸✻✳

        2 ✸✳✹✳✸ ▼ét♦❞♦ C

        ◆♦ ♣r❡s❡♥t❡ ♠ét♦❞♦✱ ♦ ✐♠♣✉❧s♦✱ t❛❧ ❝♦♠♦ r❡❢❡r✐❞♦ ❡♠ ✷✳✹✳✸✱ ❡♥❝♦♥tr❛✲s❡ ❞✐✈✐❞✐❞♦ ❡♠ ❞♦✐s ♦✉ três tr♦ç♦s✱ ❝♦♥s♦❛♥t❡ ❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ❛ ✐♥❝❧✐♥❛çã♦ ❞♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ s❡ ❡♥❝♦♥tr❡ ❛❝✐♠❛ ❞♦ t♦♣♦ ❞♦ ♠✉r♦ ♦✉ ❛❜❛✐①♦ ❞❡st❡✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ P♦rt❛♥t♦✱ ❛ ❢♦rç❛ ❞❡ ❛tr✐t♦ r❡❢❡r✐❞❛ é✱ ❝♦♠ ❡❢❡✐t♦✱ ❝♦♥trár✐❛ ❛♦ s♦♠❛tór✐♦ ❞❛s ❝♦♠♣♦♥❡♥t❡s ❤♦r✐③♦♥t❛✐s ❞❛s r❡s✉❧t❛♥t❡s ❞♦s ❞✐❛❣r❛♠❛s q✉❡ ❝♦♠♣õ❡ ♦ ✐♠♣✉❧s♦ ❣❡r❛❞♦✳ ❖ ♠♦❞❡❧♦ q✉❡ ❡♥❣❧♦❜❛ t♦❞❛s ❛s ❣r❛♥❞❡③❛s ♥❡❝❡ssár✐❛s ♣❛r❛ ✉♠❛ ❝♦rr❡❝t❛ ♣❡r❝❡♣çã♦ ❞♦ ❡①♣♦st♦ é ❞❡t❛❧❤❛❞❛♠❡♥t❡ ❛♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✸✳✶✶✳

        ∗ ∗

        C2

        ≤

      ✭❛✮ ❈❛s♦ β C2 β ✳ ✭❜✮ ❈❛s♦ β C2 > β ✳

      C2

        ❋✐❣✉r❛ ✸✳✶✶✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ❣r❛♥❞❡③❛s✿ ♠ét♦❞♦ C

        2 ✳

        ✭✸✳✹✼✮

        ❆ss✐♠✱ é ♣♦ssí✈❡❧ ❡s❝r❡✈❡r ❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦✿ V = W

        γK

        2

        s3

        s2

        s1

        2

        1

        ) ✭✸✳✹✻✮ s❡♥❞♦ I a1 ❡ I a4 ❝❛❧❝✉❧❛❞♦s ❛tr❛✈és ❞❛s ❡①♣r❡ssõ❡s ✸✳✷✹ ❡ ✸✳✷✺✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳

        2 (H − e + B

        ′

        C2

        sin (θ

        a4

        p

        sin δ

        a1

        a1 "

        2

        V a4

        − 90)

        − 90)

        ′

        C2

        sin (β

        2

        − e #

        1

        C2

        tan i) e + e

        − (H − e) tan (β

        2

        H + B

        a4 "

        1 γK

        p

        sin δ

        2 #

        = I

        V a1

        ✸✳✹✳ ❈❖◆❉■➬➹❖ ❉❊ ❉❊❙▲■❩❆▼❊◆❚❖ ✸✶

        s1

        s1

        W

        ✱ s❡♥❞♦ ❛s ❡①♣r❡ssõ❡s r❡❧❛t✐✈❛s ❛ ❡st❡s ❞❛❞❛s ♣♦r✿

        s3

        ❡ W

        s2

        ✱ W

        ✱ r❡s✉❧t❛ ❞♦ s♦♠❛tór✐♦ ❞♦s ♣❡s♦s ♣❛r❝✐❛✐s W

        2

        s

        ✳ ❆ss✐♠✱ r❡❧❡♠❜r❛♥❞♦ ❛s ❡①♣r❡ssõ❡s ❛♣r❡s❡♥t❛❞❛s ♥❛ s❡❝çã♦ ✸✳✸✳✸✱ ♦ ♣❡s♦ t♦t❛❧ ❞♦ s♦❧♦✱ ❞❛❞♦ ♣♦r W

        2

        ❋✐❣✉r❛ ✸✳✶✷✿ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ♣❡s♦ ♣r❡s❡♥t❡ ♥❛ ❝✉♥❤❛ ❞❡ s♦❧♦✿ ♠ét♦❞♦ C

        ✳

        ✭❜✮ P♦r♠❡♥♦r ❞♦ ♣❡s♦ ❞♦ s♦❧♦✿ ❝❛s♦ β C2 ≤ β ∗ C2

        ∗ C2 ✳

        ✭❛✮ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ♣❡s♦ ❞♦ s♦❧♦✿ ❝❛s♦ β C2 ≤ β

        = γ (B

        (H − e)) − (H − e) (H − e) tan θ

        = I

        

      2

        a

        I V

        ✭✸✳✹✺✮ ❆ ❝♦♠♣♦♥❡♥t❡ ✈❡rt✐❝❛❧ ❞❛ r❡s✉❧t❛♥t❡ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ é ❞❛❞❛ ♣❡❧❛ ❡①♣r❡ssã♦✿

        2 γ

        ) h

        3

        − l

        (l

        C2

        ✭✸✳✹✹✮ W s3 =

        2 γ

        × h

        

      3

        = l

        s2

        W

        2 ✭✸✳✹✸✮

      • I
      • I
      • φ
      • W
      • W
      • W
      • W
      • 1
      • φ

        ✸✷ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲ ×

        B

        2 B 2 tan (90 − θ C2 )

        W = γ

        s

        ✭✸✳✹✽✮

        2 ❆ ❝♦♠♣♦♥❡♥t❡ ✈❡rt✐❝❛❧ ❞❛ r❡s✉❧t❛♥t❡ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ é ❞❛❞❛ ♣♦r✿

        V V

        V V ′

        I = I + I + I = I a1 sin δ p + I a2 sin (θ C2 + φ ) + I a3 sin δ p

        a a1 a2 a3

        ✭✸✳✹✾✮ ❡♠ q✉❡ I a1 ✱ I a2 ❡ I a3 sã♦ ❞❛❞♦s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♣❡❧❛s ❡①♣r❡ssõ❡s ✸✳✷✹✱ ✸✳✷✽ ❡ ✸✳✷✾✳ ❆ss✐♠✱ é ♣♦ssí✈❡❧ ❡s❝r❡✈❡r ❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦✿ 1 2 1 2 2 !

        s γK a1 2 (H − e + B tan i) e + e sin δ p + V = W + W + W + 2 ! 1

        2 2 2 22 γK a2 2 (B tan (180 − β C2 ) (H − e − B tan (180 − β C2 ))) + (B tan (180 − β C2 )) sin (β C2 + φ − 90) + ! 2

      • 1
      • 2 γK a3 H − e − B tan (180 − β C2 ) sin δ p ✭
      • 2

        ❆ ❝♦♠♣♦♥❡♥t❡ ❤♦r✐③♦♥t❛❧ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ é ❝❛❧❝✉❧❛❞❛ ❛tr❛✈és ❞❛ ❡①♣r❡ssã♦ ✸✳✷✼✱ ❞✐s♣♦st❛ ♥❛ s❡❝çã♦ ✸✳✸✳✸✳ ❆s ❣r❛♥❞❡③❛s ♥❡❝❡ssár✐❛s ♣❛r❛ ❛ ❡①♣r❡ssã♦ ✸✳✸✻ ❡♥❝♦♥tr❛♠✲s❡ ❛ss✐♠ ❞❡✜♥✐❞❛s✱ s❡❣✉♥❞♦ ♦ ♠ét♦❞♦

        C

        2

        ✳ ′

        

      ✸✳✺ ❆♥á❧✐s❡ ♣❛r❛♠étr✐❝❛✿ ✐♥✢✉ê♥❝✐❛ ❞❡ φ ✱ i ❡ ❞♦ ❝♦♠♣r✐♠❡♥t♦

        1

        ❞❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ B ✸✳✺✳✶ ■♠♣✉❧s♦s

        ✸✳✺✳✶✳✶ ▼ét♦❞♦s R ❡ C

        1

        ❖ ❡st✉❞♦ ❡♠ q✉❡stã♦ é ❢❡✐t♦ t❡♥❞♦ ♣♦r ❜❛s❡ ♦s ♣❛râ♠❡tr♦s ✐♥✐❝✐❛✐s ❛♣r❡s❡♥t❛❞♦s ♥❛ ❚❛❜❡❧❛ ✸✳✶✳ ❆ss✐♠✱ t♦❞❛s ❛s r❡st❛♥t❡s ❞✐♠❡♥sõ❡s sã♦ ❡♥❝♦♥tr❛❞❛s ❛ ♣❛rt✐r ❞❛q✉❡❧❡s✳

        ′

        1

        ✸✳✺✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋✳ ❉❊ φ ✱ I ❊ ❈❖▼P✳ ❉❆ ❇❆❙❊ ❉❆ ❊❙❚❘❯❚❯❘❆ B ✸✸ ❚❛❜❡❧❛ ✸✳✶✿ P❛râ♠❡tr♦s ✐♥✐❝✐❛✐s ✉s❛❞♦s ♥❛s ❛♥á❧✐s❡s ❞♦s ♠ét♦❞♦s R ❡ C

        1 ✳

        P❛râ♠❡tr♦s ✐♥✐❝✐❛✐s H(m)

        ✽ e(m) ✶ b (m)

        1 ✵✱✺

        b

        2 (m)

        ✵✱✺

        o

        α( ) ✾✵

        

      3

        γ kN/m

        

      b ✷✺

        

      3

        γ kN/m ✷✵

        Pr♦❝✉r❛✲s❡✱ ❛♦ ♠❡s♠♦ t❡♠♣♦✱ ❝♦♥❤❡❝❡r ❛ ✐♥✢✉ê♥❝✐❛ q✉❡ ❞❡t❡r♠✐♥❛❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ t❡rr❡♥♦✱

        ′

        ✈✐❞❡ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦ φ ❡ ✐♥❝❧✐♥❛çã♦ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦ i✱ tê♠ ♥♦ r❡s✉❧t❛❞♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ❡✱ ♣♦r t❛❧✱ é ❝♦♥s✐❞❡r❛❞❛ ✉♠❛ ❣❛♠❛ ✈❛r✐á✈❡❧ ❞❡ ✈❛❧♦r❡s ♣❛r❛ ❡ss❡s ♣❛râ♠❡tr♦s✱ ❡①✐st✐♥❞♦ ✉♠❛ ♣❛♥ó♣❧✐❛ ❞❡ ❝♦♠❜✐♥❛çõ❡s ❡♥tr❡ ❛♠❜♦s✳ ➱ ❛♣r❡s❡♥t❛❞❛✱ ❞❡ s❡❣✉✐❞❛✱ ❛ ❚❛❜❡❧❛ ✸✳✷ ❝♦♠ ♦s ✈❛❧♦r❡s ❝♦♥s✐❞❡r❛❞♦s ♣❛r❛ ♦s r❡❢❡r✐❞♦s â♥❣✉❧♦s ❡ ❛s r❡s♣❡❝t✐✈❛s ❝♦♠❜✐♥❛çõ❡s ❞♦s ♠❡s♠♦s✳ ❚❛❜❡❧❛ ✸✳✷✿ ❱❛❧♦r❡s ❞♦s â♥❣✉❧♦s ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦ ❡ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ ❛♥❛❧✐s❛❞♦s✳

        ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ■♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ t❡rr❡♥♦ (i)

        ′ o o o o o o o o

        )

        5

        10

        15

        20

        25

        30

        35 ❛♦ ❝♦rt❡ ❞♦ s♦❧♦ (φ

        o

        20 ➺ ➺ ➺ ➺ ✲ ✲ ✲ ✲

        o

        30 ➺ ➺ ➺ ➺ ➺ ➺ ✲ ✲

        o

        40 ➺ ➺ ➺ ➺ ➺ ➺ ➺ ➺

        o

        45 ➺ ➺ ➺ ➺ ➺ ➺ ➺ ➺

        ❖ ❡st✉❞♦ ❜❛s❡✐❛✲s❡ ♥♦s r❡s✉❧t❛❞♦s ❞❡ 2×3×(4 + 6 + 16) = 156 ❝á❧❝✉❧♦s✱ ❝♦❜r✐♥❞♦ ✉♠ ❧❡q✉❡ r❛③♦á✈❡❧ ❞❡ s✐t✉❛çõ❡s ❞✐st✐♥t❛s✳ ✸✳✺✳✶✳✷ ▼ét♦❞♦ C

        2

        ✸✹ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

        

      INPUT

      Parâmetros Parâmetros  do Muro  do Solo o

        B

        4

        30 1  (m)

        Ø` )  ( o a i( )

        10  (m)

        3 b

        2  (m) 0,5

        20 ) Ɣ s  (kN/m b

        1  (m) 0,5 H

        8  (m) e

        1  (m)

        3 ) Ɣ b  (kN/m

        25

        2

        ❋✐❣✉r❛ ✸✳✶✸✿ ▲❛②♦✉t ❞♦ ✐♥♣✉t✿ ▼ét♦❞♦ C ✳ ❆♣ós ❛ ✐♥s❡rçã♦ ❞♦s ❞❛❞♦s✱ sã♦ ❛♣r❡s❡♥t❛❞♦s ♥✉♠ ♦✉tr♦ ❧❛②♦✉t✱ ♦s ✈❛❧♦r❡s ❝❛❧❝✉❧❛❞♦s ♣❡❧♦ ♣r♦❣r❛♠❛✱ s❡♥❞♦ ❡st❡s ♦s ❝♦♥st❛♥t❡s ♥♦ ♦✉t♣✉t ♣r❡s❡♥t❡ ♥❛ ❋✐❣✉r❛ ✸✳✶✹✳

        

      OUTPUT

      Muro Relação  B /H Solo 2 o B /H ) B 3,5 2  (m) ‐solo o 2 0,438 δ solo  (

        30 ξ  ( ) o o δ  ( ) 90 solo

        20 α ( ) ‐est. o ) ϕ ( o 117

        β* ( ) H o β C2 ( ) (I ) 251,6 115 a max   w  (kN/m) 87,5 1 H

      2

      o

        β ( )

      w  (kN/m) 100,0 [I /(0,5* )] 0,393 C2,IaH 115

      2 a ɣ*H max   w  (kN/m) 3 o

        β ( )

      w  (kN/m) [tan( δ)] 0,334 C2,tan( 115

      4 max δ) 

        ❋✐❣✉r❛ ✸✳✶✹✿ ▲❛②♦✉t ❞♦ ♦✉t♣✉t✿ ▼ét♦❞♦ C

        2 ✳

        ❖s ✈❛❧♦r❡s ❝♦♥s✐❞❡r❛❞♦s ♥❛ ❛♥á❧✐s❡ ♣❛r❛♠étr✐❝❛ sã♦ ♦s ❥á ✐♥❞✐❝❛❞♦s ♥❛ ❚❛❜❡❧❛ ✸✳✷✳ P❛r❛ ❛ r❡❧❛çã♦

        e

        / H ❛❞♦♣t❛✲s❡ ♦ ✈❛❧♦r ❞❡ ✵✱✶✷✺✳ ❖s r❡s✉❧t❛❞♦s ❞❡st❛ ❛♥á❧✐s❡ ♣❛r❛♠étr✐❝❛ sã♦ ❛♣r❡s❡♥t❛❞♦s ♥❛ s❡❝çã♦

        ✸✳✺✳✸✳

        ′

        1

        ✸✳✺✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋✳ ❉❊ φ ✱ I ❊ ❈❖▼P✳ ❉❆ ❇❆❙❊ ❉❆ ❊❙❚❘❯❚❯❘❆ B ✸✺ ❚❛❜❡❧❛ ✸✳✸✿ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣♦r ❇❛r❣❤♦✉t❤✐ ✭✶✾✾✵✮ ✭✐♥❞✐❝❛❞♦s ❝♦♠ ♦ í♥❞✐❝❡ B✮❀ ❝♦♠♣❛r❛çã♦ ❝♦♠ ♦s r❡s✉❧t❛❞♦s ❞♦ ♠ét♦❞♦ C

        2 ✳ o o ∗ ∗

        β = 10 β = 20 C2 C2 o o o o

        P❛râ♠❡tr♦ i = 0 i = 10 i = 0 i = 10 o o o o o o o o

        δ p = 0 δ p = 20 δ p = 0 δ p = 20 δ p = 0 δ p = 20 δ p = 0 δ p = 20 ❛♥❛❧✐s❛❞♦ ′ o o o o o o o o

        β 120 112 117 110, 5 120 116 115, 5 113, 5 B H o o o o o o o o

        

      β 120 112 119 111 120 116 117 113

      H C2,I 1 a 2 I a γH / 2 0, 333 0, 310 0, 374 0, 358 0, 333 0, 328 0, 391 0, 389 H 1 2 B

        I

      a / 0, 333 0, 311 0, 379 0, 358 0, 333 0, 328 0, 392 0, 389

      2 γH C2 ✸✳✺✳✷ ❈♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦

        ✸✳✺✳✷✳✶ ▼ét♦❞♦s R ❡ C

        1

        ❆❞♦♣t❛♥❞♦ t♦❞❛s ❛s ❝♦♥s✐❞❡r❛çõ❡s ❢❡✐t❛s ♣❛r❛ ♦s ♣r❡s❡♥t❡s ♠ét♦❞♦s✱ ♣r❡t❡♥❞❡✲s❡ ❛♥❛❧✐s❛r ❛ ✐♥✢✉ê♥❝✐❛ ❞♦ 2 B

        

      H

        / ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦✱ tr❛♥s♠✐t✐❞❛ ♣♦r ♥❛ r❡❧❛çã♦ ❡♥tr❡ ❛s ❝❛r❣❛s ✈❡rt✐❝❛✐s ❡ ❤♦r✐③♦♥t❛✐s ♣r❡s❡♥t❡s ♥♦ ♣r♦❜❧❡♠❛ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦✳ ❆ss✐♠✱ t♦❞❛s ❛s ❞✐♠❡♥sõ❡s ❡ ❣r❛♥❞❡③❛s ♥❡❝❡ssár✐❛s ♣❛r❛ ✉♠❛ ❝♦rr❡❝t❛ ♣❡r❝❡♣çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❡♥❝♦♥tr❛♠✲s❡ ✐❧✉str❛❞❛s

        1

        ♥❛s ❋✐❣✉r❛s ✸✳✾ ❡ ✸✳✶✵✱ ♣r❡s❡♥t❡s ♥❛s s❡❝çõ❡s ✸✳✹✳✶ ❡ ✸✳✹✳✷✱ r❡s♣❡❝t✐✈❛♠❡♥t❡ ♣❛r❛ ♦s ♠ét♦❞♦s R ❡ C ✳ ❆♥á❧♦❣❛♠❡♥t❡ ❛♦ ❝á❧❝✉❧♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧✱ ❛s ❝♦♠❜✐♥❛çõ❡s ❡♥tr❡ ❛ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦ ❡ ❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦ sã♦ ❛s ❛♣r❡s❡♥t❛❞❛s ♥❛ ❚❛❜❡❧❛ ✸✳✷✳

        ❆s ❞✐♠❡♥sõ❡s ❛❞♦♣t❛❞❛s ♣❛r❛ ♦ ♠✉r♦ sã♦ ❛s ❝♦♥s✐❞❡r❛❞❛s ♥❛ ❚❛❜❡❧❛ ✸✳✶✱ ♣r❡s❡♥t❡ ♥❛ s❡❝çã♦ ✸✳✺✳✶✳✶✳ ❉❛❞♦ q✉❡✱ ♥♦ ♣r❡s❡♥t❡ ❡st✉❞♦✱ ❛s ❢❛❝❡s ❡①t❡r✐♦r ❡ ✐♥t❡r✐♦r ❞❛ ❡str✉t✉r❛ sã♦ ❝♦♥s✐❞❡r❛❞❛s ✈❡rt✐❝❛✐s✱

        ❡①✐st❡ ✉♥✐❝❛♠❡♥t❡ ✉♠ ❞♦s ♣❡s♦s r❡s♣❡✐t❛♥t❡s à ❡str✉t✉r❛ q✉❡ s❡ r❡✈❡❧❛ ✜①♦✱ s❡♥❞♦ ♣❛r❛ ❛s ❞✐♠❡♥sõ❡s ❞✐s♣♦st❛s ♥❛ ❚❛❜❡❧❛ ✸✳✶✱ ♦ ❛♣r❡s❡♥t❛❞♦ ♥❛ ❚❛❜❡❧❛ ✸✳✹✳ ❖s r❡st❛♥t❡s ♣❡s♦s ♣r❡s❡♥t❡s ♥♦ ❡st✉❞♦ ✈ê❡♠ ♦ s❡✉ ✈❛❧♦r ✈❛r✐❛r ❝♦♥s♦❛♥t❡ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦✳

        ❚❛❜❡❧❛ ✸✳✹✿ P❡s♦s ♣r❡s❡♥t❡s ♥♦ ♠♦❞❡❧♦ ❞❡ ❝á❧❝✉❧♦✳ P❡s♦ ❱❛❧♦r

        W (kN/m)

        

      1 ✽✼✱✺

        W (kN/m)

        

      2 ✈❛r✐á✈❡❧

        W s (kN/m) ✈❛r✐á✈❡❧

        2

        ✸✳✺✳✷✳✷ ▼ét♦❞♦ C ❖ ❧❛②♦✉t ♣r❡s❡♥t❡ ♥❛ s❡❝çã♦ ✸✳✺✳✶✳✷ s❡r✈❡ ❞❡ ❜❛s❡ t❛♠❜é♠ ♣❛r❛ ♦ ♣r❡s❡♥t❡ ❝❛s♦✱ ♦❜t❡♥❞♦✲s❡ ♦s r❡s✉❧t❛❞♦s ✈✐sí✈❡✐s ♥♦ ♦✉t♣✉t ❞♦ ♠❡s♠♦✳

        ✸✻ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

        ✸✳✺✳✸ ❘❡s✉❧t❛❞♦s ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦

        ✸✳✺✳✸✳✶ ❆♣r❡s❡♥t❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ◆❛s ❋✐❣✉r❛s ✸✳✶✺ ❛ ✸✳✷✵ ❛♣r❡s❡♥t❛✲s❡ ❛ ❡✈♦❧✉çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦✱ t❛♠❜é♠ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛✱ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❛ ✐♥❝❧✐♥❛çã♦ ❞♦ t❡rr❡♥♦ ❡ ✈ár✐♦s ✈❛❧♦r❡s ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦✳ ❆ss✐♠✱ ♥❛ ❋✐❣✉r❛ ✸✳✶✺ ❛♣r❡s❡♥t❛♠✲s❡ ♦s

        ′ o ′ o

        = 20 = 30 r❡s✉❧t❛❞♦s ♣❛r❛ φ ❀ ♥❛ ❋✐❣✉r❛ ✸✳✶✻ ❛♣r❡s❡♥t❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♣❛r❛ φ ❀ ♥❛s ❋✐❣✉r❛s ✸✳✶✼

        ′ o ′ o

        = 40 = 45

        ❡ ✸✳✶✽ ♣❛r❛ φ ❀ ♥❛s ❋✐❣✉r❛s ✸✳✶✾ ❡ ✸✳✷✵ ❛♣r❡s❡♥t❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♣❛r❛ φ ✳

        < β

        i=5

        ✸✳✺✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋✳ ❉❊ φ

        ′

        ✱ I ❊ ❈❖▼P✳ ❉❆ ❇❆❙❊ ❉❆ ❊❙❚❘❯❚❯❘❆ B

        1

        ✸✼

      • C
      • 2 ✭❜✮ i = 5 o

          β C 2

          2 )

          I H a /(0,5 γ H

          i=0

          I H a /(0,5 γ H

          2 )

        • C
        • 2 ✭❛✮ i = 0 o

            < β

          1 B

          • C
          • 2 ✭❞✮ i =
          • C
          • 2 ✭❝✮ i = 10 o

              1 B

              2 /H

              i=15

              I H a /(0,5 γ H

              2 )

              β C 2

              < β

              0,4 0,6 0,8

              Método R Método C

              

            1

            Método C

              2

              ❋✐❣✉r❛ ✸✳✶✺✿ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦

              ′ o e

            H

              1 0,2 0,4 0,6 0,8

              < β

              0,4 0,45 0,5 0,55 0,6

              β C 2

              2 )

              I H a /(0,5 γ H

              i=10

              2 /H

              1 0,2 0,4 0,6 0,8

              0,4 0,6 0,8

              0,4 0,45 0,5 0,55 0,6

              0,2 0,4 0,6 0,8

              2 /H

              β C 2

              2 /H

              1 B

              0,2 0,4 0,6 0,8

            1 B

            • C
            • 2 ✭❜✮ i
            • C
            • 2 β

              • C
              • 2 ✭❛✮ i = 0 o

                1 B

                  < β

                  2 )

                  β C 2

                  < β

                  0,2 0,3 0,4 0,5 0,6

                  0,2 0,4 0,6 0,8

                  1 B

                  2 /H

                  i=15

                  I H a /(0,5 γ H

                  2 )

                  β C 2

                  1

                  0,4 0,6 0,8

                  i=20

                  I H a /(0,5 γ H

                  2 )

                  β C 2

                  < β

                  1

                  i=25

                  I H a /(0,5 γ H

                  2 )

                  β C 2

                  < β

                  I H a /(0,5 γ H

                  i=10

                  2 /H

                  0,2 0,25 0,3 0,35 0,4

                  ✸✽ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

                  0,2 0,25 0,3 0,35 0,4

                  0,2 0,4 0,6 0,8

                  2 /H

                  i=0

                  I H a /(0,5 γ H

                  2 )

                  β C 2

                  0,2 0,4 0,6 0,8

                  < β

                  0,2 0,4 0,6 0,8

                  1 B

                  2 /H

                  i=5

                  I H a /(0,5 γ H

                  2 )

                  β C 2

                  < β

                  C 2 <

                  β

                • C
                • 2 ✭❞✮ i = 15 o

                  • C
                  • 2 ✭❝✮ i = 10 o

                      0,2 0,3 0,4 0,5 0,6

                    1 B

                    • C
                    • 2

                    • C
                    • 2 0,4 0,6 0,8

                      • C
                      • 2 ✭❜✮ i
                      • C
                      • 2 ✭❛✮ i = 0 o

                        1 B

                        • C
                        • 2 ✭❞✮ i = 15 o

                            I H a /(0,5 γ H

                            I H a /(0,5 γ H

                            2 )

                            β C 2

                            < β

                            0,1 0,2 0,3 0,4

                            0,2 0,4 0,6 0,8

                            1 B

                            2 /H

                            i=15

                            β C 2

                            2 )

                            < β

                          • C
                          • 2 ✭❝✮ i = 10 o

                              Método R Método C

                              

                            1

                            Método C

                              2

                              ❋✐❣✉r❛ ✸✳✶✼✿ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦

                              ′

                              = 40

                              o e

                              / H = 0, 125

                              i=10

                              0,2 0,4 0,6 0,8

                              2 /H

                              2 )

                              ✸✳✺✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋✳ ❉❊ φ

                              ′

                              ✱ I ❊ ❈❖▼P✳ ❉❆ ❇❆❙❊ ❉❆ ❊❙❚❘❯❚❯❘❆ B

                              1

                              ✸✾

                              0,1 0,15 0,2 0,25 0,3

                              0,2 0,4 0,6 0,8

                              2 /H

                              i=0

                              I H a /(0,5 γ H

                              β C 2

                              0,1 0,2 0,3 0,4

                              < β

                              0,1 0,15 0,2 0,25 0,3

                              0,2 0,4 0,6 0,8

                              1 B

                              2 /H

                              i=5

                              I H a /(0,5 γ H

                              2 )

                              β C 2

                              < β

                            1 B

                            • C
                            • 2 ✭❜✮ i =
                            • C
                            • 2 ✭❛✮ i =
                            • C
                            • 2 ✭❝✮ i =
                            • C
                            • 2 ✭❞✮ i = 35 o

                                < β

                                < β

                                0,2 0,4 0,6 0,8

                                1 0,2 0,4 0,6 0,8

                                1 B

                                2 /H

                                i=35

                                I H a /(0,5 γ H

                                2 )

                                β C 2

                                Método R Método C

                                2 )

                                2

                                ❋✐❣✉r❛ ✸✳✶✽✿ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

                                ′

                                = 40

                                o

                                ❀

                                e

                                /

                                

                              H

                                = 0, 125 ✭❝♦♥t✐♥✉❛çã♦✮✳

                                β C 2

                                I H a /(0,5 γ H

                                ✹✵ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

                                0,2 0,4 0,6 0,8

                                0,2 0,3 0,4 0,5 0,6

                                0,2 0,4 0,6 0,8

                                1 B

                                2 /H

                                i=20

                                I H a /(0,5 γ H

                                2 )

                                β C 2

                                < β

                                0,2 0,3 0,4 0,5 0,6

                                1 B

                                i=30

                                2 /H

                                i=25

                                I H a /(0,5 γ H

                                2 )

                                β C 2

                                < β

                                0,2 0,4 0,6 0,8

                                1 0,2 0,4 0,6 0,8

                                1 B

                                2 /H

                              1 Método C

                              • C
                              • 2 ✭❜✮ i = 5 o

                                • C
                                • 2 ✭❛✮ i
                                • C
                                • 2 ✭❞✮ i =
                                • C
                                • 2 ✭❝✮ i = 10 o

                                    2 /H

                                    i=0

                                    I H a /(0,5 γ H

                                    2 )

                                    β C 2

                                    < β

                                    0,05 0,1 0,15 0,2 0,25 0,3

                                    0,2 0,4 0,6 0,8

                                    1 B

                                    2 /H

                                    I H a /(0,5 γ H

                                    i=0

                                    2 )

                                    β C 2

                                    < β

                                    Método R Método C

                                    

                                  1

                                  Método C

                                    2

                                    ❋✐❣✉r❛ ✸✳✶✾✿ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦

                                    ′

                                    = 45

                                    o e

                                    1 B

                                    0,05 0,1 0,15 0,2 0,25 0,3

                                    0,2 0,4 0,6 0,8

                                    I H a /(0,5 γ H

                                    ✸✳✺✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋✳ ❉❊ φ

                                    ′

                                    ✱ I ❊ ❈❖▼P✳ ❉❆ ❇❆❙❊ ❉❆ ❊❙❚❘❯❚❯❘❆ B

                                    1

                                    ✹✶

                                    0,05 0,1 0,15 0,2 0,25 0,3

                                    0,2 0,4 0,6 0,8

                                    1 B

                                    2 /H

                                    i=0

                                    2 )

                                    < β

                                    β C 2

                                    < β

                                    0,05 0,1 0,15 0,2 0,25 0,3

                                    0,2 0,4 0,6 0,8

                                    1 B

                                    2 /H

                                    i=5

                                    I H a /(0,5 γ H

                                    2 )

                                    β C 2

                                    / H = 0, 125

                                  • C
                                  • 2 ✭❜✮ i =
                                  • C
                                  • 2 ✭❛✮ i =
                                  • C
                                  • 2 ✭❞✮ i =
                                  • C
                                  • 2 ✭❝✮ i = 30 o

                                      < β

                                      < β

                                      0,1 0,2 0,3 0,4 0,5 0,6 0,7

                                      0,2 0,4 0,6 0,8

                                      1 B

                                      2 /H

                                      i=35

                                      I H a /(0,5 γ H

                                      2 )

                                      β C 2

                                      Método R Método C

                                      2 )

                                      2

                                      ❋✐❣✉r❛ ✸✳✷✵✿ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ φ

                                      ′

                                      = 45

                                      o

                                      ❀

                                      e

                                      /

                                      

                                    H

                                      = 0, 125 ✭❝♦♥t✐♥✉❛çã♦✮✳

                                      β C 2

                                      I H a /(0,5 γ H

                                      ✹✷ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

                                      0,2 0,4 0,6 0,8

                                      0,1 0,2 0,3 0,4 0,5

                                      0,2 0,4 0,6 0,8

                                      1 B

                                      2 /H

                                      i=20

                                      I H a /(0,5 γ H

                                      2 )

                                      β C 2

                                      < β

                                      0,1 0,2 0,3 0,4 0,5

                                      1 B

                                      i=30

                                      2 /H

                                      i=25

                                      I H a /(0,5 γ H

                                      2 )

                                      β C 2

                                      < β

                                      0,1 0,2 0,3 0,4 0,5 0,6 0,7

                                      0,2 0,4 0,6 0,8

                                      1 B

                                      2 /H

                                    1 Método C

                                      ′

                                      1

                                      ✸✳✺✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋✳ ❉❊ φ ✱ I ❊ ❈❖▼P✳ ❉❆ ❇❆❙❊ ❉❆ ❊❙❚❘❯❚❯❘❆ B ✹✸ ✸✳✺✳✸✳✷ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ❉❛ ❛♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❡ r❡♣r❡s❡♥t❛❞♦s ♥❛s ❋✐❣✉r❛s ✸✳✶✺ ❛ ✸✳✷✵ é ♣♦ssí✈❡❧ ❝♦♥❝❧✉✐r q✉❡✿ H 1 2 I a 2 γH

                                      / ❼ ♦ ♠ét♦❞♦ R ❝♦♥❞✉③ ❛ ✈❛❧♦r❡s ❞❛ r❡❧❛çã♦ s✉♣❡r✐♦r❡s ❛♦s r❡st❛♥t❡s ♠ét♦❞♦s s❡♠♣r❡ q✉❡ i < δ

                                      ❀ sã♦ ✐❣✉❛✐s ❛♦s ❞♦ ♠ét♦❞♦ C

                                      2 q✉❛♥❞♦ i = δ ❡ sã♦ ❧✐❣❡✐r❛♠❡♥t❡ ✐♥❢❡r✐♦r❡s q✉❛♥❞♦ i > δ❀ ′

                                      φ

                                      2

                                      /

                                      

                                    2

                                      ❼ ♣❛r❛ ♦s ❝❛s♦s ❡♠ q✉❡ i ≥ ✱ ♦ ♠ét♦❞♦ C ❛♣r❡s❡♥t❛ ✈❛❧♦r❡s s❡♠❡❧❤❛♥t❡s ❛♦s ❞♦ ♠ét♦❞♦ R❀

                                      ′ φ

                                      2

                                      / ♣❛r❛ i < ❛s ❞✐❢❡r❡♥ç❛s sã♦ ♠❛✐♦r❡s❀ 2 B

                                      H

                                      /

                                      1

                                      ❼ ❡①✐st❡ ✉♠❛ ❣❛♠❛ ❞❡ ✈❛❧♦r❡s ❞❛ r❡❧❛çã♦ ♣❛r❛ ♦s q✉❛✐s ♦s r❡s✉❧t❛❞♦s ❞♦ ♠ét♦❞♦ R ❡ C sã♦ ♣r❛t✐❝❛♠❡♥t❡ ✐❣✉❛✐s❀ 2 B

                                      / H ❼ ❛té ❞❡t❡r♠✐♥❛❞♦s ✈❛❧♦r❡s ❞❡ ✱ ❤á ✉♠❛ r❡❧❛t✐✈❛ s❡♠❡❧❤❛♥ç❛ ❡♥tr❡ ♦s r❡s✉❧t❛❞♦s ❞♦ ♠ét♦❞♦

                                      C

                                      1 ❡ C 2 ❀ 2 B H

                                      / ❼ ♦ ♠ét♦❞♦ C

                                      

                                    1 ❛❢❛st❛✲s❡ ❞♦s r❡st❛♥t❡s✱ s♦❜r❡t✉❞♦✱ ♣❛r❛ r❡❧❛çõ❡s ❡❧❡✈❛❞❛s✳

                                      P❛r❛ ✉♠❛ ❛♥á❧✐s❡ ♠❛✐s ❞❡t❛❧❤❛❞❛✱ r❡s✉♠❡♠✲s❡✱ ♥❛ ❋✐❣✉r❛ ✸✳✷✶✱ t♦❞♦s ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❞♦ ♠ét♦❞♦ C

                                      

                                    2 ✱ r❡♣r❡s❡♥t❛❞♦s ♥❛s ❋✐❣✉r❛s ✸✳✶✺ ❛ ✸✳✷✵✳ ❆ ❛♥á❧✐s❡ ❞❛ ❋✐❣✉r❛ ✸✳✷✶ ♠♦str❛ q✉❡ ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦

                                    2 o

                                    B

                                    H

                                      / ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❛✉♠❡♥t❛ ❝♦♥t✐♥✉❛♠❡♥t❡ ❝♦♠ ✱ ❝♦♠ ❡①❝❡♣çã♦ ❞♦ ❝❛s♦ ❡♠ q✉❡ i = 0 ✱ ♦♥❞❡ é ❛t✐♥❣✐❞♦ ✉♠ ♣❛t❛♠❛r✱ t❛❧ ❝♦♠♦ r❡❢❡r✐❞♦ ♣♦r ❇❛r❣❤♦✉t❤✐ ✭✶✾✾✵✮✳ ◆❛ ❋✐❣✉r❛ ✸✳✷✶❜ s♦❜r❡♣õ❡♠✲s❡✱ ♣❛r❛

                                      ′ o o ′

                                      2

                                      3

                                      φ = 30 / φ

                                      ✱ ❛ tít✉❧♦ ❡①❡♠♣❧✐✜❝❛t✐✈♦✱ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❡❧♦ ♠ét♦❞♦ R ♣❛r❛ ♦s ❝❛s♦s i = 0 ✱ i =

                                      o o 2 B H

                                      / ❡ i = 25 ✳ ❱❡r✐✜❝❛✲s❡✱ ❞❛ ❛♥á❧✐s❡ ❞❡st❛ ❋✐❣✉r❛ q✉❡✿ ♣❛r❛ i = 0 ✱ ❛ ♣❛rt✐r ❞❡ ❞❛❞♦ ✈❛❧♦r ❞❡ ✱ ♦s ✐♠♣✉❧s♦s ♦❜t✐❞♦s ❞♦ ♠ét♦❞♦ C

                                      2 ❝♦rr❡s♣♦♥❞❡♠✱ ❛♣r♦①✐♠❛❞❛♠❡♥t❡✱ ❛♦ ✐♠♣✉❧s♦ ❞❡ ❘❛♥❦✐♥❡❀ ♦s ✐♠♣✉❧s♦s

                                      ♦❜t✐❞♦s ❞♦ ♠ét♦❞♦ C

                                      2 sã♦ ❡①❛❝t❛♠❡♥t❡ ♦s ✐♠♣✉❧s♦s ❞❡ ❘❛♥❦✐♥❡ ♣❛r❛ ♦ ❝❛s♦ i = δ❀ ♦s ✐♠♣✉❧s♦s ♦❜t✐❞♦s

                                      2

                                      ❞♦ ♠ét♦❞♦ C sã♦ ✐♥❢❡r✐♦r❡s ❛♦s ❞❡ ❘❛♥❦✐♥❡ ♣❛r❛ i < δ ❡ s✉♣❡r✐♦r❡s ✭❧✐❣❡✐r❛♠❡♥t❡✮ ♣❛r❛ i > δ✳

                                      ∗ C2 < β

                                      ❆ r❛③ã♦ ♣❛r❛ ♦s ✐♠♣✉❧s♦s s❡r❡♠ ❞✐❢❡r❡♥t❡s ❞♦s ❞❡ ❘❛♥❦✐♥❡✱ ♣❛r❛ β ✱ ♥♦s ❝❛s♦s i < δ ❡

                                      C2

                                      i > δ ✱ ♣r❡♥❞❡✲s❡ ❝♦♠ ❛ ❛❧t✉r❛ e ❞❛ s❛♣❛t❛✳ ❈♦♠ ❡❢❡✐t♦✱ ♥♦ ♣r❡s❡♥t❡ ❡st✉❞♦ t❛❧ ❛❧t✉r❛ é ❝♦♥s✐❞❡r❛❞❛✱

                                      ′

                                      2

                                      3

                                      / φ ❛♦ ♣❛ss♦ q✉❡ ❇❛r❣❤♦✉t❤✐ ✭✶✾✾✵✮ ❞❡s♣r❡③❛✲❛✳ ❆ss✉♠✐♥❞♦✲s❡ δ = ✱ é ❛♣❡♥❛s ♣❛r❛ ♦ ❝❛s♦ i = δ q✉❡ ❛s ❞✉❛s s♦❧✉çõ❡s ❝♦✐♥❝✐❞❡♠✳ ❖ ❛ss✉♥t♦ s❡rá ❛❧✈♦ ❞❡ ❛♥á❧✐s❡ ❡s♣❡❝í✜❝❛ ♥❛ s❡❝çã♦ ✸✳✼✳ H

                                      ❆ ❋✐❣✉r❛ ✸✳✷✷✱ ❛♥á❧♦❣❛ à ✸✳✷✶✱ ❛♣r❡s❡♥t❛ ❡♠ ♦r❞❡♥❛❞❛s ♦ ✈❛❧♦r ❞❡ β ❡♠ ✈❡③ ❞♦ ✐♠♣✉❧s♦

                                      C2,I a

                                      ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦✳ ❊st❡ â♥❣✉❧♦ r❡s✉❧t❛ ❞❛ ♠❛①✐♠✐③❛çã♦ ❞❛ ❝♦♠♣♦♥❡♥t❡ ❤♦r✐③♦♥t❛❧ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✳ ❆♦s r❡s✉❧t❛❞♦s sã♦ s♦❜r❡♣♦st♦s ♦s ♦❜t✐❞♦s ❛tr❛✈és ❞❛ ❡①♣r❡ssã♦ ✷✳✶✹ ✭❇❛r❣❤♦✉t❤✐✱ ✶✾✾✵✮✱ ♣❛r❛ ♦ ❝❛s♦

                                      ∗

                                      < β ❡♠ q✉❡ ♦ ♣❛r❛♠❡♥t♦ s❡ ❡♥❝♦♥tr❛ ❛❝✐♠❛ ❞♦ t♦♣♦ ❞♦ ♠✉r♦✱ ✐st♦ é✱ β C2 ✳

                                      C2

                                      ✹✹ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

                                      1 0,6 0,55

                                      0,9 0,5 0,8

                                    • <

                                      β β C C 0,45 2 2

                                      ) )

                                      2

                                      2 H H

                                      γ γ

                                      0,7 0,4

                                      /(0,5 /(0,5

                                      H a H a

                                      I I 0,35 0,6

                                      0,3

                                    • <

                                      β β C C 2 2

                                      0,5 0,25 0,4

                                      0,2 0,2 0,4 0,6 0,8 1 0,2 0,4 0,6 0,8

                                      1 B /H B /H

                                      2 2 o o ′

                                      ′

                                    ✭❛✮ φ = 20 ✭❜✮ φ = 30

                                    0,4

                                      0,3 0,35 0,25 0,3

                                      ) )

                                      2

                                      2 H H

                                      γ γ

                                      0,25 0,2

                                      /(0,5 /(0,5

                                      H a H a

                                      I I 0,2

                                      0,15

                                      < <

                                      β β β β

                                      C C 2 2 C C 2 2 0,15 0,1

                                      0,1 0,2 0,4 0,6 0,8 1 0,2 0,4 0,6 0,8

                                      1 B /H B /H

                                      2 2 o o ′

                                      ′ = 40

                                      = 45 ✭❝✮ φ ✭❞✮ φ B /H

                                      2 o o o o o

                                      (i=0 ) (i=25 ) i=0 i=10 i=20 R R o o o o

                                      (i=20 ) i=5 i=15 i=25 R

                                      ❋✐❣✉r❛ ✸✳✷✶✿ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦

                                      ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s

                                      0,2 0,4 0,6 0,8

                                      0,2 0,4 0,6 0,8

                                      1 B

                                      2 /H

                                      β C 2 ,I H a

                                      ( o

                                      ) ✭❝✮ φ

                                      ′ = 40 o

                                      90

                                      95 100 105 110 115 120 125 130 135 140

                                      1 B

                                      90

                                      2 /H

                                      β C 2 ,I H a

                                      ( o

                                      ) ✭❞✮ φ

                                      ′ = 45 o i=0 o i=5 o i=10 o i=15 o

                                      β

                                      ’ B

                                      ❋✐❣✉r❛ ✸✳✷✷✿ ❱❛r✐❛çã♦ ❞❛ ✐♥❝❧✐♥❛çã♦ β

                                      C2,I H a

                                      95 100 105 110 115 120 125 130 135 140

                                      ′ = 30 o

                                      ✸✳✺✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋✳ ❉❊ φ

                                      β C 2 ,I H a

                                      ′

                                      ✱ I ❊ ❈❖▼P✳ ❉❆ ❇❆❙❊ ❉❆ ❊❙❚❘❯❚❯❘❆ B

                                      1

                                      ✹✺

                                      90

                                      95 100 105 110 115 120 125 130 135 140

                                      0,2 0,4 0,6 0,8

                                      1 B

                                      2 /H

                                      ( o

                                      ) ✭❜✮ φ

                                      ) ✭❛✮ φ

                                      ′ = 20 o

                                      90

                                      95 100 105 110 115 120 125 130 135 140

                                      0,2 0,4 0,6 0,8

                                      1 B

                                      2 /H

                                      β C 2 ,I H a

                                      ( o

                                    • C
                                    • 2 β

                                        ✹✻ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲ 2 ′ B

                                        H

                                        / ❱❡r✐✜❝❛✲s❡ ❞❛ ❛♥á❧✐s❡ ❞❡st❛ ✜❣✉r❛ q✉❡✱ ❛ ♣❛rt✐r ❞❡ ❝❡rt♦ ✈❛❧♦r ❞❡ ✭✈❛r✐á✈❡❧ ❝♦♠ φ ✮✱ ♦ â♥❣✉❧♦ H

                                        β ❡st❛❜✐❧✐③❛✱ ♠❛♥t❡♥❞♦✲s❡ ❝♦♥st❛♥t❡✱ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞♦ ❛✉♠❡♥t♦ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦✳ ❖s ✈❛❧♦r❡s

                                        C2,I a H

                                        ❞❡ β ✱ ❛♣ós ❛ s✉❛ ❡st❛❜✐❧✐③❛çã♦✱ ♠♦str❛♠✲s❡ s❡♠❡❧❤❛♥t❡s ❛♦s ♦❜t✐❞♦s ♣♦r ❇❛r❣❤♦✉t❤✐ ✭✶✾✾✵✮✳ P❛r❛

                                        C2,I a

                                        ✐❧✉str❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡s❝r✐t♦✱ ❛♣r❡s❡♥t❛✲s❡ ❛ ❋✐❣✉r❛ ✸✳✷✸✱ ♥❛ q✉❛❧ s❡ r❡♣r❡s❡♥t❛♠ ♦s â♥❣✉❧♦s H ′ o o 2 B β = 20

                                        / H ♣❛r❛ ♦ ❝❛s♦ φ ❡ i = 5 ✱ ♣❛r❛ três ✈❛❧♦r❡s ❜❛✐①♦s ❞❛ r❡❧❛çã♦ ✭✵✱✶✽✽✱ ✵✱✸✶✸ ❡ ✵✱✹✸✽✮ ❡

                                        C2,I a

                                        ♣❛r❛ três ✈❛❧♦r❡s ❡❧❡✈❛❞♦s ❞❛ ♠❡s♠❛ r❡❧❛çã♦ ✭✵✱✻✽✽✱ ✵✱✽✶✸ ❡ ✵✱✾✸✽✮✳

                                        ✭❛✮ ❇❛s❡s ❞❡ ♣❡q✉❡♥❛ ❞✐♠❡♥sã♦✳ ✭❜✮ ❇❛s❡s ❞❡ ❣r❛♥❞❡ ❞✐♠❡♥sã♦✳ ′ o o H e H

                                        = 20 / = 0, 125 ❋✐❣✉r❛ ✸✳✷✸✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ✐♥❝❧✐♥❛çã♦ β C2,I ♣❛r❛ φ ✱ ❡ i = 5 ✿ ♠ét♦❞♦ C a

                                        2 ✳

                                        ❈♦♥❢♦r♠❡ s❡ ♠♦str❛ ♥❛ ✜❣✉r❛✱ ✈❡r✐✜❝❛✲s❡✱ ❞❡ ❢❛❝t♦✱ q✉❡ ♣❛r❛ ❜❛s❡s ❞❡ ♣❡q✉❡♥❛ ❞✐♠❡♥sã♦ ❡①✐st❡ ✉♠ H ❛✉♠❡♥t♦ ❞❡ β C2,I ✭❝♦♠ ❛ ❞✐♠❡♥sã♦ ❞❛ ❜❛s❡✮ ❡ q✉❡ ♣❛r❛ ❜❛s❡s ❞❡ ❣r❛♥❞❡ ❞✐♠❡♥sã♦ ♦ ♠❡s♠♦ ♥ã♦ s❡ a H

                                        ✈❡r✐✜❝❛✳ ➱ ✐♥t❡r❡ss❛♥t❡ ❢❛③❡r✲s❡ ♥♦t❛r q✉❡✱ ❛♣❡s❛r ❞❡✱ ♥❡st❡ ú❧t✐♠♦ ❝❛s♦✱ ♥ã♦ ❤❛✈❡r ❡✈♦❧✉çã♦ ❞❡ β C2,I ✱ a

                                        H o

                                        ❡①✐st✐r ✉♠ ❛✉♠❡♥t♦ ❞❡ I a ✱ ♣❛r❛ i 6= 0 ✭❋✐❣✉r❛ ✸✳✷✶✮✳ ❚❛❧ ❞❡✈❡✲s❡ ❛♦ ❛✉♠❡♥t♦ ❞❛ ❛❧t✉r❛ ✈✐rt✉❛❧ ❞♦ ♠✉r♦ ❞❡ s✉♣♦rt❡✳

                                        ✸✳✺✳✹ ❘❡s✉❧t❛❞♦s ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦

                                        ✸✳✺✳✹✳✶ ❆♣r❡s❡♥t❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ◆❛s ❋✐❣✉r❛s ✸✳✷✹ ❛ ✸✳✷✾ ❛♣r❡s❡♥t❛✲s❡ ❛ ❡✈♦❧✉çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦ ✭❡①♣r❡ssã♦ ✸✳✸✻✮✱ ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦ ✭t❛♠❜é♠ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛✮ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡ ✐♥❝❧✐♥❛çã♦ ❞♦ t❡rr❡♥♦ ❡ ✈ár✐♦s ✈❛❧♦r❡s ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦✳ ❆ss✐♠✱ ♥❛ ❋✐❣✉r❛

                                        o ′

                                        = 20 ✸✳✷✹ ❛♣r❡s❡♥t❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♣❛r❛ φ ✱ ❛♣r❡s❡♥t❛♥❞♦✲s❡✱ ♥❛ ❋✐❣✉r❛ ✸✳✷✺✱ ♦s r❡s✉❧t❛❞♦s ♣❛r❛

                                        o o ′

                                        ′

                                        φ = 30 = 40

                                        ✳ ◆❛s ❋✐❣✉r❛s ✸✳✷✻ ❡ ✸✳✷✼ ❛♣r❡s❡♥t❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♣❛r❛ φ ❡ ♥❛s ❋✐❣✉r❛s ✸✳✷✽ ❡ ✸✳✷✾

                                        ′ o

                                        = 45 ♦s r❡s✉❧t❛❞♦s ♣❛r❛ φ ✳

                                      • C
                                      • 2 ✭❜✮ i = 5 o

                                          ′ o e H

                                          1 0,2 0,4 0,6 0,8

                                          1 B

                                          2 /H

                                          i=10

                                          tg δ

                                          β C 2

                                          < β

                                          0,2 0,4 0,6 0,8

                                          1 0,2 0,4 0,6 0,8

                                          1 B

                                          2 /H

                                          i=15

                                          tg δ

                                          β C 2

                                          < β

                                          Método R Método C

                                          

                                        1

                                        Método C

                                          2

                                          ❋✐❣✉r❛ ✸✳✷✹✿ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

                                          0,2 0,4 0,6 0,8

                                          β C 2

                                          < β

                                          1 0,2 0,4 0,6 0,8

                                          i=5

                                          ✸✳✺✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋✳ ❉❊ φ

                                          ′

                                          1 0,2 0,4 0,6 0,8

                                          ✱ I ❊ ❈❖▼P✳ ❉❆ ❇❆❙❊ ❉❆ ❊❙❚❘❯❚❯❘❆ B

                                          1

                                          ✹✼

                                          tg δ

                                          i=0

                                          tg δ

                                        • C
                                        • 2 ✭❛✮ i = 0 o

                                            1 B

                                            0,2 0,4 0,6 0,8

                                            β C 2

                                            < β

                                            0,2 0,4 0,6 0,8

                                            1 B

                                            2 /H

                                            2 /H

                                          • C
                                          • 2 ✭❞✮ i =
                                          • C
                                          • 2 ✭❝✮ i = 10 o

                                            • C
                                            • 2 ✭❜✮ i
                                            • C
                                            • 2 ✭❛✮ i
                                            • C
                                            • 2 ✭❞✮ i = 15 o

                                              • C
                                              • 2 ✭❝✮ i = 10 o

                                                  β C 2

                                                  < β

                                                  0,2 0,4 0,6 0,8

                                                  1 0,2 0,4 0,6 0,8

                                                  1 B

                                                  2 /H

                                                  i=15

                                                  tg δ

                                                  β C 2

                                                  0,2 0,4 0,6 0,8

                                                  < β

                                                  1

                                                  i=20

                                                  tg δ

                                                  β C 2

                                                  < β

                                                  1

                                                  i=25

                                                  tg δ

                                                  β C 2

                                                  tg δ

                                                  2 /H

                                                  i=10

                                                  < β

                                                  ✹✽ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

                                                  0,2 0,4 0,6 0,8

                                                  1 0,2 0,4 0,6 0,8

                                                  1 B

                                                  2 /H

                                                  i=0

                                                  tg δ

                                                  β C 2

                                                  0,2 0,4 0,6 0,8

                                                  1 B

                                                  1 0,2 0,4 0,6 0,8

                                                  1 B

                                                  2 /H

                                                  i=5

                                                  tg δ

                                                  β C 2

                                                  < β

                                                  0,2 0,4 0,6 0,8

                                                  1 0,2 0,4 0,6 0,8

                                                • C
                                                • 2 0,2 0,4 0,
                                                • C
                                                • 2

                                                  < β

                                                • C
                                                • 2 ✭❛✮ i
                                                • C
                                                • 2 ✭❜✮ i = 5 o

                                                    1 B

                                                    1 B

                                                    2 /H

                                                    i=10

                                                    tg δ

                                                    β C 2

                                                    < β

                                                    0,2 0,4 0,6 0,8

                                                    1 0,2 0,4 0,6 0,8

                                                    2 /H

                                                    0,2 0,4 0,6 0,8

                                                    i=15

                                                    tg δ

                                                    β C 2

                                                    < β

                                                    Método R Método C

                                                    

                                                  1

                                                  Método C

                                                    2

                                                    ❋✐❣✉r❛ ✸✳✷✻✿ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

                                                    1 0,2 0,4 0,6 0,8

                                                    < β

                                                    ′ o e H

                                                    2 /H

                                                    ✸✳✺✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋✳ ❉❊ φ

                                                    ′

                                                    ✱ I ❊ ❈❖▼P✳ ❉❆ ❇❆❙❊ ❉❆ ❊❙❚❘❯❚❯❘❆ B

                                                    1

                                                    ✹✾

                                                    0,2 0,4 0,6 0,8

                                                    1 0,2 0,4 0,6 0,8

                                                    1 B

                                                    i=0

                                                    β C 2

                                                    tg δ

                                                    β C 2

                                                    < β

                                                    0,2 0,4 0,6 0,8

                                                    1 0,2 0,4 0,6 0,8

                                                    1 B

                                                    2 /H

                                                    i=5

                                                    tg δ

                                                  • C
                                                  • 2 ✭❝✮ i =
                                                  • C
                                                  • 2 ✭❞✮ i = 15 o

                                                      ✺✵ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲ i=20 i=25

                                                      1 1 0,8

                                                      0,8 0,6 0,6

                                                      δ δ tg tg

                                                      < <

                                                      β β β β

                                                      C 2 C 2 C 2 C 2 0,4

                                                      0,4 0,2 0,2 0,2 0,4 0,6 0,8

                                                      1 0,2 0,4 0,6 0,8

                                                      1 B /H B /H

                                                      2

                                                      2 o o

                                                      

                                                    ✭❛✮ i = 20 ✭❜✮ i = 25

                                                      i=30 i=35

                                                      1 1 0,8

                                                      0,8

                                                      β C C 2 2

                                                    • β <

                                                      0,6 0,6

                                                    • <

                                                      β β C C 2 2

                                                      δ δ tg tg

                                                      0,4 0,4 0,2 0,2 0,2 0,4 0,6 0,8

                                                      1 0,2 0,4 0,6 0,8

                                                      1 B /H B /H

                                                      2

                                                      2 o o

                                                      

                                                    ✭❝✮ i = 30 ✭❞✮ i = 35

                                                    Método C Método C Método R

                                                      

                                                    1

                                                      2

                                                      ❋✐❣✉r❛ ✸✳✷✼✿ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

                                                      ′ o e H

                                                      = 40 / = 0, 125 ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ ❀ ✭❝♦♥t✐♥✉❛çã♦✮✳

                                                    • C
                                                    • 2 ✭❛✮ i
                                                    • C
                                                    • 2 ✭❜✮ i = 5 o

                                                        tg δ

                                                      • C
                                                      • 2 ✭❝✮ i =
                                                      • C
                                                      • 2 ✭❞✮ i = 15 o

                                                          β C 2

                                                          < β

                                                          0,2 0,4 0,6 0,8

                                                          1 0,2 0,4 0,6 0,8

                                                          1 B

                                                          2 /H

                                                          i=15

                                                          tg δ

                                                          β C 2

                                                          Método R Método C

                                                          < β

                                                          

                                                        1

                                                        Método C

                                                          2

                                                          ❋✐❣✉r❛ ✸✳✷✽✿ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

                                                          ′

                                                          = 45

                                                          o

                                                          ❀

                                                          e

                                                          /

                                                          H

                                                          i=10

                                                          1 B

                                                          2 /H

                                                          tg δ

                                                          ✸✳✺✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋✳ ❉❊ φ

                                                          ′

                                                          ✱ I ❊ ❈❖▼P✳ ❉❆ ❇❆❙❊ ❉❆ ❊❙❚❘❯❚❯❘❆ B

                                                          1

                                                          ✺✶

                                                          0,2 0,4 0,6 0,8

                                                          1 0,2 0,4 0,6 0,8

                                                          1 B

                                                          2 /H

                                                          i=0

                                                          β C 2

                                                          1 0,2 0,4 0,6 0,8

                                                          < β

                                                          0,2 0,4 0,6 0,8

                                                          1 0,2 0,4 0,6 0,8

                                                          1 B

                                                          2 /H

                                                          i=5

                                                          tg δ

                                                          β C 2

                                                          < β

                                                          0,2 0,4 0,6 0,8

                                                          = 0, 125 ✳

                                                        • C
                                                        • 2 ✭❛✮ i =
                                                        • C
                                                        • 2 ✭❜✮ i =
                                                        • C
                                                        • 2 ✭❝✮ i =
                                                        • C
                                                        • 2 ✭❞✮ i = 35 o

                                                            Método R Método C

                                                            0,2 0,4 0,6 0,8

                                                            1 0,2 0,4 0,6 0,8

                                                            1 B

                                                            2 /H

                                                            i=35

                                                            tg δ

                                                            β C 2

                                                            < β

                                                            2

                                                            β C 2

                                                            ❋✐❣✉r❛ ✸✳✷✾✿ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦✿ φ

                                                            ′

                                                            = 45

                                                            o

                                                            ❀

                                                            e

                                                            /

                                                            H

                                                            = 0, 125 ✭❝♦♥t✐♥✉❛çã♦✮✳

                                                            < β

                                                            tg δ

                                                            ✺✷ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

                                                            1 0,2 0,4 0,6 0,8

                                                            0,2 0,4 0,6 0,8

                                                            1 0,2 0,4 0,6 0,8

                                                            1 B

                                                            2 /H

                                                            i=20

                                                            tg δ

                                                            β C 2

                                                            < β

                                                            0,2 0,4 0,6 0,8

                                                            1 B

                                                            i=30

                                                            2 /H

                                                            i=25

                                                            tg δ

                                                            β C 2

                                                            < β

                                                            0,2 0,4 0,6 0,8

                                                            1 0,2 0,4 0,6 0,8

                                                            1 B

                                                            2 /H

                                                          1 Método C

                                                            ′

                                                            1

                                                            ✸✳✺✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋✳ ❉❊ φ ✱ I ❊ ❈❖▼P✳ ❉❆ ❇❆❙❊ ❉❆ ❊❙❚❘❯❚❯❘❆ B ✺✸ ✸✳✺✳✹✳✷ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ❆♥❛❧✐s❛♥❞♦ ♦s r❡s✉❧t❛❞♦s é ♣♦ssí✈❡❧ ❝♦♥❝❧✉✐r q✉❡✿

                                                            ❼ ♦s r❡s✉❧t❛❞♦s ❞❡ tan δ ♦❜t✐❞♦s ❞♦ ♠ét♦❞♦ R sã♦✱ ♥♦r♠❛❧♠❡♥t❡✱ s✉♣❡r✐♦r❡s ❛♦s r❡st❛♥t❡s❀

                                                            ′

                                                            2

                                                            3

                                                            / φ ❼ ❛ ❡①❝❡♣çã♦ ♦❝♦rr❡ ♣❛r❛ i > δ ✭❝♦♥s✐❞❡r❛❞♦✱ ♥♦s ❝á❧❝✉❧♦s ❛♣r❡s❡♥t❛❞♦s✱ ✐❣✉❛❧ ❛ ✮✱ ❡♠ ❡s♣❡❝✐❛❧✱ 2 B

                                                            H

                                                            /

                                                            2

                                                            ♣❛r❛ ♦s ❝❛s♦s ❞❡ ♣❡q✉❡♥♦s❀ ♣❛r❛ ❡st❡s ❝❛s♦s✱ ♦ ♠ét♦❞♦ C ❢♦r♥❡❝❡ ✈❛❧♦r❡s s✉♣❡r✐♦r❡s❀

                                                            2

                                                            ❼ ❣❧♦❜❛❧♠❡♥t❡✱ ♦s r❡s✉❧t❛❞♦s ❞♦s ♠ét♦❞♦s R ❡ C sã♦ s❡♠❡❧❤❛♥t❡s❀ sã♦ ❡①❛❝t❛♠❡♥t❡ ✐❣✉❛✐s q✉❛♥❞♦

                                                            ′

                                                            2

                                                            3

                                                            i = δ / φ ✭= ✱ ♦ ✈❛❧♦r ❛❞♦♣t❛❞♦✮❀

                                                            ′ o ′ o

                                                            = 20 = 30 ❼ ♣❛r❛ â♥❣✉❧♦s ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ φ ❡ φ ✱ ♦s r❡s✉❧t❛❞♦s ❞❡ tan δ sã♦ ♠✉✐t♦ 2 B

                                                            / H s❡♠❡❧❤❛♥t❡s ♣❛r❛ ♦s três ♠ét♦❞♦s✳ P❛r❛ r❡❧❛çõ❡s ❡❧❡✈❛❞❛s ❡ ♣❛r❛ ✈❛❧♦r❡s ❞❡ i ❡❧❡✈❛❞♦s ♦s r❡s✉❧t❛❞♦s ❞♦ ♠ét♦❞♦ C

                                                            1 ❛❢❛st❛♠✲s❡ ✉♠ ♣♦✉❝♦ ❞♦s r❡st❛♥t❡s❀ ′ o ′ o 2 B H

                                                            = 40 = 45 /

                                                            ❼ ♣❛r❛ φ ❡ φ ♦s r❡s✉❧t❛❞♦s sã♦ s❡♠❡❧❤❛♥t❡s ❡♥tr❡ ♦s três ♠ét♦❞♦s ♣❛r❛ r❡❧❛çõ❡s ✐♥t❡r♠é❞✐❛s✳

                                                            ❘❡s✉♠❡♠✲s❡✱ ♥❛ ❋✐❣✉r❛ ✸✳✸✵✱ t♦❞♦s ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❞♦ ♠ét♦❞♦ C

                                                            2 ✱ ♣❛r❛ ✉♠❛ ❛♥á❧✐s❡ ♠❛✐s

                                                            ❞❡t❛❧❤❛❞❛✳ ❉❡st❛ ✜❣✉r❛ é ♣♦ssí✈❡❧ ❝♦♥st❛t❛r q✉❡ ♦ ✈❛❧♦r ❞❡ tan δ ♥ã♦ é ♠✉✐t♦ s❡♥sí✈❡❧ à ✐♥❝❧✐♥❛çã♦ ❞♦

                                                            ′ o

                                                            ≥

                                                            30 t❡rr❡♥♦✱ ❡♠ ❡s♣❡❝✐❛❧ ♣❛r❛ φ ✳ Pr♦❝❡❞❡✲s❡✱ ❞❡ ❢♦r♠❛ ❛♥á❧♦❣❛ à r❡❛❧✐③❛❞❛ ❛ ♣r♦♣ós✐t♦ ❞❛ ❛♥á❧✐s❡ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧✱ ❛♦ tr❛ç❛❞♦ ❞❛ ❝✉r✈❛ q✉❡ r❡❧❛❝✐♦♥❛ β C2,tan δ ✭q✉❡ r❡s✉❧t❛ ❞❛ ♠❛①✐♠✐③❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦✮ 2 B

                                                            H

                                                            / ❝♦♠ ✳ ❚❛❧ é ❛♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✸✳✸✶✳ ❆♦s r❡s✉❧t❛❞♦s sã♦ s♦❜r❡♣♦st♦s ♦s ♦❜t✐❞♦s ❛tr❛✈és ❞❛

                                                            ∗ C2 < β

                                                            ❡①♣r❡ssã♦ ✷✳✶✹ ✭❇❛r❣❤♦✉t❤✐✱ ✶✾✾✵✮✱ ♣❛r❛ ♦ ❝❛s♦ β ✳

                                                            C2 H C2,tan δ

                                                            ❱❡r✐✜❝❛✲s❡✱ ❞❛ ❋✐❣✉r❛ ✸✳✸✶✱ q✉❡✱ t❛❧ ❝♦♠♦ s❡ ✈❡r✐✜❝♦✉ ♣❛r❛ ♦ ❝❛s♦ ❞❡ β C2,I ✱ t❛♠❜é♠ β ❡st❛✲ 2 a

                                                            B H

                                                            / ❜✐❧✐③❛ ❛ ♣❛rt✐r ❞❡ ❞❛❞♦ ✈❛❧♦r ❞❡ ✱ s❡♥❞♦ ♦s r❡s✉❧t❛❞♦s✱ ♥❡st❡ ❝❛s♦✱ ❝♦✐♥❝✐❞❡♥t❡s ❝♦♠ ♦s ❛♣r❡s❡♥t❛❞♦s H

                                                            C2,tan δ

                                                            ♥❛ ❋✐❣✉r❛ ✸✳✷✸✳ ❉♦ ♠❡s♠♦ ♠♦❞♦ q✉❡ ♣❛r❛ β C2,I a ✱ ♦s ✈❛❧♦r❡s ❡st❛❜✐❧✐③❛❞♦s ❞❡ β ♠♦str❛♠✲s❡ ❝♦✐♥❝✐❞❡♥t❡s ❝♦♠ ♦s ♦❜t✐❞♦s ❛ ♣❛rt✐r ❞❛ ❡①♣r❡ssã♦ ❛♣r❡s❡♥t❛❞❛ ♣♦r ❇❛r❣❤♦✉t❤✐ ✭✶✾✾✵✮✳

                                                            ✺✹ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

                                                            1

                                                            1

                                                            β C C 2 2

                                                          • β <

                                                            0,8 0,8 0,6 0,6

                                                          • <

                                                            β β C C 2 2

                                                            δ δ tg tg

                                                            0,4 0,4 0,2 0,2 0,2 0,4 0,6 0,8

                                                            1 0,2 0,4 0,6 0,8

                                                            1 B /H B /H

                                                            2 2 o o ′

                                                            ′

                                                          ✭❛✮ φ = 20 ✭❜✮ φ = 30

                                                          0,8

                                                            0,6 0,5 0,6

                                                            0,4

                                                          • <
                                                          • C C

                                                            β β

                                                            < 2 2 β β

                                                            C C 2 2 δ

                                                            δ 0,4

                                                            0,3 tg tg

                                                            0,2 0,2 0,1 0,2 0,4 0,6 0,8

                                                            1 0,2 0,4 0,6 0,8

                                                            1 B /H B /H

                                                            2 2 o o ′

                                                            ′ = 40

                                                            = 45 ✭❝✮ φ ✭❞✮ φ B /H

                                                            2 o o o o o

                                                            (i=0 ) (i=25 ) i=0 i=10 i=20 R R o o o o

                                                            (i=20 ) i=5 i=15 i=25 R

                                                            ❋✐❣✉r❛ ✸✳✸✵✿ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

                                                            ❋✐❣✉r❛ ✸✳✸✶✿ ❱❛r✐❛çã♦ ❞❛ ✐♥❝❧✐♥❛çã♦ β C2,tan δ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s

                                                            90

                                                            95 100 105 110 115 120 125 130 135 140

                                                            0,2 0,4 0,6 0,8

                                                            1 B

                                                            2 /H

                                                            β C 2 ,tan(

                                                            δ )

                                                            ( o

                                                            ) ✭❝✮ φ

                                                            ′ = 40 o

                                                            95 100 105 110 115 120 125 130 135 140

                                                            ′ = 30 o

                                                            0,2 0,4 0,6 0,8

                                                            1 B

                                                            2 /H

                                                            β C 2 ,tan(

                                                            δ )

                                                            ( o

                                                            ) ✭❞✮ φ

                                                            ′ = 45 o i=0 o i=5 o i=10 o i=15 o

                                                            β

                                                            ’ B

                                                            90

                                                            ) ✭❜✮ φ

                                                            ✸✳✺✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋✳ ❉❊ φ

                                                            β C 2 ,tan(

                                                            ′

                                                            ✱ I ❊ ❈❖▼P✳ ❉❆ ❇❆❙❊ ❉❆ ❊❙❚❘❯❚❯❘❆ B

                                                            1

                                                            ✺✺

                                                            90

                                                            95 100 105 110 115 120 125 130 135 140

                                                            0,2 0,4 0,6 0,8

                                                            1 B

                                                            2 /H

                                                            δ )

                                                            ( o

                                                            ( o

                                                            ) ✭❛✮ φ

                                                            ′ = 20 o

                                                            90

                                                            95 100 105 110 115 120 125 130 135 140

                                                            0,2 0,4 0,6 0,8

                                                            1 B

                                                            2 /H

                                                            β C 2 ,tan(

                                                            δ )

                                                          • C
                                                          • 2 β

                                                              ✺✻ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

                                                              ✸✳✻ ❆♥á❧✐s❡ ♣❛r❛♠étr✐❝❛✿ ✐♥✢✉ê♥❝✐❛ ❞❡ δ ✸✳✻✳✶ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s

                                                              P❛r❛ ♦ ❡st✉❞♦ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ ❞♦ ❝♦♥t❛❝t♦ s♦❧♦✲❡str✉t✉r❛ é ❝♦♥s✐❞❡r❛❞♦ ✉♠ s♦❧♦ ❝♦♠

                                                              o

                                                              ✉♠❛ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞❡ 30 ✳ ❋❛③✱ ❛♣❡♥❛s✱ s❡♥t✐❞♦ r❡❛❧✐③❛r ❡st❡ ❡st✉❞♦ s♦❜r❡ ♦ ♠ét♦❞♦ C

                                                              2 ✱ ❞❛❞♦

                                                              q✉❡ ♥♦ ♠ét♦❞♦ R ♦ ✐♠♣✉❧s♦ ♥ã♦ ❞❡♣❡♥❞❡ ❞❡ δ ❡ ♥♦ ♠ét♦❞♦ C

                                                              1 ♦ ✐♠♣✉❧s♦ é ❛❞♠✐t✐❞♦ ❛♣❧✐❝❛❞♦ s♦❜r❡ ❛ ′

                                                              ❝✉♥❤❛ ♠♦rt❛ ❞♦ s♦❧♦✱ ♦✉ s❡❥❛✱ ❝♦♠ δ = φ ✳ P❛r❛ ❛s ♠❡s♠❛s ❝♦♥❞✐çõ❡s ❞♦ s♦❧♦ ❡ ❞❛ ❡str✉t✉r❛ sã♦ ❝♦♥s✐❞❡r❛❞❛s ❞✐❢❡r❡♥t❡s ✐♥❝❧✐♥❛çõ❡s ❞❛ s✉✲

                                                              ♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦✱ ♣❛r❛ s❡ ❛♥❛❧✐s❛r t❛♠❜é♠ ❛ ❡✈♦❧✉çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ✭❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ♣❡❧❛ H 1 2 I a 2 γH / r❛③ã♦ ✮ ❡ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ✭❞❛❞❛ ♣♦r tan δ✮ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛q✉❡❧❛ ✐♥❝❧✐♥❛çã♦✳

                                                              ❙ã♦ ❛♥❛❧✐s❛❞♦s ❞♦✐s ❝❛s♦s✿ ✉♠ ❡♠ q✉❡ ♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ s❡ ❡♥❝♦♥tr❛ ❛❜❛✐①♦ ❞♦ t♦♣♦ ❞♦ ♠✉r♦✱ ♦✉

                                                              ∗ C2 > β

                                                              s❡❥❛✱ β ✱ ❡ ♦✉tr♦ ❡♠ q✉❡ ❛q✉❡❧❡ ♣❛r❛♠❡♥t♦ s❡ ❡♥❝♦♥tr❛ ❛❝✐♠❛ ❞♦ t♦♣♦ ❞♦ ♠✉r♦ ❡ ♥❡st❡ ❝❛s♦

                                                              C2 ∗

                                                              β C2 < β ✳ ❆ss✐♠✱ ♦s ❞♦✐s ❝❛s♦s ❞❡s❝r✐t♦s sã♦ ❛♣r❡s❡♥t❛❞♦s ♣❡❧❛ ❝♦♥s✐❞❡r❛çã♦ ❞❡ ❞✉❛s ❧❛r❣✉r❛s ❞♦

                                                              C2 ∗ C2 > β

                                                              ♠✉r♦ ❞✐st✐♥t❛s✳ P❛r❛ ♦ ♣r✐♠❡✐r♦ ❝❛s♦ ✭β ✮ ♦ ♠✉r♦ t❡♠ ✉♠❛ ❜❛s❡ ❞❡ 2 m ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❡

                                                              C2 ∗ C2 < β

                                                              ♣❛r❛ ♦ s❡❣✉♥❞♦ ❝❛s♦ ✭β ✮ ❛q✉❡❧❛ t❡♠ ✉♠ ❝♦♠♣r✐♠❡♥t♦ ❞❡ 7 m✳

                                                              C2 ✸✳✻✳✷ ❘❡s✉❧t❛❞♦s H 1 2 I a

                                                              / 2 γH ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ ❛♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ✭❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ♣❡❧❛ r❛③ã♦ ✮✱ ♣❛r❛ ♦ t✐♣♦ ❞❡ s♦❧♦ ❝♦♥s✐❞❡r❛❞♦✱ sã♦ ❛♣r❡s❡♥t❛❞♦s ♥❛s ❋✐❣✉r❛s ✸✳✸✷ ❡ ✸✳✸✸✱ ❡♠ ❢✉♥çã♦ ❞❛ r❡❧❛çã♦ ❡♥tr❡

                                                              ′

                                                              ♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ s♦❧♦✲❡str✉t✉r❛ δ ❡ ♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦ φ ✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱

                                                              s−e ∗ ∗

                                                              > β < β ♣❛r❛ ♦ ❝❛s♦ β C2 ❡ β C2 ✳

                                                            C2 C2

                                                              ◆❛s ❋✐❣✉r❛s ✸✳✸✹ ❡ ✸✳✸✺ ❡♥❝♦♥tr❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ❞❛ ❡✈♦❧✉çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞❛

                                                              ∗ ∗

                                                              > β < β ❡str✉t✉r❛ ❡♠ ❢✉♥çã♦ ❞♦ ♣❛râ♠❡tr♦ ❛♥❛❧✐s❛❞♦✱ ♣❛r❛ ♦s ❝❛s♦s β C2 ❡ β C2 ✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳

                                                            C2 C2

                                                              ❊♠ ❛♠❜❛s ❛s ❋✐❣✉r❛s ❛♣r❡s❡♥t♠❛✲s❡✱ s♦❜r❡♣♦st♦s✱ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❡❧♦s ♠ét♦❞♦s R ✭❡♠ q✉❡

                                                              ′

                                                              δ = i = φ ✮ ❡ C

                                                              1 ✭❡♠ q✉❡ δ ✮✳ s−e s−e

                                                              ✸✳✻✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋▲❯✃◆❈■❆ ❉❊ δ ✺✼

                                                              s−e

                                                              2 )

                                                              ✭❞✮ i = 15 o

                                                              0,35 0,4 0,45 0,5

                                                              1/3 1/2 2/3

                                                              1 δ s−e

                                                              / φ

                                                              ’ a

                                                              ✭❡✮ i = 20 o

                                                              ❋✐❣✉r❛ ✸✳✸✷✿ ■♥✢✉ê♥❝✐❛ ❞♦ ♣❛râ♠❡tr♦ δ

                                                              ♥♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ♣❛r❛ B

                                                              ’

                                                              1

                                                              = 2 m

                                                              B 2 H

                                                              = 0, 188 ❀

                                                              φ

                                                              ′

                                                              = 30

                                                              o

                                                              ✳ ❈❛s♦ β C2 > β

                                                              ∗ C2

                                                              I H a /(0,5 γ H

                                                              / φ

                                                              0,25 0,3 0,35 0,4

                                                              1

                                                            δ

                                                            s−e

                                                              1/3 1/2 2/3

                                                              1 δ s−e

                                                              / φ

                                                              ’

                                                              I H a /(0,5 γ H

                                                              2 )

                                                              ✭❛✮ i = 0 o

                                                              0,25 0,3 0,35 0,4

                                                              1/3 1/2 2/3

                                                              / φ

                                                              

                                                            1

                                                            δ s−e

                                                              ’ a

                                                              

                                                            ✭❜✮ i = 5

                                                            o

                                                              0,25 0,3 0,35 0,4

                                                              1/3 1/2 2/3

                                                              1 δ s−e

                                                              / φ

                                                              ’ a

                                                              ✭❝✮ i = 10 o

                                                              0,35 0,4 0,45 0,5

                                                              1/3 1/2 2/3

                                                              ✳

                                                              ✺✽ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

                                                              s−e

                                                              2 )

                                                              ✭❞✮ i = 15 o

                                                              0,45 0,5 0,55 0,6 0,65 0,7

                                                              1/3 1/2 2/3

                                                              1 δ s−e

                                                              / φ

                                                              ’ a

                                                              ✭❡✮ i = 20 o

                                                              ❋✐❣✉r❛ ✸✳✸✸✿ ■♥✢✉ê♥❝✐❛ ❞♦ ♣❛râ♠❡tr♦ δ

                                                              ♥♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ♣❛r❛ B

                                                              ’

                                                              1

                                                              = 7 m

                                                              B 2 H

                                                              = 0, 813 ❀

                                                              φ

                                                              ′

                                                              = 30

                                                              o

                                                              ✳ ❈❛s♦ β C2 < β

                                                              ∗ C2

                                                              I H a /(0,5 γ H

                                                              / φ

                                                              0,3 0,35 0,4 0,45 0,5

                                                              1

                                                            δ

                                                            s−e

                                                              1/3 1/2 2/3

                                                              1 δ s−e

                                                              / φ

                                                              ’

                                                              I H a /(0,5 γ H

                                                              2 )

                                                              ✭❛✮ i = 0 o

                                                              0,3 0,35 0,4 0,45 0,5

                                                              1/3 1/2 2/3

                                                              / φ

                                                              

                                                            1

                                                            δ s−e

                                                              ’ a

                                                              

                                                            ✭❜✮ i = 5

                                                            o

                                                              0,3 0,35 0,4 0,45 0,5

                                                              1/3 1/2 2/3

                                                              1 δ s−e

                                                              / φ

                                                              ’ a

                                                              ✭❝✮ i = 10 o

                                                              0,45 0,5 0,55 0,6 0,65 0,7

                                                              1/3 1/2 2/3

                                                              ✳

                                                              ✸✳✻✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋▲❯✃◆❈■❆ ❉❊ δ ✺✾

                                                              ❋✐❣✉r❛ ✸✳✸✹✿ ■♥✢✉ê♥❝✐❛ ❞♦ ♣❛râ♠❡tr♦ δ s−e ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦ ♣❛r❛ B

                                                              / φ ’ tg δ

                                                              ✭❞✮ i = 15 o

                                                              0,5 0,55 0,6 0,65 0,7 0,75 0,8

                                                              1/3 1/2 2/3

                                                              1 δ s−e

                                                              / φ ’ ✭❡✮ i = 20 o

                                                              1 = 2 m B 2 H

                                                              1/3 1/2 2/3

                                                              = 0, 188 ❀ φ

                                                              ′

                                                              = 30

                                                              o

                                                              ✳ ❈❛s♦ β

                                                              C2 > β ∗ C2

                                                              

                                                            1

                                                            δ s−e

                                                              0,5 0,55 0,6 0,65 0,7 0,75 0,8

                                                              0,4 0,45 0,5 0,55 0,6 0,65 0,7

                                                              1/3 1/2 2/3

                                                              1/3 1/2 2/3

                                                              1 δ s−e

                                                              / φ

                                                              ’ tg δ

                                                              ✭❛✮ i = 0 o

                                                              0,4 0,45 0,5 0,55 0,6 0,65 0,7

                                                              1

                                                            δ

                                                            s−e

                                                              ’ ✭❝✮ i = 10 o

                                                              / φ

                                                              ’

                                                            ✭❜✮ i = 5

                                                            o

                                                              0,4 0,45 0,5 0,55 0,6 0,65 0,7

                                                              1/3 1/2 2/3

                                                              1 δ s−e

                                                              / φ

                                                              ✳

                                                              ✻✵ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

                                                              ❋✐❣✉r❛ ✸✳✸✺✿ ■♥✢✉ê♥❝✐❛ ❞♦ ♣❛râ♠❡tr♦ δ s−e ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦ ♣❛r❛ B

                                                              / φ ’ tg δ

                                                              ✭❞✮ i = 15 o

                                                              0,15 0,2 0,25 0,3 0,35

                                                              1/3 1/2 2/3

                                                              1 δ s−e

                                                              / φ ’ ✭❡✮ i = 20 o

                                                              1 = 7 m B 2 H

                                                              1/3 1/2 2/3

                                                              = 0, 813 ❀ φ

                                                              ′

                                                              = 30

                                                              o

                                                              ✳ ❈❛s♦ β

                                                              C2 < β ∗ C2

                                                              

                                                            1

                                                            δ s−e

                                                              0,15 0,2 0,25 0,3 0,35

                                                              0,15 0,2 0,25 0,3 0,35

                                                              1/3 1/2 2/3

                                                              1/3 1/2 2/3

                                                              1 δ s−e

                                                              / φ

                                                              ’ tg δ

                                                              ✭❛✮ i = 0 o

                                                              0,15 0,2 0,25 0,3 0,35

                                                              1

                                                            δ

                                                            s−e

                                                              ’ ✭❝✮ i = 10 o

                                                              / φ

                                                              ’

                                                            ✭❜✮ i = 5

                                                            o

                                                              0,15 0,2 0,25 0,3 0,35

                                                              1/3 1/2 2/3

                                                              1 δ s−e

                                                              / φ

                                                              ✳

                                                              E H

                                                              / ✸✳✼✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋▲❯✃◆❈■❆ ❉❊ ✻✶

                                                              ✸✳✻✳✸ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s

                                                              ❆♥❛❧✐s❛♥❞♦ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❡❧♦ ♠ét♦❞♦ C

                                                              2 ♣♦❞❡ ❛✜r♠❛r✲s❡ q✉❡ ♦ ❛✉♠❡♥t♦ ❞❡ δ ✭✐❣✉❛❧ ❛ δ p ✮ s−e H

                                                              ✐♠♣❧✐❝❛ ❛ ❞✐♠✐♥✉✐çã♦ ❞❡ I ❡ ❞❡ tan δ✳

                                                              a 2 B H

                                                              / = 0, 188 P❛r❛ ♦ ❝❛s♦ ❞❛ r❡❧❛çã♦ ♣♦❞❡✲s❡ ❝♦♥❝❧✉✐r q✉❡✿

                                                              ′ p = φ

                                                              2

                                                              ❼ ♣❛r❛ ✈❛❧♦r❡s ❞❡ δ ✱ ♦s r❡s✉❧t❛❞♦s ❞♦ ♠ét♦❞♦ C ♠♦str❛♠✲s❡ ♠✉✐t♦ s❡♠❡❧❤❛♥t❡s ❛♦s ❞♦

                                                              1

                                                              ♠ét♦❞♦ C ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ ❛♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ❡ à ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦❀

                                                              p = i

                                                              2

                                                              ❼ ♣❛r❛ ✈❛❧♦r❡s ❞❡ δ ✱ ♦s r❡s✉❧t❛❞♦s ❞♦ ♠ét♦❞♦ C sã♦ ❝♦✐♥❝✐❞❡♥t❡s ❛♦s ♦❜t✐❞♦s ❛tr❛✈és ❞♦ ♠ét♦❞♦ R

                                                              ✳ ❊st❡ ❢❛❝t♦ é ✈á❧✐❞♦ ♣❛r❛ ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ❡ ♣❛r❛ ❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦✳ 2 B / H = 0, 813

                                                              P❛r❛ ❛ r❡❧❛çã♦ ♣♦❞❡✲s❡ ❝♦♥❝❧✉✐r q✉❡✿ ❼ ♦s ✈❛❧♦r❡s ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ❡ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ♦❜t✐❞♦s ♣❡❧♦s ♠ét♦❞♦s C

                                                              1

                                                              ❡ C

                                                              2 ❛❢❛st❛♠✲s❡ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦❀ 2 B H

                                                              / = i ❼ ❞❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ♣❛r❛ ❛ r❡❧❛çã♦ ❛♥t❡r✐♦r✱ q✉❛♥❞♦ δ p ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❡❧♦

                                                              ♠ét♦❞♦ C

                                                              2 sã♦ ❝♦✐♥❝✐❞❡♥t❡s ❝♦♠ ♦s ❞♦ ♠ét♦❞♦ R✳ 2 H 1 2 B

                                                              I a H γH

                                                              / / 2 ❱❡r✐✜❝❛✲s❡✱ ❛ss✐♠✱ q✉❡✱ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞❛ ❞✐♠❡♥sã♦ ✱ ❛s r❡❧❛çõ❡s ❡ tan δ t♦♠❛♠ ✈❛❧♦r❡s ✐❣✉❛✐s ♣❛r❛ ♦s ♠ét♦❞♦s R ❡ C

                                                              2 q✉❛♥❞♦ δ = i✳

                                                              e H

                                                              / ✸✳✼ ❆♥á❧✐s❡ ♣❛r❛♠étr✐❝❛✿ ✐♥✢✉ê♥❝✐❛ ❞❡ ✸✳✼✳✶ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s e H

                                                              / ❈♦♥❢♦r♠❡ r❡❢❡r✐❞♦ ♥❛ s❡❝çã♦ ✸✳✺✳✸✳✷✱ ❛tr✐❜✉✐✲s❡ ❛♦ ♣❛râ♠❡tr♦ ❛ r❛③ã♦ ♣❡❧❛ q✉❛❧ ❛❧❣✉♥s r❡s✉❧t❛❞♦s ❡♥tã♦ ❛♣r❡s❡♥t❛❞♦s ❞✐❢❡r❡♠ ❞❛s ❝♦♥❝❧✉sõ❡s ❞❡ ❇❛r❣❤♦✉t❤✐ ✭✶✾✾✵✮✳ ❆ ✐♥✢✉ê♥❝✐❛ ❞❛ ❡s♣❡ss✉r❛ ❞❛ ❜❛s❡ ❞♦

                                                              e H

                                                              / ♠✉r♦✱ ❞❛❞❛ ❛tr❛✈és ❞❛ r❛③ã♦ ❛❞✐♠❡♥s✐♦♥❛❧ ✱ ♥♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦✱ é✱ ❛ss✐♠✱ ❛♥❛❧✐s❛❞❛ ♥❛ ♣r❡s❡♥t❡ s❡❝çã♦✳ ❖ s♦❧♦ é ❝❛r❛❝t❡r✐③❛❞♦ ♣♦r ✉♠ â♥❣✉❧♦ ❞❡

                                                              o

                                                              r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞❡ 30 ❡ ❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦ é ❤♦r✐③♦♥t❛❧✳ ❆s ❞✐♠❡♥sõ❡s ❞❛ ❡str✉t✉r❛ sã♦ ❛s ♣r❡s❡♥t❡s ♥❛ ❚❛❜❡❧❛ ✸✳✶✱ ❡①❝❡♣t✉❛♥❞♦ ❛ ❡s♣❡ss✉r❛ ❞❛ ❜❛s❡ e✱ ♣❛râ♠❡tr♦ ❛ ❛♥❛❧✐s❛r✳

                                                              ✸✳✼✳✷ ❘❡s✉❧t❛❞♦s

                                                              ◆❛ ❋✐❣✉r❛ ✸✳✸✻ sã♦ ❛♣r❡s❡♥t❛❞♦s ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❛r❛ ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ❛❞✐♠❡♥s✐♦♥❛✲ ❧✐③❛❞♦✳ ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ à ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❡♥❝♦♥tr❛♠✲s❡ ♥❛ ❋✐❣✉r❛

                                                              e

                                                              / H ✸✳✸✼✳ ❆s ❝✉r✈❛s ❝♦rr❡s♣♦♥❞❡♥t❡s ❛♦s ♠ét♦❞♦s R ❡ C

                                                              1 ♥ã♦ ❞❡♣❡♥❞❡♠ ❞❡ ✱ ♣❡❧♦ q✉❡ sã♦ ❛s ♠❡s♠❛s

                                                              ❡♠ t♦❞♦s ♦s ❣rá✜❝♦s ❛♣r❡s❡♥t❛❞♦s ❡♠ ❝❛❞❛ ✉♠❛ ❞❛s ❋✐❣✉r❛s✳

                                                            • C
                                                            • 2
                                                            • C
                                                            • 2 ✭❜✮ e

                                                                2 /H

                                                                i=0

                                                                I H a /(0,5 γ H

                                                                2 )

                                                                β C 2

                                                                < β

                                                                / H

                                                                = 0, 125 0,2 0,25 0,3 0,35 0,4

                                                                0,2 0,4 0,6 0,8

                                                                1 B

                                                                i=0

                                                              • C
                                                              • 2
                                                              • C
                                                              • 2
                                                              • C
                                                              • 2

                                                                I H a /(0,5 γ H

                                                                2 )

                                                                β C 2

                                                                < β

                                                                / H

                                                                = 0, 25 0,25 0,3 0,35 0,4

                                                                i=0

                                                                I H a /(0,5 γ H

                                                                2 )

                                                                β C

                                                              2

                                                                2 /H

                                                                0,2 0,4 0,6 0,8

                                                                1 B

                                                                < β

                                                                ✻✷ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

                                                                0,2 0,25 0,3 0,35 0,4

                                                                0,2 0,4 0,6 0,8

                                                                1 B

                                                                2 /H

                                                                i=0

                                                                I H a /(0,5 γ H

                                                                2 )

                                                                β C 2

                                                                / H

                                                                = 0, 0625 0,2 0,25 0,3 0,35 0,4

                                                                = 0 0,2 0,25 0,3 0,35 0,4

                                                                0,2 0,4 0,6 0,8

                                                                1 B

                                                                2 /H

                                                                i=0

                                                                I H a /(0,5 γ H

                                                                2 )

                                                                β C 2

                                                                < β

                                                                / H

                                                                

                                                              < β

                                                              • C
                                                              • 2
                                                              • C
                                                              • 2 ✭❜✮ e

                                                                  1 B

                                                                  1 B

                                                                  2 /H

                                                                  i=0

                                                                  tg δ

                                                                  β C 2

                                                                  < β

                                                                  / H

                                                                  = 0, 125 0,2 0,4 0,6 0,8

                                                                  1 0,2 0,4 0,6 0,8

                                                                  2 /H

                                                                  = 0, 0625 0,2 0,4 0,6 0,8

                                                                  i=0

                                                                  tg δ

                                                                  β C 2

                                                                  < β

                                                                  / H

                                                                  = 0, 25 0,2 0,4 0,6 0,8

                                                                  1

                                                                  i=0

                                                                  tg δ

                                                                  β C 2

                                                                  1 0,2 0,4 0,6 0,8

                                                                  / H

                                                                  

                                                                < β

                                                                  i=0

                                                                  ✸✳✼✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆✿ ■◆❋▲❯✃◆❈■❆ ❉❊

                                                                  E

                                                                  /

                                                                  H

                                                                  ✻✸

                                                                  0,2 0,4 0,6 0,8

                                                                  1 0,2 0,4 0,6 0,8

                                                                  1 B

                                                                  2 /H

                                                                  tg δ

                                                                  < β

                                                                  β C 2

                                                                  < β

                                                                  / H

                                                                  = 0 0,2 0,4 0,6 0,8

                                                                  1 0,2 0,4 0,6 0,8

                                                                  1 B

                                                                  2 /H

                                                                  i=0

                                                                  tg δ

                                                                  β C 2

                                                                • C
                                                                • 2
                                                                • C
                                                                • 2
                                                                • *

                                                                  C
                                                                • 2

                                                                  ✻✹ ❈❆P❮❚❯▲❖ ✸✳ ❆◆➪▲■❙❊ ❉❊ ❊❙❚❘❯❚❯❘❆❙ ❉❊ ❙❯P❖❘❚❊ ❊▼ ▲

                                                                  ✸✳✼✳✸ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s e H

                                                                  / ❆♥❛❧✐s❛♥❞♦ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s r❡❧❛t✐✈❛♠❡♥t❡ à ✐♥✢✉ê♥❝✐❛ ❞❡ ♣♦❞❡ ❛✜r♠❛r✲s❡ q✉❡✿

                                                                  e H

                                                                  / = 0 ❼ q✉❛♥❞♦ ♦s r❡s✉❧t❛❞♦s ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ❝♦✐♥❝✐❞❡♠ ❡♥tr❡ ♦s ♠ét♦❞♦s R ❡ C

                                                                  2 ✱ ∗

                                                                  ≤ β

                                                                  ♣❛r❛ β C2 ❀

                                                                  C2

                                                                  ❼ à ♠❡❞✐❞❛ q✉❡ ❛ ❡s♣❡ss✉r❛ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦ ❛✉♠❡♥t❛✱ ♦s r❡s✉❧t❛❞♦s ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ♦❜t✐❞♦s ❞♦s ❞♦✐s ♠ét♦❞♦s r❡❢❡r✐❞♦s t❡♥❞❡♠ ❛ ❛❢❛st❛r✲s❡❀

                                                                  ❼ ♦s r❡s✉❧t❛❞♦s r❡❧❛t✐✈♦s à ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ♣♦ss✉❡♠ ♦ ♠❡s♠♦ ❝♦♠♣♦rt❛♠❡♥t♦ q✉❡ ♦s

                                                                  e

                                                                  / H = 0 r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❛r❛ ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧✳ ❆ss✐♠✱ q✉❛♥❞♦ ♦s ✈❛❧♦r❡s ❞❡ tan δ

                                                                  ∗

                                                                  2 ♣❛r❛ β C2 ✳ ❊st❛ ❝♦✐♥❝✐❞ê♥❝✐❛ ❞❡ ✈❛❧♦r❡s t❡♥❞❡ ❛ C2

                                                                  < β sã♦ ❝♦✐♥❝✐❞❡♥t❡s ❡♥tr❡ ♦s ♠ét♦❞♦s R ❡ C

                                                                  ♣❡r❞❡r✲s❡ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ ❡s♣❡ss✉r❛ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦❀ ❼ ♣❛r❛ ♦ ❝❛s♦ ❛♥❛❧✐s❛❞♦✱ ❛♣❡s❛r ❞❛s ✐♠♣♦rt❛♥t❡s ❞✐❢❡r❡♥ç❛s ❡♥tr❡ ♦s ✐♠♣✉❧s♦s ❞♦s ♠ét♦❞♦s C

                                                                  1 ❡

                                                                  C

                                                                  2 ✱ ✈❡r✐✜❝❛✲s❡ ✉♠❛ r❡❧❛t✐✈❛ ♣r♦①✐♠✐❞❛❞❡ ♥♦s r❡s✉❧t❛❞♦s ❞❡ tan δ✳

                                                                  ❈❛♣ít✉❧♦ ✹ ❆♣❧✐❝❛çã♦ ❞❡ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ✹✳✶ ■♥tr♦❞✉çã♦

                                                                  ◆♦ ❈❛♣ít✉❧♦ ✸ ❛♣❧✐❝❛r❛♠✲s❡ ♦s ♠ét♦❞♦s ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ✐♠♣✉❧s♦s s♦❜r❡ ❛s ❡str✉t✉r❛s ❞❡ s✉♣♦rt❡ ❡♠ L ♦✉ T ✐♥✈❡rt✐❞♦ ❛ ❞✐✈❡rs♦s ❝❛s♦s ❞❡ ❡str✉t✉r❛s ❞❡st❡ t✐♣♦✱ ❛tr❛✈és ❞❡ ❛♥á❧✐s❡ ♣❛r❛♠étr✐❝❛

                                                                  ′ 2 B

                                                                  / H q✉❡ ✐♥❝✐❞✐✉ s♦❜r❡ ♦s ♣❛râ♠❡tr♦s φ ✱ i ❡ ✳ ◆♦ ♣r❡s❡♥t❡ ❝❛♣ít✉❧♦ ♣r❡t❡♥❞❡✲s❡ ❢❛③❡r ✉♠❛ ❛♥á❧✐s❡ ♣❛r❛♠étr✐❝❛✱ ❛tr❛✈és ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ❛♦ ♣r♦❜❧❡♠❛ ❡♠ ❝❛✉s❛✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦s ♠❡s♠♦s ♣❛râ♠❡tr♦s✳ ❆ ✐♥t❡r❛❝çã♦ ❡♥tr❡ ♦ s♦❧♦ ❡ ❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡ é t❛♠❜é♠ ❛♥❛❧✐s❛❞❛ ♥♦ ♣r❡s❡♥t❡ ❝❛♣ít✉❧♦ ❛tr❛✈és ❞❛ ❝♦♥s✐❞❡r❛çã♦ ❞❡ ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ❝♦♥t❛❝t♦ ♥❛ ✐♥t❡r❢❛❝❡ ❡♥tr❡ ❛♠❜♦s✳ ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s sã♦ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦s ❡♥❝♦♥tr❛❞♦s ❛tr❛✈és ❞♦s ♠ét♦❞♦s tr❛❞✐❝✐♦♥❛✐s✳

                                                                  ❉❡ ♠♦❞♦ ❛ ❝❧❛r✐✜❝❛r ♦ ♣r♦❝❡ss♦ ❞❡ ❝á❧❝✉❧♦ é ❛♣r❡s❡♥t❛❞♦ ✉♠ ❝❛s♦ ❜❛s❡✳ ❖ r❡❝✉rs♦ ❛ ♠ét♦❞♦s ♥✉♠ér✐❝♦s✱ ♥♦♠❡❛❞❛♠❡♥t❡ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s é ✐♠♣♦rt❛♥t❡ ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❡

                                                                  ♣r♦❜❧❡♠❛s ❣❡♦té❝♥✐❝♦s ❛♦ ♣❡r♠✐t✐r ♠♦❞❡❧❛r✱ ❞❡ ❢♦r♠❛ r❡❛❧✐st✐❝❛♠❡♥t❡ ❛♣r♦①✐♠❛❞❛✱ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ♠❡❝â♥✐❝♦ ❞♦ s♦❧♦✱ ❞❛ ♣ró♣r✐❛ ❡str✉t✉r❛ ❡ ❞❛ ✐♥t❡r❛❝çã♦ ❡♥tr❡ ❛♠❜♦s✳

                                                                  P❧❛①✐s ✭✈❡rsã♦ ✽✮ é ✉♠ ♣r♦❣r❛♠❛ ❞❡ ❝á❧❝✉❧♦ ❛✉t♦♠át✐❝♦✱ ❜✐❞✐♠❡♥s✐♦♥❛❧✱ ❜❛s❡❛❞♦ ♥♦ ♠ét♦❞♦ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ❞❡st✐♥❛❞♦✱ ❡s♣❡❝✐✜❝❛♠❡♥t❡✱ à ❛♥á❧✐s❡ ❞❡ ❞❡❢♦r♠❛çã♦ ❡ ❡st❛❜✐❧✐❞❛❞❡ ❞❡ ♣r♦❜❧❡♠❛s ❣❡♦té❝♥✐❝♦s✳ ➱ ❡st❡ ♦ ♣r♦❣r❛♠❛ ❞❡ ❝á❧❝✉❧♦ ❛✉t♦♠át✐❝♦ ✉s❛❞♦ ♥♦ ♣r❡s❡♥t❡ ❝❛♣ít✉❧♦✳

                                                                  ✹✳✷ ▼♦❞❡❧♦ ❝♦♥st✐t✉t✐✈♦ ▼♦❤r✲❈♦✉❧♦♠❜

                                                                  ❖ ♣r♦❣r❛♠❛ P❧❛①✐s ♣❡r♠✐t❡ s✐♠✉❧❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ♠❡❝â♥✐❝♦ ❞♦ s♦❧♦ ❛tr❛✈és ❞❡ ✈ár✐♦s ♠♦❞❡❧♦s✱ ❝♦♠♦ ♦ ❡❧ást✐❝♦✲❧✐♥❡❛r✱ ♦ ❡❧ást✐❝♦ ♣❡r❢❡✐t❛♠❡♥t❡ ♣❧ást✐❝♦ ❞❡ ▼♦❤r✲❈♦✉❧♦♠❜ ♦✉ ♦ ♠♦❞❡❧♦ ❡❧❛st♦✲♣❧ást✐❝♦ ❝♦♠ ❡♥❞✉r❡❝✐♠❡♥t♦ ❍❛r❞❡♥✐♥❣ s♦✐❧✳ P❛r❛ ❛s ❛♥á❧✐s❡s ❡①❡❝✉t❛❞❛s ♥♦ ♣r❡s❡♥t❡ ❝❛♣ít✉❧♦✱ ❛❞♦♣t❛✲s❡ ♦ ♠♦❞❡❧♦ ▼♦❤r✲❈♦✉❧♦♠❜✳

                                                                  ✻✻ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖ ❋✐❣✉r❛ ✹✳✶✿ ▼♦❞❡❧♦ ❡❧ást✐❝♦ ♣❡r❢❡✐t❛♠❡♥t❡ ♣❧ást✐❝♦✳

                                                                  ❆ ❡q✉❛çã♦ q✉❡ ❞❡✜♥❡ ♦ ❝❛s♦ ❛♣r❡s❡♥t❛❞♦ ♥❛ ✜❣✉r❛ ❛❝✐♠❛✱ ❛♥t❡s ❞❛ ♣❧❛st✐✜❝❛çã♦ ❞♦ s♦❧♦✱ é ❞❛❞❛ ♣♦r✿

                                                                  ′

                                                                  σ = E × ε ✭✹✳✶✮

                                                                  ◆❛ ❋✐❣✉r❛ ✹✳✷ ❡♥❝♦♥tr❛✲s❡ r❡♣r❡s❡♥t❛❞♦✱ ❞❡ ❢♦r♠❛ ❣rá✜❝❛✱ ♦ ❝r✐tér✐♦ ❞❡ ❝❡❞ê♥❝✐❛ ❞❡ ▼♦❤r✲❈♦✉❧♦♠❜✳ ❋✐❣✉r❛ ✹✳✷✿ ❈r✐tér✐♦ ❞❡ ❝❡❞ê♥❝✐❛ ❞❡ ▼♦❤r✲❈♦✉❧♦♠❜ ✭❇r✐♥❦❣r❡✈❡ ❡t ❛❧✳✱ ✷✵✵✹✮✳

                                                                  ◆❛ ❋✐❣✉r❛ ✹✳✸ ❡♥❝♦♥tr❛✲s❡ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❣❡r❛❧✱ ♥♦ ❡s♣❛ç♦ ❞❛s t❡♥sõ❡s ♣r✐♥❝✐♣❛✐s✱ ❞♦ ❝r✐tér✐♦ ❞❡ ❝❡❞ê♥❝✐❛✱ ❡♠ q✉❡ ♥ã♦ é ❝♦♥s✐❞❡r❛❞❛ ❛ ❝♦❡sã♦ ❡❢❡❝t✐✈❛ ❞♦ s♦❧♦✳

                                                                  ✹✳✸✳ ❈❆❙❖ ❇❆❙❊ ✻✼

                                                                  o ′

                                                                  30 ✱ s❡♥❞♦ q✉❡✱ ♣❛r❛ ✈❛❧♦r❡s ❞❡ φ ✐♥❢❡r✐♦r❡s àq✉❡❧❡✱ ψ é ❛ss✉♠✐❞♦ ❝♦♠♦ ♥✉❧♦✳ ◆♦ ❡♥t❛♥t♦✱ ♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❛❞♠✐t❡✲s❡ ❛ ❧❡✐ ❞❡ ✢✉①♦ ❛ss♦❝✐❛❞❛✱ ♣❡❧♦ q✉❡ ♦ â♥❣✉❧♦ ❞❡ ❞✐❧❛tâ♥❝✐❛ é ❛❞♦♣t❛❞♦ ❝♦♠ ✈❛❧♦r ✐❣✉❛❧

                                                                  ′

                                                                  ❛♦ ❞❛ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ φ ✳ ❆ ❚❛❜❡❧❛ ✹✳✶ ❛♣r❡s❡♥t❛ ♦s ♣❛râ♠❡tr♦s ♥❡❝❡ssár✐♦s ♣❛r❛ ❛ ❞❡✜♥✐çã♦ ❞♦ ♠♦❞❡❧♦✱ ❝❧❛ss✐✜❝❛❞♦s ❞❡

                                                                  ❛❝♦r❞♦ ❝♦♠ ❛ ❞❡s✐❣♥❛çã♦ ❞✐s♣♦st❛ ♥♦ ♣r♦❣r❛♠❛ r❡❢❡r✐❞♦✳ ❚❛❜❡❧❛ ✹✳✶✿ P❛râ♠❡tr♦s ✉t✐❧✐③❛❞♦s ♣❡❧♦ ♠♦❞❡❧♦ ▼♦❤r✲❈♦✉❧♦♠❜✳

                                                                  ❚✐♣♦ P❛râ♠❡tr♦ ❉❡s✐❣♥❛çã♦ ❯♥✐❞❛❞❡ E kP a

                                                                  ❘✐❣✐❞❡③ ref ▼ó❞✉❧♦ ❞❡ ❨♦✉♥❣ υ

                                                                  ❈♦❡✜❝✐❡♥t❡ ❞❡ P♦✐ss♦♥ ✲

                                                                  ,

                                                                  c kP a ❈♦❡sã♦ ❡❢❡❝t✐✈❛

                                                                  , o

                                                                  φ )

                                                                  ❘❡s✐stê♥❝✐❛ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ●r❛✉s (

                                                                  o

                                                                  ψ )

                                                                  ➶♥❣✉❧♦ ❞❡ ❞✐❧❛tâ♥❝✐❛ ●r❛✉s (

                                                                  ✹✳✸ ❈❛s♦ ❜❛s❡

                                                                  ❉❡ ♠♦❞♦ ❛ ❡①❡♠♣❧✐✜❝❛r t♦❞♦ ♦ ♣r♦❝❡ss♦ ❞❡ ❝á❧❝✉❧♦✱ ❛♣r❡s❡♥t❛✲s❡ ♦ ❝❛s♦ ❜❛s❡✱ ❝♦♠✉♠ ❛ t♦❞❛s ❛s ❛♥á❧✐s❡s ♣❛r❛♠étr✐❝❛s✱ q✉❡ s❡rã♦ ♣♦st❡r✐♦r♠❡♥t❡ ❛♣r❡s❡♥t❛❞❛s✳

                                                                  ✹✳✸✳✶ ❉❡s❝r✐çã♦ ❞♦ ❝❛s♦ ❜❛s❡

                                                                  ❖ ♠✉r♦✱ ❡♠ L✱ é ♠♦❞❡❧❛❞♦ ❝♦♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❡❧ást✐❝♦ ❧✐♥❡❛r✱ s❡♥❞♦ ♦ s♦❧♦ ♠♦❞❡❧❛❞♦ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ▼♦❤r✲❈♦✉❧♦♠❜✱ r❡❢❡r✐❞♦ ♥❛ s❡❝çã♦ ✹✳✷ ❡ t❡♥❞♦ ❛ ❝❛♠❛❞❛ ❞❡st❡ ♠❛t❡r✐❛❧ ✭❝♦♠ s✉♣❡r❢í❝✐❡ ❤♦r✐✲ ③♦♥t❛❧✮ ✉♠❛ ❡s♣❡ss✉r❛ ❞❡ ✽ ♠❡tr♦s ✭❋✐❣✉r❛ ✹✳✹✮✳ ❙♦❜ ❡st❡s ♠❛t❡r✐❛✐s ❝♦♥s✐❞❡r❛✲s❡ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ❡str❛t♦ s✉✜❝✐❡♥t❡♠❡♥t❡ rí❣✐❞♦✱ ❝♦♠ ❡❧❡✈❛❞❛s ❝❛r❛❝t❡ríst✐❝❛s ♠❡❝â♥✐❝❛s✱ ❞❡ ♠♦❞♦ ❛ q✉❡ s❡ ♣♦ss❛♠ s✉♣♦r ❞❡s❧♦❝❛♠❡♥t♦s ❤♦r✐③♦♥t❛✐s ❡ ✈❡rt✐❝❛✐s ♥✉❧♦s✳ ❖ ♠✉r♦ q✉❡ s✉♣♦rt❛ ♦ t❡rr❡♥♦ t❡♠ ❛s ❞✐♠❡♥sõ❡s r❡♣r❡✲

                                                                  ✻✽ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖ ❋✐❣✉r❛ ✹✳✹✿ ❉✐♠❡♥sõ❡s ❞❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡✿ ♠♦❞❡❧♦ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳ ❈❛s♦ ❜❛s❡✳

                                                                  ❆ ♠❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛ ❞❡✜♥✐çã♦ ❞♦s ♠♦❞❡❧♦s ❛ ❛♥❛❧✐s❛r é ❝♦♠♣♦st❛ ♣♦r ❡❧❡♠❡♥t♦s ❞❡ ✶✺ ♥ós ♥✉♠ ❡st❛❞♦ ♣❧❛♥♦ ❞❡ ❞❡❢♦r♠❛çã♦✳ ❆ ❋✐❣✉r❛ ✹✳✺ ✐❧✉str❛ ❛ r❡❢❡r✐❞❛ ♠❛❧❤❛✱ ❝♦♠♣♦st❛ ♣♦r ✶✷✾✽ ❡❧❡♠❡♥t♦s ❡ ✶✵✼✸✽ ♥ós✱ s❡♥❞♦ ❛ s✉❛ ❧❛r❣✉r❛ t♦t❛❧ ❞❡ ✸✵ ♠❡tr♦s✳

                                                                  ❋✐❣✉r❛ ✹✳✺✿ ▼❛❧❤❛ ❞♦ ♠♦❞❡❧♦ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✿ ❝❛s♦ ❜❛s❡✳ ◆❛ ❚❛❜❡❧❛ ✹✳✷ ✐♥❞✐❝❛♠✲s❡ ♦s ♣❛râ♠❡tr♦s ♥❡❝❡ssár✐♦s ♣❛r❛ ❛ ❞❡s❝r✐çã♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ s♦❧♦ ❡

                                                                  ❞❛ ❡str✉t✉r❛✳ ❚❛❜❡❧❛ ✹✳✷✿ ❈❛r❛❝t❡ríst✐❝❛s ❞♦ s♦❧♦ ❡ ❡str✉t✉r❛ ❝♦♥s✐❞❡r❛❞♦s✳

                                                                  ❆r❡✐❛ ✭❙♦❧♦✮ ❇❡tã♦ ✭❊str✉t✉r❛ ❞❡ s✉♣♦rt❡✮

                                                                  3

                                                                  3

                                                                  γ kN/m 20 γ kN/m

                                                                  25

                                                                  s b

                                                                  υ υ ✵✱✸ ✵✱✷

                                                                  K K ✵✱✺ ✵✱✺

                                                                  3 ′

                                                                  c E (kP a) 34 × 10

                                                                  4 E ref (kP a) 2,5 × 10 o ′

                                                                  ✹✳✸✳ ❈❆❙❖ ❇❆❙❊ ✻✾

                                                                  P♦r ❢♦r♠❛ ❛ ♠♦❜✐❧✐③❛r ♦ ❡st❛❞♦ ❛❝t✐✈♦ ❞♦ s♦❧♦ é ✐♠♣♦st♦✱ à ❡str✉t✉r❛✱ ✉♠ ❞❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧ d ✱ ♥♦ s❡♥t✐❞♦ ♦♣♦st♦ ❛♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦✳ ❖s ❞❡s❧♦❝❛♠❡♥t♦s sã♦ ✐♥❝r❡♠❡♥t❛❞♦s ❡♠ ♠ú❧t✐♣❧♦s ❞❡ 5 mm

                                                                  ❛té s❡ ❛t✐♥❣✐r ✉♠ ✈❛❧♦r ♠í♥✐♠♦ ✭❡st❛❜✐❧✐③❛❞♦✮ ❞❛ ❝♦♠♣♦♥❡♥t❡ ❤♦r✐③♦♥t❛❧ ❞♦ ✐♠♣✉❧s♦✳ ❆ ♣❛rt✐r ❞❡ss❡ ✈❛❧♦r q✉❛❧q✉❡r ❛✉♠❡♥t♦ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧ ♥ã♦ t❡♠ ✐♥✢✉ê♥❝✐❛ s✐❣♥✐✜❝❛t✐✈❛ ♥♦ r❡s✉❧t❛❞♦ ❞♦ ✐♠♣✉❧s♦✳ ❉❡✜♥❡✲s❡ ❝♦♠♦ ❝r✐tér✐♦ ❞❡ ♣❛r❛❣❡♠ ❛ ♦❜t❡♥çã♦ ❞❡ ✉♠ ✈❛❧♦r ❞♦ ✐♠♣✉❧s♦ ✐♥❢❡r✐♦r ❛ ✶✪ ❞♦ ♣r❡❝❡❞❡♥t❡✱ ♦✉ s❡❥❛✱ q✉❛♥❞♦ s❡ ✈❡r✐✜❝❛ q✉❡✿

                                                                  I

                                                                  i+1

                                                                  × 100 − 100 < 1% ✭✹✳✷✮

                                                                  I

                                                                  i

                                                                  ❖s ✐♠♣✉❧s♦s ❤♦r✐③♦♥t❛✐s sã♦ ❞❡t❡r♠✐♥❛❞♦s ♣♦r ✐♥t❡❣r❛çã♦ ❞❛s t❡♥sõ❡s ❞❡ ❞✐r❡❝çã♦ ❤♦r✐③♦♥t❛❧ ♥♦s ❝♦♥t❛❝t♦s ✭❡❧❡♠❡♥t♦s ❞❡ ✐♥t❡r❢❛❝❡✮ s♦❧♦✲❡str✉t✉r❛✱ s❡♥❞♦ ❛s ❝❛r❣❛s ✈❡rt✐❝❛✐s ♦❜t✐❞❛s ❛tr❛✈és ❞❛ ✐♥t❡❣r❛✲ çã♦ ❞♦ ❞✐❛❣r❛♠❛ ❞❡ t❡♥sõ❡s ❞❡ ❞✐r❡❝çã♦ ✈❡rt✐❝❛❧ ♥❛ ❜❛s❡ ❞♦ ♠✉r♦✳

                                                                  ✹✳✸✳✷ ❘❡s✉❧t❛❞♦s ❡ ❛♥á❧✐s❡

                                                                  ◆♦ q✉❡ r❡s♣❡✐t❛ ❛♦ ❝❛s♦ ❜❛s❡✱ ❝♦♥❢♦r♠❡ s❡ ♣♦❞❡ ♦❜s❡r✈❛r ♥❛ ❋✐❣✉r❛ ✹✳✻✱ ♦ ✐♠♣✉❧s♦ ❡st❛❜✐❧✐③❛ q✉❛♥❞♦ s❡ ✐♠♣õ❡ ✉♠ ❞❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧ ❞❡ 15 mm✳ ❈♦♥✜r♠❛✲s❡ t❛♠❜é♠ q✉❡ ❛ ✐♠♣♦s✐çã♦ ❞❡ ✉♠ ❞❡s❧♦✲ ❝❛♠❡♥t♦ ❞❡ 20 mm ♥ã♦ r❡✈❡❧❛ ✐♥✢✉ê♥❝✐❛ s✐❣♥✐✜❝❛t✐✈❛ ♥♦ ✈❛❧♦r ❞♦ ✐♠♣✉❧s♦✳

                                                                  320 300 280 260

                                                                  (kPa) H

                                                                  I 240 220 200 0,005 0,01 0,015 0,02

                                                                  Deslocamento horizontal (m)

                                                                  ❋✐❣✉r❛ ✹✳✻✿ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❤♦r✐③♦♥t❛❧ ❡♠ ❢✉♥çã♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧✿ ❝❛s♦ ❜❛s❡✳

                                                                  ✼✵ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖

                                                                  0,5 0,45 0,4

                                                                  δ tg

                                                                  0,35 0,3 0,25 0,005 0,01 0,015 0,02

                                                                  Deslocamento horizontal (m)

                                                                  ❋✐❣✉r❛ ✹✳✼✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ r❡❧❛çã♦ ❡♥tr❡ ❛s ❝❛r❣❛s ❤♦r✐③♦♥t❛✐s ❡ ✈❡rt✐❝❛✐s ✭❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦✮ ❡♠ ❢✉♥çã♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧✿ ❝❛s♦ ❜❛s❡✳

                                                                  ❆ ❋✐❣✉r❛ ✹✳✽ ❛♣r❡s❡♥t❛ ❛ ❞❡❢♦r♠❛❞❛ ♦r✐❣✐♥❛❞❛ ♣❛r❛ ♦ ❝❛s♦ ❜❛s❡ ❡ ♣❛r❛ ♦ ❞❡s❧♦❝❛♠❡♥t♦ ❞❡ 15 mm✳ ❆ ❋✐❣✉r❛ ✹✳✾ ♠♦str❛ ♦s ❞❡s❧♦❝❛♠❡♥t♦s ❤♦r✐③♦♥t❛✐s✳ ◆❡st❛ ✜❣✉r❛ ✭✹✳✾✮ ♣♦❞❡ ♥♦t❛r✲s❡ ❛ ♣♦s✐çã♦ ❞❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧✱ ❛ss✐♠ ❝♦♠♦ ❛ s✉♣❡r❢í❝✐❡ q✉❡ ❞❡✜♥❡ ❛ ❝✉♥❤❛ ❛❝t✐✈❛✳ ❋✐❣✉r❛ ✹✳✽✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❞❡❢♦r♠❛çã♦ ❞♦ s♦❧♦ ❛♣ós ❛ ✐♠♣♦s✐çã♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧ ✭d = 15 mm

                                                                  ✮✿ ❝❛s♦ ❜❛s❡✳ ❋✐❣✉r❛ ✹✳✾✿ ❘❡♣r❡s❡♥t❛çã♦✱ ♣♦r ❣r❛❞❛çã♦ ❞❡ ❝♦r❡s✱ ❞♦s ❞❡s❧♦❝❛♠❡♥t♦s ❤♦r✐③♦♥t❛✐s ♥♦ ♠❛❝✐ç♦ ✭d = 15 mm

                                                                  ✮✿ ❝❛s♦ ❜❛s❡✳

                                                                  ✹✳✸✳ ❈❆❙❖ ❇❆❙❊ H 1 2 2 ✼✶

                                                                  B I a

                                                                  / 2 γH = ❚❛❜❡❧❛ ✹✳✸✿ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❛tr❛✈és ❞♦s ❞✐❢❡r❡♥t❡s ♠ét♦❞♦s✿ ❡ tan δ✳ ❈❛s♦ ❜❛s❡✿

                                                                  H ′ o 2 o

                                                                  0, 438 = 30 = ❀ φ ❀ R inter ❀ i = 0 ✳

                                                                3 H

                                                                  1 2 H

                                                                  I a 2 γH

                                                                  I [kN/m] / V [kN/m] tan δ ▼ét♦❞♦

                                                                  a

                                                                  R ✷✶✸✱✸ ✵✱✸✸✸ ✻✼✼✱✺ ✵✱✸✶✺

                                                                  C

                                                                  1 ✷✶✵✱✷ ✵✱✸✷✽ ✻✽✼✱✸ ✵✱✸✵✻

                                                                  C

                                                                  2 ✷✵✹✱✾ ✵✱✸✷✵ ✻✾✸✱✸ ✵✱✷✾✻

                                                                  ▼ét♦❞♦ ♥✉♠ér✐❝♦ ✷✵✶✱✽ ✵✱✸✶✹ ✻✾✵✱✽ ✵✱✷✾✷ ◆♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ ❛♦s r❡s✉❧t❛❞♦s ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❡ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ♦❜t✐❞♦s✱ ♣♦❞❡✲ s❡ ❛✜r♠❛r q✉❡ ❡st❡s s❡ r❡✈❡❧❛♠ ❜❛st❛♥t❡ ♣ró①✐♠♦s ❞♦s ♦❜t✐❞♦s ❛tr❛✈és ❞♦s ♠ét♦❞♦s tr❛❞✐❝✐♦♥❛✐s✳ ◆ã♦

                                                                  ♦❜st❛♥t❡✱ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❡❧♦ ♠ét♦❞♦ R ♠♦str❛♠✲s❡ s✉♣❡r✐♦r❡s ❛♦s r❡st❛♥t❡s✳ ❆s s✉♣❡r❢í❝✐❡s ❛ q✉❡ s❡ ❢❡③ r❡❢❡rê♥❝✐❛ ❛♥t❡r✐♦r♠❡♥t❡✱ ❛ ♣r♦♣ós✐t♦ ❞❛ ❋✐❣✉r❛ ✹✳✾✱ sã♦ ✐❣✉❛❧♠❡♥t❡

                                                                  ✈✐sí✈❡✐s ❛tr❛✈és ❞❛ r❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s✱ q✉❡ s❡ ✈❡r✐✜❝❛ ❡st❛r❡♠ ❝♦♥❝❡♥tr❛❞♦s ❡♠ ❜❛♥❞❛s✳ ◆❛ ❋✐❣✉r❛ ✹✳✶✵ ❛♣r❡s❡♥t❛♠✲s❡ ♦s ♣♦♥t♦s ♣❧ást✐❝♦s ♣❛r❛ ♦s ✈ár✐♦s ❞❡s❧♦❝❛♠❡♥t♦s ❞♦ ♠✉r♦✱ s♦❜r❡♣♦♥❞♦✲s❡

                                                                  2

                                                                  ❛s s✉♣❡r❢í❝✐❡s q✉❡ ❞❡✜♥❡♠ ♦ ♣❛r❛♠❡♥t♦ ✈✐rt✉❛❧ ❞♦ ♠✉r♦ ♦❜t✐❞❛s ❛tr❛✈és ❞♦ ♠ét♦❞♦ C ✳ ❊ss❛s s✉♣❡r❢í❝✐❡s H

                                                                  C2,tan δ

                                                                  sã♦ ✐❞❡♥t✐✜❝❛❞❛s ♣❡❧❛s ✐♥❝❧✐♥❛çõ❡s β C2,I ❡ β ✱ q✉❡ r❡s✉❧t❛♠ ❞❛ ♠❛①✐♠✐③❛çã♦ ❞❛ ❝♦♠♣♦♥❡♥t❡ a ❤♦r✐③♦♥t❛❧ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❡ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❈♦♠♣❧❡♠❡♥t❛r♠❡♥t❡✱ s♦❜r❡♣õ❡♠✲s❡ ❛s s✉♣❡r❢í❝✐❡s ♦❜t✐❞❛s ❛tr❛✈és ❞❛ ❡①♣r❡ssã♦ ✷✳✶✺ ✭❇❛r❣❤♦✉t❤✐✱ ✶✾✾✵✮✱ ♣r❡s❡♥t❡ ♥❛ s❡❝çã♦ ✷✳✹✳✸✳ ◆❛ ❋✐❣✉r❛ ✹✳✶✵ ❛♣❡♥❛s é ❛♣r❡s❡♥t❛❞❛ ❛ ár❡❛ ❡♠ q✉❡ s❡ ❡♥❝♦♥tr❛ ♦ ♠✉r♦ ❡ ♦s ♣♦♥t♦s ♣❧❛st✐✜❝❛❞♦s ❞♦ s♦❧♦✱ ✉♠❛ ✈❡③ q✉❡ ❛ r❡st❛♥t❡ ár❡❛ ❞♦ t❡rr❡♥♦ ♥ã♦ s♦❢r❡ q✉❛❧q✉❡r t✐♣♦ ❞❡ ♣❧❛st✐✜❝❛çã♦ r❡❧❡✈❛♥t❡✳

                                                                ✭❛✮ d = 0 mm. ✭❜✮ d = 5 mm. ✭❝✮ d = 10 mm.

                                                                  

                                                                ✭❞✮ d = 15 mm. ✭❡✮ d = 20 mm.

                                                                  ✼✷ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖ ❞❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧ ✐♥❢❡r✐♦r ❛♦ ❝♦rr❡s♣♦♥❞❡♥t❡ à ❡st❛❜✐❧✐③❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✳ ❊ss❛ s✉♣❡r❢í❝✐❡ é✱ ♣❛r❛ ♦ ❝❛s♦ ❜❛s❡✱ ♠✉✐t♦ ♣ró①✐♠❛ ❞❛ ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ♠ét♦❞♦ C

                                                                  2 ✳

                                                                  ◆♦t❡✲s❡✱ ✜♥❛❧♠❡♥t❡✱ q✉❡ ♥♦ ❝❛s♦ ❡s❝♦❧❤✐❞♦ ❝♦♠♦ ❜❛s❡✱ ❤❛✈✐❛ ✉♠❛ r❛③♦á✈❡❧ ❝♦✐♥❝✐❞ê♥❝✐❛ ❡♥tr❡ ♦s r❡s✉❧t❛❞♦s ❞♦s ♠ét♦❞♦s R✱ C

                                                                  1 ❡ C 2 ✱ ❝♦♥❢♦r♠❡ s❡ ♣♦❞❡ ✈❡r ♥❛ ❚❛❜❡❧❛ ✹✳✸ ❡ ✈❡r✐✜❝❛r ♥♦ ❈❛♣ít✉❧♦ ✸✳ ❖s

                                                                  r❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ♦❜t✐❞♦s sã♦✱ ♣♦r s✉❛ ✈❡③✱ t❛♠❜é♠ s❡♠❡❧❤❛♥t❡s àq✉❡❧❡s✳

                                                                  ✹✳✹ ❆♥á❧✐s❡ ♣❛r❛♠étr✐❝❛ ✹✳✹✳✶ ❉❡s❝r✐çã♦ ❞♦s ❝❛s♦s ❛♥❛❧✐s❛❞♦s

                                                                  P❛r❛ ❛ ♣r❡s❡♥t❡ ❛♥á❧✐s❡ ♣❛r❛♠étr✐❝❛✱ ♦ ♣r♦❝❡ss♦ ❞❡ ❝á❧❝✉❧♦ é ✐❞ê♥t✐❝♦ ❛♦ ❞♦ ❝❛s♦ ❜❛s❡✳ ❆❞♦♣t❛♠✲s❡ ❛s ❞✐♠❡♥sõ❡s ✐❧✉str❛❞❛s ♥❛ ❋✐❣✉r❛ ✹✳✹ ♣❛r❛ ❛ ❡str✉t✉r❛ ❡ ✈❛r✐❛♠✲s❡ ♦s ✈❛❧♦r❡s r❡❧❛t✐✈♦s à r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦✱ à ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ ❡ ❛♦ ❢❛❝t♦r ❞❡ r❡❞✉çã♦ ♣r❡s❡♥t❡ ♥♦ ❝♦♥t❛❝t♦

                                                                  ′

                                                                  s♦❧♦✲❡str✉t✉r❛✱ φ ✱ i ❡ R inter ✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❆ ✐♥✢✉ê♥❝✐❛ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ ✭B

                                                                  

                                                                1 ✮ é t❛♠❜é♠ ❛❧✈♦ ❞❡ ❛♥á❧✐s❡✱ ♣❡❧♦ q✉❡ ♦s ✈❛❧♦r❡s r❡❢❡r❡♥t❡s àq✉❡❧❛ sã♦ ✈❛r✐❛❞♦s✱ ❝♦♠❜✐♥❛♥❞♦✲♦s

                                                                  ❝♦♠ ♦s r❡st❛♥t❡s ♣❛râ♠❡tr♦s✳ ❆ ❚❛❜❡❧❛ ✹✳✹ ❛♣r❡s❡♥t❛ t♦❞♦s ♦s ♣❛râ♠❡tr♦s ❛ ❛♥❛❧✐s❛r✱ ❡①♣♦♥❞♦✲s❡ ❛s ❝♦♠❜✐♥❛çõ❡s ❝♦♠ ♦s r❡st❛♥t❡s✳

                                                                  ❚❛❜❡❧❛ ✹✳✹✿ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s✳

                                                                  P❛râ♠❡tr♦ ❛ B 2 ′ o 1 o

                                                                  B (m) R inter φ ( ) i ( )

                                                                  H ❛♥❛❧✐s❛r 1 1 2 3 ,5 = 0, 438

                                                                  

                                                                R inter ✵❀ ❀ ❀ ❀ 1 ✸✵ ✹ ✵❀ ✺❀ ✶✵❀ ✶✺❀ ✷✵

                                                                3 2 ✷✵❀ ✷✺❀ ✸✵❀ 2 3 8 o ′

                                                                  φ ( ) 3 ✹ [0, 438] ✵❀ ✺❀ ✶✵❀ ✶✺❀ ✷✵ ✸✺❀ ✹✵❀ ✹✺ ✵✱✺[0]❀ ✵✱✻[0, 013]❀ ✶[0, 063]❀ ✵ ❛ ✸✺✱ 1 B 2 2 ✶✱✺[0, 125]❀ ✷[0, 188]❀ ✸[0, 313]❀

                                                                  B (m) ✸✵❀ ✹✵❀ ✹✺ ❝♦♠ ♠á①✐♠♦ ❞❡ H 3

                                                                  ✹[0, 438]❀ ✺[0, 563]❀ ✻[0, 688]❀ o ′

                                                                  − φ

                                                                  5 2 ✼[0, 813]❀ ✽[0, 938]❀ ✾[1, 063]❀ ✶✵[1, 188] o

                                                                  i ( ) 3 ✸✵ ✹ [0, 438] ✵ ❛ ✷✺ ❖ ❡st✉❞♦ ❜❛s❡✐❛✲s❡ ♥♦s r❡s✉❧t❛❞♦s ❞❡ (4 × 5) + (5 × 5) + (13 × 16) + (12 × 6) + 6 = 331 ❝á❧❝✉❧♦s✱

                                                                  ❝♦❜r✐♥❞♦ ✉♠ ❧❡q✉❡ ❝♦♥s✐❞❡rá✈❡❧ ❞❡ s✐t✉❛çõ❡s ❞✐st✐♥t❛s✳

                                                                  ✹✳✹✳✷ ❆♥á❧✐s❡ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞♦ ❢❛❝t♦r R inter

                                                                  ✹✳✹✳✷✳✶ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s P❛r❛ ♦ ❡st✉❞♦ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞♦ ❢❛❝t♦r ❞❡ r❡❞✉çã♦✱ ♣r❡s❡♥t❡ ♥♦ ❝♦♥t❛❝t♦ s♦❧♦✲❡str✉t✉r❛✱ é ❝♦♥s✐❞❡r❛❞♦

                                                                  o

                                                                  ✉♠ s♦❧♦ ❝❛r❛❝t❡r✐③❛❞♦ ❝♦♠ ✉♠ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞❡ 30 ✳ ❆s ❞✐♠❡♥sõ❡s ❞❛ ❡str✉t✉r❛ ❛❞♦♣t❛❞❛s ♣❛r❛ ❛ ❛♥á❧✐s❡ ♣r❡s❡♥t❡ sã♦ ❛s ❞✐s♣♦st❛s ♥❛ ❋✐❣✉r❛ ✹✳✹✳ P❛r❛ ❛s ♠❡s♠❛s ❝♦♥❞✐çõ❡s ❞♦ s♦❧♦ ❡ ❞♦ ♠✉r♦✱ sã♦ ❝♦♥s✐❞❡r❛❞❛s ❞✐❢❡r❡♥t❡s ✐♥❝❧✐♥❛çõ❡s ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦✱ ❝♦♠ ❛ ✜♥❛❧✐❞❛❞❡ H 1 2 I a 2 / γH

                                                                  / ❞❡ s❡ ❛♥❛❧✐s❛r t❛♠❜é♠ ❛ ❡✈♦❧✉çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ✭❞❛❞♦ ♣❡❧❛ r❡❧❛çã♦ ✮ ❡ ❞❛ ❝♦♥❞✐çã♦ ❞❡

                                                                  ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✼✸

                                                                  ✹✳✹✳✷✳✷ ❘❡s✉❧t❛❞♦s ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s✱ ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ ❛♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✱ ♣❛r❛ ♦ t✐♣♦ ❞❡ s♦❧♦ ❝♦♥s✐❞❡r❛❞♦✱ sã♦ ❛♣r❡s❡♥t❛❞♦s ♥❛ ❋✐❣✉r❛ ✹✳✶✶ ❡♠ ❢✉♥çã♦ ❞♦ ♣❛râ♠❡tr♦ R inter ✳ ❖s r❡s✉❧t❛❞♦s sã♦ s♦❜r❡♣♦st♦s ❛♦s ♦❜t✐❞♦s ❛tr❛✈és ❞♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✱ ♣♦r ❢♦r♠❛ ❛ ♣♦❞❡r❡♠ ❝♦♠♣❛r❛r✲s❡ ❡♥tr❡ s✐✳

                                                                  ◆❛ ❋✐❣✉r❛ ✹✳✶✷ ❡♥❝♦♥tr❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s r❡❢❡r❡♥t❡s à ❡✈♦❧✉çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦ ✭❞❛❞❛ ♣♦r tan δ✮✱ ❡♠ ❢✉♥çã♦ ❞♦ ♣❛râ♠❡tr♦ ❛♥❛❧✐s❛❞♦✳

                                                                  0,45 0,45 0,45 0,4 0,4 0,4 )

                                                                2 H

                                                                  γ /(0,5

                                                                  H a a a

                                                                  I 0,35 0,35 0,35 0,3 0,3 0,3

                                                                  1/3 1/2 2/3 1 1/3 1/2 2/3 1 1/3 1/2 2/3

                                                                  1 R R R inter inter inter o o o

                                                                  

                                                                ✭❛✮ i = 0 ✭❜✮ i = 5 ✭❝✮ i = 10

                                                                0,55 0,55 0,5 0,5

                                                                  )

                                                                2 H

                                                                  γ /(0,5

                                                                  H a a

                                                                  I 0,45 0,45 0,4 0,4

                                                                  1/3 1/2 2/3 1 1/3 1/2 2/3

                                                                  1 R R inter inter o o

                                                                  

                                                                ✭❞✮ i = 15 ✭❡✮ i = 20

                                                                2 B ′ o

                                                                  = 0, 438 = 30 ❋✐❣✉r❛ ✹✳✶✶✿ ■♥✢✉ê♥❝✐❛ ❞♦ ❢❛❝t♦r R inter ♥♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ♣❛r❛ ❀ φ ✳

                                                                  ✼✹ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖

                                                                  0,4 0,4 0,4 0,35 0,35 0,35 δ tg

                                                                  0,3 0,3 0,3 0,25 0,25 0,25 0,2 0,2 0,2 1/3 1/2 2/3

                                                                  1 1/3 1/2 2/3 1 1/3 1/2 2/3

                                                                  1 R R R inter inter inter o o o

                                                                  

                                                                ✭❛✮ i = 0 ✭❜✮ i = 5 ✭❝✮ i = 10

                                                                0,45 0,45 0,4 0,4

                                                                  δ tg

                                                                  0,35 0,35 0,3 0,3 1/3 1/2 2/3 1 1/3 1/2 2/3

                                                                  1 R R inter inter o o

                                                                  

                                                                ✭❞✮ i = 15 ✭❡✮ i = 20

                                                                2 B

                                                                  = 0, 438 ❋✐❣✉r❛ ✹✳✶✷✿ ■♥✢✉ê♥❝✐❛ ❞♦ ❢❛❝t♦r R inter ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦ ♣❛r❛ ❀

                                                                  H ′ o

                                                                  φ = 30 ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳

                                                                  ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✼✺

                                                                  ❆♣r❡s❡♥t❛♠✲s❡ ❞✉❛s ❋✐❣✉r❛s ❡♠ q✉❡ s❡ ✐❧✉str❛♠ ♦s ♣♦♥t♦s ♣❧ást✐❝♦s ♦❜t✐❞♦s ♣❡❧♦ ♠ét♦❞♦ ♥✉♠ér✐❝♦✱

                                                                  o o

                                                                  ✈❡r✐✜❝❛♥❞♦✲s❡ q✉❡ ❢♦r♠❛♠ ❜❛♥❞❛s✳ ❯♠❛ ✭❋✐❣✉r❛ ✹✳✶✸✮ ❡♠ q✉❡ i = 0 ❡ ♦✉tr❛ ❡♠ q✉❡ i = 15 ✭❋✐❣✉r❛ ✹✳✶✹✮✳ ❆s s✉♣❡r❢í❝✐❡s sã♦ ❛♣r❡s❡♥t❛❞❛s ❡♠ ❢✉♥çã♦ ❞♦ ❢❛❝t♦r R inter ❛❞♦♣t❛❞♦✱ s♦❜r❡♣♦♥❞♦✲s❡ àq✉❡❧❛s ❛s ♦❜t✐❞❛s ❛tr❛✈és ❞♦ ♠ét♦❞♦ C

                                                                  2 ✳ 1 inter = 0

                                                                  

                                                                ✭❛✮ R ✭❜✮ R inter =

                                                                2

                                                                ✭❝✮ R inter = 1

                                                                  ′ o o

                                                                  = 4 m = 30 ❋✐❣✉r❛ ✹✳✶✸✿ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞❡ R inter ♣❛r❛ B

                                                                  1 ❀ φ ❀ i = 0 ✳

                                                                  ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ C

                                                                  2 ✳

                                                                  ✼✻ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖

                                                                  

                                                                ✭❛✮ R inter = 0

                                                                  1

                                                                ✭❜✮ R inter =

                                                                2

                                                                  ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✼✼

                                                                  ✹✳✹✳✷✳✸ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s 2 B

                                                                  H

                                                                  / P❛r❛ ♦ ❝❛s♦ ❞❛ r❡❧❛çã♦ ❡st✉❞❛❞❛✱ ♣♦❞❡ ❛✜r♠❛r✲s❡ q✉❡ ♥ã♦ ❡①✐st❡ ❝♦✐♥❝✐❞ê♥❝✐❛ ❞❛ ❡✈♦❧✉çã♦ ❞❡

                                                                  H

                                                                  I ❡ ❞❡ tan δ ❝♦♠ ♦ ♣❛râ♠❡tr♦ R inter ❡♥tr❡ ♦ ♠ét♦❞♦ C

                                                                  2 ❡ ♦ ♠ét♦❞♦ ♥✉♠ér✐❝♦✳ ◆♦ q✉❡ r❡s♣❡✐t❛ ❛♦ a H

                                                                  ♠ét♦❞♦ C

                                                                  2 ✱ ♦ ❛✉♠❡♥t♦ ❞❡ R inter ✐♠♣❧✐❝❛ ❛ ❞✐♠✐♥✉✐çã♦ ❞♦s r❡s✉❧t❛❞♦s ❞❡ I a ❡ ❞❡ tan δ✱ ❛♦ ♣❛ss♦ q✉❡

                                                                  ♥♦ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ❛q✉❡❧❡ ♣❛râ♠❡tr♦ ♣❛r❡❝❡ t❡r ❡❢❡✐t♦ ♠✉✐t♦ r❡❞✉③✐❞♦✱ ♥ã♦ ❤❛✈❡♥❞♦ ♣r❛t✐❝❛♠❡♥t❡

                                                                  o inter

                                                                  ✈❛r✐❛çã♦ ❞❛q✉❡❧❛s ❣r❛♥❞❡③❛s ❝♦♠ R ✭❛s ❡①❝❡♣çõ❡s ✈❡r✐✜❝❛♠✲s❡ ♣❛r❛ i ≥ 15 ✮✳ P❡❧❛ ❛♥á❧✐s❡ ❞♦s

                                                                  H

                                                                  2

                                                                  r❡s✉❧t❛❞♦s ❝♦♥st❛t❛✲s❡ q✉❡ ♦s ✈❛❧♦r❡s ❞❡ I a ❞❛❞♦s ♣❡❧♦ ♠ét♦❞♦ C sã♦ ♠❛✐♦r❡s ❞♦ q✉❡ ♦s ♦❜t✐❞♦s ♣❡❧♦

                                                                  inter = 1

                                                                  ♠ét♦❞♦ ♥✉♠ér✐❝♦✱ s❡♥❞♦ ♣ró①✐♠♦s q✉❛♥❞♦ R ✳

                                                                  inter

                                                                  ◆ã♦ ♦❜st❛♥t❡✱ ❛s ❋✐❣✉r❛s ✹✳✶✶ ❡ ✹✳✶✷ ♠♦str❛♠ ✉♠❛ ✐♥✢✉ê♥❝✐❛ ♣❡q✉❡♥❛ ❞❡ R ♥♦s r❡s✉❧t❛❞♦s✳ ❉♦ ♠❡s♠♦ ♠♦❞♦✱ ♣❡❧❛ ❛♥á❧✐s❡ ❞❛s ❋✐❣✉r❛s ✹✳✶✸ ❡ ✹✳✶✹✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ❛❧t❡r❛çã♦ ❞♦ ❢❛❝t♦r ❞❡ r❡❞✉çã♦ R inter ♥ã♦ ♣r♦❞✉③ ✐♥✢✉ê♥❝✐❛ s✐❣♥✐✜❝❛t✐✈❛ ♥❛s s✉♣❡r❢í❝✐❡s ♦❜t✐❞❛s ❛tr❛✈és ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s✳ H

                                                                  ■♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞♦ ✈❛❧♦r ❞❡ i✱ ❛s s✉♣❡r❢í❝✐❡s ❞❡✜♥✐❞❛s ♣♦r β ❡ β C2,tan δ ♠♦str❛♠✲s❡ ❝♦✐♥❝✐❞❡♥✲

                                                                  C2,I a

                                                                  t❡s ❡♥tr❡ s✐ ❡ s❡♠❡❧❤❛♥t❡s às ❜❛♥❞❛s ♦❜t✐❞❛s ♥✉♠❡r✐❝❛♠❡♥t❡✳ P❡❧❛ ❛♥á❧✐s❡ ❞❛s s✉♣❡r❢í❝✐❡s ♦❜t✐❞❛s ♣♦r ❇❛r❣❤♦✉t❤✐ ♣❡r❝❡❜❡✲s❡ q✉❡ ❛q✉❡❧❛s sã♦ ♣ró①✐♠❛s ❞❛s ❜❛♥❞❛s ❢♦r♠❛❞❛s ♣❡❧♦s ♣♦♥t♦s ♣❧ást✐❝♦s✳

                                                                  ′ ✹✳✹✳✸ ❆♥á❧✐s❡ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦✱ φ

                                                                  ✹✳✹✳✸✳✶ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s

                                                                  2

                                                                  /

                                                                  3 P❛r❛ ❛ ♣r❡s❡♥t❡ ❛♥á❧✐s❡✱ é ❝♦♥s✐❞❡r❛❞♦ ✉♠ ❢❛❝t♦r ❞❡ r❡❞✉çã♦ R inter ❞❡ ✱ ✈❛r✐❛♥❞♦✲s❡ ♦ ✈❛❧♦r ❞❛ ′

                                                                  r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦✱ ❞❛❞❛ ♣♦r φ ✳ P❛r❛ ❛s ♠❡s♠❛s ❝♦♥❞✐çõ❡s ❞♦ s♦❧♦ ❡ ❞♦ ♠✉r♦✱ sã♦ ❝♦♥s✐❞❡r❛❞❛s ❞✐❢❡r❡♥t❡s ✐♥❝❧✐♥❛çõ❡s ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦✱ ❝♦♠ ❛ ✜♥❛❧✐❞❛❞❡ ❞❡ s❡ ❛♥❛❧✐s❛r t❛♠❜é♠ ❛ ❡✈♦❧✉çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❡ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛q✉❡❧❛ ✐♥❝❧✐♥❛çã♦✳ ✹✳✹✳✸✳✷ ❘❡s✉❧t❛❞♦s H 1 2 I a 2

                                                                  / / γH ❆ ❋✐❣✉r❛ ✹✳✶✺ ❛♣r❡s❡♥t❛ ❛ ❡✈♦❧✉çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✱ ❞❛❞❛ ♣❡❧❛ r❛③ã♦ ❛❞✐♠❡♥s✐♦♥❛❧ ✱ ❡♠

                                                                  ′

                                                                  ❢✉♥çã♦ ❞❛ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦ φ ✳ ❖s r❡s✉❧t❛❞♦s sã♦ s♦❜r❡♣♦st♦s ❛♦s ♦❜t✐❞♦s ❛tr❛✈és ❞♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✱ ♣♦r ❢♦r♠❛ ❛ ♣♦❞❡r❡♠ ❝♦♠♣❛r❛r✲s❡ ❡♥tr❡ s✐✳

                                                                  ◆❛ ❋✐❣✉r❛ ✹✳✶✻ ❡♥❝♦♥tr❛♠✲s❡ ♣r❡s❡♥t❡s ♦s r❡s✉❧t❛❞♦s r❡❢❡r❡♥t❡s à ❡✈♦❧✉çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛✲

                                                                  ′

                                                                  ♠❡♥t♦ ❞♦ ♠✉r♦✱ ❞❛❞❛ ♣♦r tan δ✱ ❡♠ ❢✉♥çã♦ ❞♦ ♣❛râ♠❡tr♦ φ ✳

                                                                  ✼✽ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖

                                                                  25

                                                                  25

                                                                  30

                                                                  35

                                                                  40

                                                                  45 φ

                                                                  ’ ( o

                                                                  )

                                                                  I H a /(0,5 γ H

                                                                  2 )

                                                                  ✭❞✮ i = 15 o

                                                                  0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

                                                                  1

                                                                  20

                                                                  30

                                                                  1

                                                                  35

                                                                  40

                                                                  45 φ

                                                                  ’ ( o

                                                                  ) ✭❡✮ i = 20 o

                                                                  ❋✐❣✉r❛ ✹✳✶✺✿ ■♥✢✉ê♥❝✐❛ ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ φ

                                                                  ′

                                                                  ♥♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ♣❛r❛

                                                                  B 2 H

                                                                  = 0, 438

                                                                  ❀ R inter =

                                                                  2

                                                                  3

                                                                  20

                                                                  0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

                                                                  0,1 0,2 0,3 0,4 0,5 0,6 0,7

                                                                  25

                                                                  20

                                                                  25

                                                                  30

                                                                  35

                                                                  40

                                                                  45 φ

                                                                  ’ ( o

                                                                  )

                                                                  I H a /(0,5 γ H

                                                                  2 )

                                                                  ✭❛✮ i = 0 o

                                                                  0,1 0,2 0,3 0,4 0,5 0,6 0,7

                                                                  20

                                                                  

                                                                30

                                                                  ) ✭❝✮ i = 10 o

                                                                  35

                                                                  40

                                                                  45 φ

                                                                  ’ ( o

                                                                  ) a

                                                                  ✭❜✮ i = 5 o

                                                                  0,1 0,2 0,3 0,4 0,5 0,6 0,7

                                                                  20

                                                                  25

                                                                  30

                                                                  35

                                                                  40

                                                                  45 φ

                                                                  ’ ( o

                                                                  ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳

                                                                  ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✼✾

                                                                  30

                                                                  25

                                                                  30

                                                                  35

                                                                  40

                                                                  45 φ

                                                                  ’ ( o

                                                                  ) tg δ

                                                                  ✭❞✮ i = 15 o

                                                                  0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

                                                                  20

                                                                  25

                                                                  35

                                                                  0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

                                                                  40

                                                                  45 φ

                                                                  ’ ( o

                                                                  ) ✭❡✮ i = 20 o

                                                                  ❋✐❣✉r❛ ✹✳✶✻✿ ■♥✢✉ê♥❝✐❛ ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ φ

                                                                  ′

                                                                  ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦ ♣❛r❛

                                                                  B 2 H

                                                                  = 0, 438 ❀ R inter

                                                                  =

                                                                  2

                                                                  3

                                                                  20

                                                                  ) ✭❝✮ i = 10 o

                                                                  0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

                                                                  25

                                                                  20

                                                                  25

                                                                  30

                                                                  35

                                                                  40

                                                                  45 φ

                                                                  ’ ( o

                                                                  ) tg δ

                                                                  ✭❛✮ i = 0 o

                                                                  0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

                                                                  20

                                                                  

                                                                30

                                                                  ’ ( o

                                                                  35

                                                                  40

                                                                  45 φ

                                                                  ’ ( o

                                                                  ) ✭❜✮ i = 5 o

                                                                  0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

                                                                  20

                                                                  25

                                                                  30

                                                                  35

                                                                  40

                                                                  45 φ

                                                                  ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳

                                                                  ✽✵ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖ ❆s s✉♣❡r❢í❝✐❡s ♦❜t✐❞❛s ❛tr❛✈és ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s sã♦ ❛♣r❡s❡♥t❛❞❛s ♥❛s ❋✐❣✉r❛s ✹✳✶✼ ❡ ✹✳✶✽✱ ❡♠

                                                                  ′ o o

                                                                  ❢✉♥çã♦ ❞❛ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦ φ ✱ ❝♦♠ ✐♥❝❧✐♥❛çõ❡s i = 0 ❡ i = 15 ✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❆ ❡st❛s sã♦ s♦❜r❡♣♦st❛s ❛s ♦❜t✐❞❛s ❛tr❛✈és ❞♦ ♠ét♦❞♦ C

                                                                  2 ♣♦r ❢♦r♠❛ ❛ s❡r❡♠ ❝♦♠♣❛r❛❞❛s✳ o o ′

                                                                  ′ = 20 = 25 ✭❛✮ φ ✭❜✮ φ o o ′

                                                                  ′

                                                                ✭❝✮ φ = 30 ✭❞✮ φ = 35

                                                                o o ′

                                                                  ′

                                                                ✭❡✮ φ = 40 ✭❢✮ φ = 45

                                                                  ′ o

                                                                  2

                                                                  = 4 m = /

                                                                  3

                                                                  ❋✐❣✉r❛ ✹✳✶✼✿ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞❡ φ ♣❛r❛ B

                                                                  1 ❀ R inter ❀ i = 0 ✳

                                                                  ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ C

                                                                  2 ✳

                                                                  ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✽✶

                                                                  ✭❛✮ φ ′

                                                                  = 20 o

                                                                  ✭❜✮ φ ′

                                                                  = 25 o

                                                                  ✭❝✮ φ ′

                                                                  = 30 o

                                                                  ✭❞✮ φ ′

                                                                  = 35 o

                                                                  ✭❡✮ φ ′

                                                                  = 40 o

                                                                  ✭❢✮ φ ′

                                                                  = 45 o

                                                                  ✽✷ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖ ✹✳✹✳✸✳✸ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s 2 B

                                                                  H

                                                                  / P❛r❛ ♦ ❝❛s♦ ❞❛ r❡❧❛çã♦ ❞❡ ❝♦♥s✐❞❡r❛❞❛ ♣♦❞❡ ❛✜r♠❛r✲s❡ q✉❡ ❡①✐st❡ q✉❛s❡ ❝♦✐♥❝✐❞ê♥❝✐❛ ❡♥tr❡ ♦s r❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ❡ ♦s ♦❜t✐❞♦s ❛tr❛✈és ❞♦s ♠ét♦❞♦s R✱ C

                                                                  1 ❡ C 2 ✳ ❖s r❡s✉❧t❛❞♦s ♠♦str❛♠✱ ♣♦r ♦✉tr♦ H

                                                                  ❧❛❞♦✱ ❛ ❝♦♥s✐❞❡rá✈❡❧ ✐♥✢✉ê♥❝✐❛ ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦ ♥♦s ✈❛❧♦r❡s ❞❡ I a ❡ ❞❡ tan δ✱ s❡♥❞♦ ♦s ♠❛✐♦r❡s ✈❛❧♦r❡s ❞❛q✉❡❧❛s r❡❧❛çõ❡s ♦❜t✐❞♦s ♣❛r❛ â♥❣✉❧♦s ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♣❡q✉❡♥♦s✳ ❆♥❛❧✐s❛♥❞♦ ❛s ❋✐❣✉r❛s ❡♠ q✉❡ s❡ ❛♣r❡s❡♥t❛♠ ❛s s✉♣❡r❢í❝✐❡s ❢♦r♠❛❞❛s ♣❡❧♦s ♣♦♥t♦s ♣❧ást✐❝♦s✱ às q✉❛✐s

                                                                  2

                                                                  sã♦ s♦❜r❡♣♦st❛s ❛s ♦❜t✐❞❛s ❛tr❛✈és ❞♦ ♠ét♦❞♦ C ✭❋✐❣✉r❛s ✹✳✶✼ ❡ ✹✳✶✽✮✱ ♣❡r❝❡❜❡✲s❡ q✉❡ ♦s ♠ét♦❞♦s sã♦

                                                                  C2,tan δ

                                                                  ❜❛st❛♥t❡ s❡♠❡❧❤❛♥t❡s✱ ❝♦♠ ❛s s✉♣❡r❢í❝✐❡s ❞❡✜♥✐❞❛s ♣♦r β ❛ r❡✈❡❧❛r❡♠✲s❡ ❝♦✐♥❝✐❞❡♥t❡s às ❞❡✜♥✐❞❛s H ♣♦r β C2,I a ✱ ❛♠❜❛s ❝❧❛r❛♠❡♥t❡ ❛♣r♦①✐♠❛❞❛s às ❜❛♥❞❛s ♦❜t✐❞❛s ♥✉♠❡r✐❝❛♠❡♥t❡✳ ❆s s✉♣❡r❢í❝✐❡s ♦❜t✐❞❛s ♣♦r ❇❛r❣❤♦✉t❤✐ ✭✶✾✾✵✮ t❛♠❜é♠ s❡ r❡✈❡❧❛♠ s❡♠❡❧❤❛♥t❡s às ❜❛♥❞❛s ❢♦r♠❛❞❛s ♣❡❧♦s ♣♦♥t♦s ♣❧ást✐❝♦s✳

                                                                  1 ✹✳✹✳✹ ❆♥á❧✐s❡ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ❞❛ ❡str✉t✉r❛ B

                                                                  ✹✳✹✳✹✳✶ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s ◆❛ ♣r❡s❡♥t❡ s❡❝çã♦✱ ♣r❡t❡♥❞❡✲s❡ ❝♦♥❤❡❝❡r ❛ ✐♥✢✉ê♥❝✐❛ q✉❡ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦ t❡♠ ♥♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞❛q✉❡❧❛ ❡str✉t✉r❛✳ ❆ss✐♠✱ ♣❛r❛ ♦ ❡st✉❞♦ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞❡st❡ ♣❛râ♠❡tr♦✱ ❞❛❞♦ ♣♦r B

                                                                  1 ✱ sã♦ ❝♦♥s✐❞❡r❛❞♦s t❡rr❡♥♦s ❝♦♠ ❞✐❢❡r❡♥t❡s r❡s✐stê♥✲

                                                                  ❝✐❛s ❡ ✐♥❝❧✐♥❛çõ❡s s❡♥❞♦ ♦ ú♥✐❝♦ ♣❛râ♠❡tr♦ ❝♦♠✉♠ ❛ t♦❞❛s ❛s ❛♥á❧✐s❡s ♣r❡s❡♥t❡s ♦ ❢❛❝t♦r ❞❡ r❡❞✉çã♦

                                                                  3

                                                                inter ✱ ❝♦♥s✐❞❡r❛❞♦ ✐❣✉❛❧ ❛ ✳ ❆s ❞✐♠❡♥sõ❡s ❞♦ ♠✉r♦ ❛❞♦♣t❛❞❛s sã♦ ❛s ✐❧✉str❛❞❛s ♥❛ ❋✐❣✉r❛ ✹✳✹

                                                                2 R /

                                                                  ❡①❝❡♣t♦ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡✱ ♣❛râ♠❡tr♦ ❛ ❛♥❛❧✐s❛r✳ ❆ ✐♥✢✉ê♥❝✐❛ ❞♦ ♣❛râ♠❡tr♦ B 2

                                                                  1 é ❞❛❞❛ ❛tr❛✈és B H

                                                                  / ❞❛ r❛③ã♦ ❛❞✐♠❡♥s✐♦♥❛❧ ✳ ✹✳✹✳✹✳✷ ❘❡s✉❧t❛❞♦s ◆❛s ❋✐❣✉r❛s ✹✳✶✾ ❛ ✹✳✷✽ ❛♣r❡s❡♥t❛✲s❡ ❛ ❡✈♦❧✉çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦ ✭t❛♠❜é♠ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦✮ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡ ✐♥❝❧✐♥❛çã♦ ❞♦ t❡rr❡♥♦ ❡ ✈ár✐♦s ✈❛❧♦r❡s ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦✳ ❆ss✐♠✱ ♥❛ ❋✐❣✉r❛ ✹✳✶✾ ❛♣r❡s❡♥t❛♠✲s❡

                                                                  ′ o ′ o

                                                                  = 30 = 40

                                                                  ♦s r❡s✉❧t❛❞♦s ♣❛r❛ φ ✳ ◆❛s ❋✐❣✉r❛s ✹✳✷✵ ❡ ✹✳✷✶ ❛♣r❡s❡♥t❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♣❛r❛ φ ❡ ♥❛s

                                                                  ′ o

                                                                  = 45 ❋✐❣✉r❛s ✹✳✷✷ ❡ ✹✳✷✸ ❛♣r❡s❡♥t❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♣❛r❛ φ ✳

                                                                  ◆❛s ❋✐❣✉r❛s ✹✳✷✹ ❛ ✹✳✷✽ ❛♣r❡s❡♥t❛✲s❡ ❛ ❡✈♦❧✉çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦✱ ❛❞✐♠❡♥✲ s✐♦♥❛❧✐③❛❞❛✱ ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦✱ t❛♠❜é♠ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦✱ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡ ✐♥❝❧✐♥❛çã♦ ❞♦ t❡rr❡♥♦ ❡ ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦✳ ❆ss✐♠✱ ♥❛ ❋✐❣✉r❛ ✹✳✷✹

                                                                  ′ o

                                                                  = 30 ❡♥❝♦♥tr❛♠✲s❡ r❡♣r❡s❡♥t❛❞♦s ♦s r❡s✉❧t❛❞♦s ♣❛r❛ φ ✳ ◆❛s ❋✐❣✉r❛s ✹✳✷✺ ❡ ✹✳✷✻ ❡♥❝♦♥tr❛♠✲s❡ ♦s

                                                                  ′ o ′ o

                                                                  = 40 = 45 r❡s✉❧t❛❞♦s ♣❛r❛ φ ❡ ♥❛s ❋✐❣✉r❛s ✹✳✷✼ ❡ ✹✳✷✽ ❡♥❝♦♥tr❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♣❛r❛ φ ✳

                                                                • C
                                                                • 2 ✭❜✮ i
                                                                • C
                                                                • 2 ✭❛✮ i = 0 o

                                                                  1 B

                                                                    1

                                                                    0,2 0,3 0,4 0,5 0,6

                                                                    0,2 0,4 0,6 0,8

                                                                    1 B

                                                                    2 /H

                                                                    i=15

                                                                    I H a /(0,5 γ H

                                                                    2 )

                                                                    β C 2

                                                                    < β

                                                                    0,4 0,6 0,8

                                                                    i=20

                                                                    β C 2

                                                                    I H a /(0,5 γ H

                                                                    2 )

                                                                    β C 2

                                                                    < β

                                                                    1

                                                                    i=25

                                                                    I H a /(0,5 γ H

                                                                    2 )

                                                                    β C 2

                                                                    < β

                                                                    < β

                                                                    2 )

                                                                    0,2 0,4 0,6 0,8

                                                                    2 /H

                                                                    i=0

                                                                    I H a /(0,5 γ H

                                                                    2 )

                                                                    β C 2

                                                                    < β

                                                                    0,2 0,25 0,3 0,35 0,4

                                                                    I H a /(0,5 γ H

                                                                    1 B

                                                                    i=5

                                                                    0,2 0,4 0,6 0,8

                                                                    I H a /(0,5 γ H

                                                                    2 )

                                                                    β C 2

                                                                    < β

                                                                    0,2 0,25 0,3 0,35 0,4

                                                                    ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✽✸

                                                                    i=10

                                                                    2 /H

                                                                  • C
                                                                  • 2 ✭❞✮ i = 15 o

                                                                    • C
                                                                    • 2 ✭❝✮ i = 10 o

                                                                        0,2 0,3 0,4 0,5 0,6

                                                                        0,2 0,4 0,6 0,8

                                                                      1 B

                                                                        2 /H

                                                                      • C
                                                                      • 2
                                                                      • C
                                                                      • 2 0,4 0,6 0,8

                                                                        • C
                                                                        • 2 ✭❜✮ i
                                                                        • C
                                                                        • 2 ✭❛✮ i = 0 o

                                                                          1 B

                                                                          • C
                                                                          • 2 ✭❞✮ i =
                                                                          • C
                                                                          • 2 ✭❝✮ i = 10 o

                                                                              < β

                                                                              0,1 0,2 0,3 0,4

                                                                              0,2 0,4 0,6 0,8

                                                                              1 B

                                                                              2 /H

                                                                              i=15

                                                                              I H a /(0,5 γ H

                                                                              2 )

                                                                              β C 2

                                                                              ❋✐❣✉r❛ ✹✳✷✵✿ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧✱ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦✱ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛✲ ❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R

                                                                              < β

                                                                              inter =

                                                                              2

                                                                              /

                                                                              3

                                                                              ❀ φ

                                                                              ′

                                                                              = 40

                                                                              o

                                                                              ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s

                                                                              β C 2

                                                                              I H a /(0,5 γ H

                                                                              2 )

                                                                              0,1 0,15 0,2 0,25 0,3

                                                                              ✽✹ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖

                                                                              0,1 0,15 0,2 0,25 0,3

                                                                              0,2 0,4 0,6 0,8

                                                                              2 /H

                                                                              i=0

                                                                              I H a /(0,5 γ H

                                                                              2 )

                                                                              β C 2

                                                                              < β

                                                                              0,2 0,4 0,6 0,8

                                                                              i=10

                                                                              1 B

                                                                              2 /H

                                                                              i=5

                                                                              I H a /(0,5 γ H

                                                                              2 )

                                                                              β C 2

                                                                              < β

                                                                              0,1 0,2 0,3 0,4

                                                                              0,2 0,4 0,6 0,8

                                                                            1 B

                                                                              2 /H

                                                                            • C
                                                                            • 2 ✭❜✮ i =
                                                                            • C
                                                                            • 2 ✭❛✮ i = 20 o

                                                                                2 )

                                                                              • C
                                                                              • 2 ✭❝✮ i =
                                                                              • C
                                                                              • 2 ✭❞✮ i = 35 o

                                                                                  β C 2

                                                                                  < β

                                                                                  0,2 0,4 0,6 0,8

                                                                                  1 0,2 0,4 0,6 0,8

                                                                                  1 B

                                                                                  2 /H

                                                                                  i=35

                                                                                  I H a /(0,5 γ H

                                                                                  2 )

                                                                                  β C 2

                                                                                  < β

                                                                                  ❋✐❣✉r❛ ✹✳✷✶✿ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧✱ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦✱ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛✲ ❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R inter

                                                                                  =

                                                                                  2

                                                                                  /

                                                                                  3

                                                                                  ❀ φ

                                                                                  ′

                                                                                  = 40

                                                                                  o

                                                                                  I H a /(0,5 γ H

                                                                                  2 /H

                                                                                  i=30

                                                                                  < β

                                                                                  ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✽✺

                                                                                  0,2 0,3 0,4 0,5 0,6

                                                                                  0,2 0,4 0,6 0,8

                                                                                  1 B

                                                                                  2 /H

                                                                                  i=20

                                                                                  I H a /(0,5 γ H

                                                                                  2 )

                                                                                  β C 2

                                                                                  0,2 0,3 0,4 0,5 0,6

                                                                                  1 B

                                                                                  0,2 0,4 0,6 0,8

                                                                                  1 B

                                                                                  2 /H

                                                                                  i=25

                                                                                  I H a /(0,5 γ H

                                                                                  2 )

                                                                                  β C 2

                                                                                  < β

                                                                                  0,2 0,4 0,6 0,8

                                                                                  1 0,2 0,4 0,6 0,8

                                                                                  ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s

                                                                                • C
                                                                                • 2 ✭❜✮ i
                                                                                • C
                                                                                • 2 ✭❛✮ i
                                                                                • C
                                                                                • 2 ✭❞✮ i = 15 o

                                                                                    2 )

                                                                                    2 )

                                                                                    β C 2

                                                                                    < β

                                                                                    0,05 0,1 0,15 0,2 0,25 0,3

                                                                                    0,2 0,4 0,6 0,8

                                                                                    1 B

                                                                                    2 /H

                                                                                    i=0

                                                                                    I H a /(0,5 γ H

                                                                                    β C 2

                                                                                    < β

                                                                                  • C
                                                                                  • 2 ✭❝✮ i = 10 o

                                                                                      ❋✐❣✉r❛ ✹✳✷✷✿ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧✱ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦✱ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛✲ ❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R

                                                                                      inter =

                                                                                      2

                                                                                      /

                                                                                      3

                                                                                      ❀ φ

                                                                                      ′

                                                                                      = 45

                                                                                      o

                                                                                      I H a /(0,5 γ H

                                                                                      2 /H

                                                                                      i=0

                                                                                      < β

                                                                                      ✽✻ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖

                                                                                      0,05 0,1 0,15 0,2 0,25 0,3

                                                                                      0,2 0,4 0,6 0,8

                                                                                      1 B

                                                                                      2 /H

                                                                                      i=0

                                                                                      I H a /(0,5 γ H

                                                                                      2 )

                                                                                      β C 2

                                                                                      0,05 0,1 0,15 0,2 0,25 0,3

                                                                                      1 B

                                                                                      0,2 0,4 0,6 0,8

                                                                                      1 B

                                                                                      2 /H

                                                                                      i=5

                                                                                      I H a /(0,5 γ H

                                                                                      2 )

                                                                                      β C 2

                                                                                      < β

                                                                                      0,05 0,1 0,15 0,2 0,25 0,3

                                                                                      0,2 0,4 0,6 0,8

                                                                                      ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s

                                                                                    • C
                                                                                    • 2 ✭❜✮ i =
                                                                                    • C
                                                                                    • 2 ✭❛✮ i =
                                                                                    • C
                                                                                    • 2 ✭❞✮ i = 35 o

                                                                                        2 )

                                                                                        2 )

                                                                                        β C 2

                                                                                        < β

                                                                                        0,1 0,2 0,3 0,4 0,5 0,6 0,7

                                                                                        0,2 0,4 0,6 0,8

                                                                                        1 B

                                                                                        2 /H

                                                                                        i=35

                                                                                        I H a /(0,5 γ H

                                                                                        β C 2

                                                                                        < β

                                                                                      • C
                                                                                      • 2 ✭❝✮ i = 30 o

                                                                                          ❋✐❣✉r❛ ✹✳✷✸✿ ❱❛r✐❛çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧✱ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦✱ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛✲ ❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R inter

                                                                                          =

                                                                                          2

                                                                                          /

                                                                                          3

                                                                                          ❀ φ

                                                                                          ′

                                                                                          = 45

                                                                                          o

                                                                                          I H a /(0,5 γ H

                                                                                          2 /H

                                                                                          i=30

                                                                                          < β

                                                                                          ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✽✼

                                                                                          0,1 0,2 0,3 0,4

                                                                                          0,2 0,4 0,6 0,8

                                                                                          1 B

                                                                                          2 /H

                                                                                          i=20

                                                                                          I H a /(0,5 γ H

                                                                                          2 )

                                                                                          β C 2

                                                                                          0,1 0,2 0,3 0,4

                                                                                          1 B

                                                                                          0,2 0,4 0,6 0,8

                                                                                          1 B

                                                                                          2 /H

                                                                                          i=25

                                                                                          I H a /(0,5 γ H

                                                                                          2 )

                                                                                          β C 2

                                                                                          < β

                                                                                          0,1 0,2 0,3 0,4 0,5 0,6 0,7

                                                                                          0,2 0,4 0,6 0,8

                                                                                          ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s

                                                                                        • C
                                                                                        • 2 ✭❜✮ i
                                                                                        • C
                                                                                        • 2 ✭❛✮ i
                                                                                        • C
                                                                                        • 2 ✭❞✮ i =
                                                                                        • C
                                                                                        • 2 ✭❝✮ i = 10 o

                                                                                            1

                                                                                            0,2 0,4 0,6 0,8

                                                                                            1 0,2 0,4 0,6 0,8

                                                                                            1 B

                                                                                            2 /H

                                                                                            i=15

                                                                                            tg δ

                                                                                            β C 2

                                                                                            < β

                                                                                            0,2 0,4 0,6 0,8

                                                                                            i=20

                                                                                            β C 2

                                                                                            tg δ

                                                                                            β C 2

                                                                                            < β

                                                                                            1

                                                                                            i=25

                                                                                            tg δ

                                                                                            β C 2

                                                                                            < β

                                                                                            C 2 <

                                                                                            < β

                                                                                            tg δ

                                                                                            β

                                                                                            0,2 0,4 0,6 0,8

                                                                                            ✽✽ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖

                                                                                            0,2 0,4 0,6 0,8

                                                                                            1 0,2 0,4 0,6 0,8

                                                                                            1 B

                                                                                            2 /H

                                                                                            i=0

                                                                                            tg δ

                                                                                            β C 2

                                                                                            < β

                                                                                            1 0,2 0,4 0,6 0,8

                                                                                            i=10

                                                                                            1 B

                                                                                            2 /H

                                                                                            i=5

                                                                                            tg δ

                                                                                            β C 2

                                                                                            < β

                                                                                            0,2 0,4 0,6 0,8

                                                                                            1 0,2 0,4 0,6 0,8

                                                                                            1 B

                                                                                            2 /H

                                                                                          • C
                                                                                          • 2 0,2 0,4 0,
                                                                                          • C
                                                                                          • 2 &
                                                                                          • C
                                                                                          • 2

                                                                                          • C
                                                                                          • 2 ✭❛✮ i
                                                                                          • C
                                                                                          • 2 ✭❜✮ i = 5 o

                                                                                              0,2 0,4 0,6 0,8

                                                                                              1 B

                                                                                              2 /H

                                                                                              i=10

                                                                                              tg δ

                                                                                              β C 2

                                                                                              < β

                                                                                              1 0,2 0,4 0,6 0,8

                                                                                              0,2 0,4 0,6 0,8

                                                                                              1 B

                                                                                              2 /H

                                                                                              i=15

                                                                                              tg δ

                                                                                              β C 2

                                                                                              < β

                                                                                              ❋✐❣✉r❛ ✹✳✷✺✿ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

                                                                                              1 0,2 0,4 0,6 0,8

                                                                                              < β

                                                                                              ′

                                                                                              tg δ

                                                                                              ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✽✾

                                                                                              0,2 0,4 0,6 0,8

                                                                                              1 0,2 0,4 0,6 0,8

                                                                                              1 B

                                                                                              2 /H

                                                                                              i=0

                                                                                              β C 2

                                                                                              β C 2

                                                                                              < β

                                                                                              0,2 0,4 0,6 0,8

                                                                                              1 0,2 0,4 0,6 0,8

                                                                                              1 B

                                                                                              2 /H

                                                                                              i=5

                                                                                              tg δ

                                                                                            • C
                                                                                            • 2 ✭❝✮ i =
                                                                                            • C
                                                                                            • 2 ✭❞✮ i = 15 o

                                                                                                ✾✵ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖ i=20 i=25

                                                                                                1 1 0,8

                                                                                                0,8 0,6 0,6

                                                                                                δ δ tg tg

                                                                                              • < β
                                                                                              • β

                                                                                                β

                                                                                                < β C C 2 2 C C 2 2

                                                                                                0,4 0,4 0,2 0,2 0,2 0,4 0,6 0,8

                                                                                                1 0,2 0,4 0,6 0,8

                                                                                                1 B /H B /H

                                                                                                2

                                                                                                2 o o

                                                                                                

                                                                                              ✭❛✮ i = 20 ✭❜✮ i = 25

                                                                                                i=30 i=35

                                                                                                1 1 0,8

                                                                                                0,8

                                                                                              • β < β

                                                                                                C C 2 2 0,6

                                                                                                0,6

                                                                                              • <

                                                                                                β β C 2 C 2

                                                                                                δ δ tg tg

                                                                                                0,4 0,4 0,2 0,2 0,2 0,4 0,6 0,8

                                                                                                1 0,2 0,4 0,6 0,8

                                                                                                1 B /H B /H

                                                                                                2

                                                                                                2 o o

                                                                                                

                                                                                              ✭❝✮ i = 30 ✭❞✮ i = 35

                                                                                                ❋✐❣✉r❛ ✹✳✷✻✿ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

                                                                                                

                                                                                                2

                                                                                                3

                                                                                                = / = 40 ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R inter ❀ φ ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s

                                                                                              • C
                                                                                              • 2 ✭❛✮ i
                                                                                              • C
                                                                                              • 2 ✭❜✮ i = 5 o

                                                                                                • C
                                                                                                • 2 ✭❝✮ i =
                                                                                                • C
                                                                                                • 2 ✭❞✮ i = 15 o

                                                                                                    1 B

                                                                                                    2 /H

                                                                                                    i=10

                                                                                                    tg δ

                                                                                                    β C 2

                                                                                                    < β

                                                                                                    0,2 0,4 0,6 0,8

                                                                                                    1 B

                                                                                                    1 0,2 0,4 0,6 0,8

                                                                                                    2 /H

                                                                                                    i=15

                                                                                                    tg δ

                                                                                                    β C 2

                                                                                                    < β

                                                                                                    ❋✐❣✉r❛ ✹✳✷✼✿ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛

                                                                                                    2

                                                                                                    1 0,2 0,4 0,6 0,8

                                                                                                    0,2 0,4 0,6 0,8

                                                                                                    < β

                                                                                                    tg δ

                                                                                                    ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✾✶

                                                                                                    0,2 0,4 0,6 0,8

                                                                                                    1 0,2 0,4 0,6 0,8

                                                                                                    1 B

                                                                                                    2 /H

                                                                                                    i=0

                                                                                                    β C 2

                                                                                                    β C 2

                                                                                                    < β

                                                                                                    0,2 0,4 0,6 0,8

                                                                                                    1 0,2 0,4 0,6 0,8

                                                                                                    1 B

                                                                                                    2 /H

                                                                                                    i=5

                                                                                                    tg δ

                                                                                                    3 ′ o

                                                                                                  • C
                                                                                                  • 2 ✭❛✮ i =
                                                                                                  • C
                                                                                                  • 2 ✭❜✮ i =
                                                                                                  • C
                                                                                                  • 2 ✭❝✮ i =
                                                                                                  • C
                                                                                                  • 2 ✭❞✮ i = 35 o

                                                                                                      < β

                                                                                                      < β

                                                                                                      0,2 0,4 0,6 0,8

                                                                                                      1 0,2 0,4 0,6 0,8

                                                                                                      1 B

                                                                                                      2 /H

                                                                                                      i=35

                                                                                                      tg δ

                                                                                                      β C 2

                                                                                                      ❋✐❣✉r❛ ✹✳✷✽✿ ❱❛r✐❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ❛ ❧❛r❣✉r❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞❛ ❞♦ ♠✉r♦ ♣❛r❛ ❞✐✈❡rs❛s ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ ❡ R inter

                                                                                                      tg δ

                                                                                                      =

                                                                                                      2

                                                                                                      /

                                                                                                      3

                                                                                                      ❀ φ

                                                                                                      

                                                                                                      = 45

                                                                                                      o

                                                                                                      β C 2

                                                                                                      i=30

                                                                                                      ✾✷ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖

                                                                                                      0,2 0,4 0,6 0,8

                                                                                                      0,2 0,4 0,6 0,8

                                                                                                      1 0,2 0,4 0,6 0,8

                                                                                                      1 B

                                                                                                      2 /H

                                                                                                      i=20

                                                                                                      tg δ

                                                                                                      β C 2

                                                                                                      < β

                                                                                                      1 0,2 0,4 0,6 0,8

                                                                                                      2 /H

                                                                                                      1 B

                                                                                                      2 /H

                                                                                                      i=25

                                                                                                      tg δ

                                                                                                      β C 2

                                                                                                      < β

                                                                                                      0,2 0,4 0,6 0,8

                                                                                                      1 0,2 0,4 0,6 0,8

                                                                                                      1 B

                                                                                                      ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s

                                                                                                      ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✾✸

                                                                                                      ❆♣r❡s❡♥t❛♠✲s❡✱ ♥❛s ❋✐❣✉r❛s ✹✳✷✾ ❛ ✹✳✸✷✱ ❛s s✉♣❡r❢í❝✐❡s ✐♥❢❡r✐❞❛s ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s✱ ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦✳ ❆ ❡st❛s s♦❜r❡♣õ❡♠✲s❡ ❛s s✉♣❡r❢í❝✐❡s ♦❜t✐❞❛s ♣❡❧♦ ♠ét♦❞♦ C

                                                                                                      2 ♣♦r o ′ o

                                                                                                      = 30 ❢♦r♠❛ ❛ ❝♦♠♣❛r❛r❡♠✲s❡✳ ❆ss✐♠✱ ♥❛ ❋✐❣✉r❛ ✹✳✷✾ ❛♣r❡s❡♥t❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♣❛r❛ i = 0 ❡ φ ✳

                                                                                                      o ′ o

                                                                                                      = 40 ◆❛ ❋✐❣✉r❛ ✹✳✸✵ ❛♣r❡s❡♥t❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♣❛r❛ i = 0 ❡ φ ✳ ◆❛ ❋✐❣✉r❛ ✹✳✸✶ ❛♣r❡s❡♥t❛♠✲s❡ ♦s

                                                                                                      ′ ′

                                                                                                      ′ o o ′ o o φ φ

                                                                                                      = 30 /

                                                                                                      2 = 15 = 40 / 2 = 20

                                                                                                      r❡s✉❧t❛❞♦s ♣❛r❛ φ ❡ i = ❡ ♥❛ ❋✐❣✉r❛ ✹✳✸✷ ♦s r❡s✉❧t❛❞♦s ♣❛r❛ φ ❡ i = ✳ 1 B 2 B 1 2 B 1 2

                                                                                                      = 0,6 m = 0,013 = 1 m = 0,063 = 1,5 m = 0,125 ✭❛✮ B ✭❜✮ B ✭❝✮ B H H H 1 B 2 B 1 2

                                                                                                      = 3 m = 0,313 = 5 m = 0,563 ✭❞✮ B ✭❡✮ B H H 1 B

                                                                                                    2 B

                                                                                                    1 2

                                                                                                      

                                                                                                    = 7 m = 0,813 = 10 m = 1,188

                                                                                                    ✭❢✮ B ✭❣✮ B

                                                                                                    H H

                                                                                                      ′ o

                                                                                                      = 30 ❋✐❣✉r❛ ✹✳✷✾✿ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ♣❛r❛ φ ❀

                                                                                                      o

                                                                                                      2

                                                                                                      3 R = / inter ❀ i = 0 ✳ ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ C 2 ✳

                                                                                                      ✾✹ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖ 1 B 2 B 1 2 B 1 2

                                                                                                      = 0,6 m = 0,013 = 1 m = 0,063 = 1,5 m = 0,125 ✭❛✮ B ✭❜✮ B ✭❝✮ B H H H 1 B 2 B 1 2

                                                                                                      

                                                                                                    ✭❞✮ B = 3 m = 0,313 ✭❡✮ B = 5 m = 0,563

                                                                                                    H H 1 B

                                                                                                    2 B

                                                                                                    1 2

                                                                                                      ✭❢✮ B = 7 m = 0,813 ✭❣✮ B = 10 m = 1,188

                                                                                                    H H

                                                                                                    o ′

                                                                                                      = 40 ❋✐❣✉r❛ ✹✳✸✵✿ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ♣❛r❛ φ ❀

                                                                                                      o

                                                                                                      2

                                                                                                      2

                                                                                                      ❀ i = 0 ✳ ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ C ✳

                                                                                                    3 R inter = /

                                                                                                      ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✾✺ 1 = 0,6 m = 0,013 B 2 B 1 = 1 m = 0,063 2 B 1 = 1,5 m = 0,125 2

                                                                                                      ✭❛✮ B ✭❜✮ B ✭❝✮ B H H H 1 B

                                                                                                    2 B

                                                                                                    1 2

                                                                                                      ✭❞✮ B = 3 m = 0,313 ✭❡✮ B = 5 m = 0,563

                                                                                                    H H

                                                                                                    1 B 2 1 B 2

                                                                                                      = 7 m = 0,813 = 10 m = 1,188 ✭❢✮ B ✭❣✮ B

                                                                                                      H H

                                                                                                      ′ o

                                                                                                      = 30 ❋✐❣✉r❛ ✹✳✸✶✿ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ♣❛r❛ φ ❀

                                                                                                      o

                                                                                                      2

                                                                                                      3 R = / inter ❀ i = 15 ✳ ❙♦❜r❡♣♦s✐çã♦ ❞❛s s✉♣❡r❢í❝✐❡s r❡s✉❧t❛♥t❡s ❞❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ C 2 ✳

                                                                                                      ✾✻ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖ 1 B 2 B 1 2 B 1 2

                                                                                                      = 0,6 m = 0,013 = 1 m = 0,063 = 1,5 m = 0,125 ✭❛✮ B ✭❜✮ B ✭❝✮ B H H H 1 B

                                                                                                    2 B

                                                                                                    1 2

                                                                                                      

                                                                                                    = 3 m = 0,313 = 5 m = 0,563

                                                                                                    ✭❞✮ B ✭❡✮ B

                                                                                                    H H

                                                                                                    1 B 2 1 B 2

                                                                                                      

                                                                                                    = 7 m = 0,813 = 10 m = 1,188

                                                                                                    ✭❢✮ B ✭❣✮ B H

                                                                                                      H ′ o

                                                                                                      = 40 ❋✐❣✉r❛ ✹✳✸✷✿ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s ❡♠ ❢✉♥çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❜❛s❡ ♣❛r❛ φ ❀

                                                                                                      ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✾✼

                                                                                                      ✹✳✹✳✹✳✸ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s P❡❧❛ ❛♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s é ♣♦ssí✈❡❧ ❛✜r♠❛r q✉❡ ❡①✐st❡ ✉♠❛ ♣r♦①✐♠✐❞❛❞❡ r❡❧❛t✐✈❛ ❡♥tr❡ ♦s H 1 2 2 I a

                                                                                                      / / γH ♠ét♦❞♦s ♥✉♠ér✐❝♦ ❡ C

                                                                                                      2 ✱ t❛♥t♦ ♥♦ q✉❡ r❡s♣❡✐t❛ à r❡❧❛çã♦ ✱ ❝♦♠♦ ❛ tan δ✳ ❊st❡ ❢❛❝t♦ é t❛♠❜é♠

                                                                                                      ♠♦str❛❞♦ ♣❡❧❛ ❝♦✐♥❝✐❞ê♥❝✐❛ ❞❛s s✉♣❡r❢í❝✐❡s ❛♣r❡s❡♥t❛❞❛s ♥❛s ❋✐❣✉r❛s ✹✳✷✾ ❛ ✹✳✸✷✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛s s✉♣❡r❢í❝✐❡s ♦❜t✐❞❛s ♣♦r ❇❛r❣❤♦✉t❤✐ ♠♦str❛♠✲s❡ ❛♣r♦①✐♠❛❞❛s às ♦❜t✐❞❛s ♥✉♠❡r✐❝❛♠❡♥t❡✳

                                                                                                      ✹✳✹✳✺ ❆♥á❧✐s❡ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ i

                                                                                                      ✹✳✹✳✺✳✶ ❆♥á❧✐s❡s r❡❛❧✐③❛❞❛s ❆ ✐♥✢✉ê♥❝✐❛ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦ ♥♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦✱ é ❛♥❛❧✐s❛❞❛ ♥❛ ♣r❡s❡♥t❡ s❡❝çã♦✳ ❆s ❞✐♠❡♥sõ❡s ❞❛ ❡str✉t✉r❛ ❛❞♦♣t❛❞❛s ♣❛r❛ ❛ ❛♥á❧✐s❡ ♣r❡s❡♥t❡ sã♦ ❛s ❝♦♥s✐❞❡r❛❞❛s ♣❛r❛ ♦ ❝❛s♦ ❜❛s❡✱ ❞✐s♣♦st❛s ♥❛ ❋✐❣✉r❛ ✹✳✹✳ P❛r❛ ❛s ♠❡s♠❛s ❝♦♥❞✐çõ❡s ❞♦ s♦❧♦ ❡ ❞♦ ♠✉r♦ ❞♦ ❝❛s♦ ❜❛s❡✱ sã♦ ❝♦♥s✐❞❡r❛❞❛s ❞✐❢❡r❡♥t❡s ✐♥❝❧✐♥❛çõ❡s✱ ❝♦♠ ❛ H 1 2 I a 2 / γH

                                                                                                      / ✜♥❛❧✐❞❛❞❡ ❞❡ s❡ ❛♥❛❧✐s❛r ❛ ❡✈♦❧✉çã♦ ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ✭❞❛❞♦ ♣❡❧❛ r❡❧❛çã♦ ✮ ❡ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦ ✭❞❛❞❛ ♣♦r tan δ✮ ❝♦♠ ♦ s❡✉ ❛✉♠❡♥t♦✳ ❆s ❛♥á❧✐s❡s ❛q✉✐ ❛♣r❡s❡♥t❛❞❛s sã♦ ✉♠ s✉❜❝♦♥❥✉♥t♦ ❞❛ s❡❝çã♦ ✹✳✹✳✹✳ ✹✳✹✳✺✳✷ ❘❡s✉❧t❛❞♦s H 1 2 I a 2 / γH

                                                                                                      / ◆❛ ❋✐❣✉r❛ ✹✳✸✸ ❛♣r❡s❡♥t❛✲s❡ ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦✱ ❞❛❞♦ ♣❡❧❛ r❛③ã♦ ❛❞✐♠❡♥s✐♦♥❛❧ ✱ ❡♠ ❢✉♥çã♦ ❞♦ ❛✉♠❡♥t♦ ❞❛ ✐♥❝❧✐♥❛çã♦ i✳ ❖s r❡s✉❧t❛❞♦s sã♦ s♦❜r❡♣♦st♦s ❛♦s ♦❜t✐❞♦s ❛tr❛✈és ❞♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✱ ♣♦r ❢♦r♠❛ ❛ ♣♦❞❡r❡♠ ❝♦♠♣❛r❛r✲s❡ ❡♥tr❡ s✐✳

                                                                                                      i=0 0,65 0,6 0,55

                                                                                                      )

                                                                                                      2 0,5

                                                                                                      H γ /(0,5

                                                                                                      0,45 H a

                                                                                                      I 0,4 0,35 0,3

                                                                                                      5

                                                                                                      10

                                                                                                      15

                                                                                                      20

                                                                                                      25 o i ( )

                                                                                                      ✾✽ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖

                                                                                                      i=0 0,5 0,45 0,4

                                                                                                      δ tg

                                                                                                      0,35 0,3 0,25

                                                                                                      5

                                                                                                      10

                                                                                                      15

                                                                                                      20

                                                                                                      25 o i ( )

                                                                                                      ❋✐❣✉r❛ ✹✳✸✹✿ ■♥✢✉ê♥❝✐❛ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦ i ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦ 2 B

                                                                                                      2 o ′

                                                                                                      = 0, 438 inter = = 30 ♣❛r❛ ❀ R ❀ φ ✳ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✳

                                                                                                      H

                                                                                                      3

                                                                                                      ❆s s✉♣❡r❢í❝✐❡s ♦❜t✐❞❛s ♣❡❧♦s ♣♦♥t♦s ♣❧ást✐❝♦s✱ ♣❛r❛ ✉♠ t❡rr❡♥♦ ❝♦♠ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ✐❣✉❛❧ ❛

                                                                                                      o

                                                                                                      30 ❡ ♣❛r❛ ✉♠ ♠✉r♦ ❝♦♠ ❛s ❞✐♠❡♥sõ❡s ❛♣r❡s❡♥t❛❞❛s ♣❛r❛ ♦ ❝❛s♦ ❜❛s❡✱ ❡♥❝♦♥tr❛♠✲s❡ r❡♣r❡s❡♥t❛❞❛s ♥❛

                                                                                                      ❋✐❣✉r❛ ✹✳✸✺✳ ❆s s✉♣❡r❢í❝✐❡s sã♦ ❛♣r❡s❡♥t❛❞❛s ❡♠ ❢✉♥çã♦ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦✳

                                                                                                      ✹✳✹✳ ❆◆➪▲■❙❊ P❆❘❆▼➱❚❘■❈❆ ✾✾

                                                                                                      o o o ✭❛✮ i = 0 ✭❜✮ i = 5 ✭❝✮ i = 10 o o

                                                                                                      ✭❞✮ i = 15 ✭❡✮ i = 20 o

                                                                                                      

                                                                                                    ✭❢✮ i = 25

                                                                                                      ✶✵✵ ❈❆P❮❚❯▲❖ ✹✳ ❆P▲■❈❆➬➹❖ ❉❊ ▼➱❚❖❉❖ ◆❯▼➱❘■❈❖ ✹✳✹✳✺✳✸ ❆♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s 2 B

                                                                                                      H

                                                                                                      = 4 m; / = 0, 438 P❛r❛ ♦ ❝❛s♦ ❛♥❛❧✐s❛❞♦ ✭B

                                                                                                      1 ✮ t♦❞♦s ♦s ♠ét♦❞♦s ❛♣r❡s❡♥t❛♠✱ ♣r❛t✐❝❛♠❡♥t❡✱ ♦s H

                                                                                                      ♠❡s♠♦s r❡s✉❧t❛❞♦s ❞❡ I ✳ ❍á✱ ❡♠ ♣❛rt✐❝✉❧❛r✱ ❣r❛♥❞❡ ♣r♦①✐♠✐❞❛❞❡ ❡♥tr❡ ♦s r❡s✉❧t❛❞♦s ❞♦ ♠ét♦❞♦

                                                                                                      a

                                                                                                      ♥✉♠❡r✐❝♦ ❡ ♦s ❞♦ ♠ét♦❞♦ C

                                                                                                      2 ✳

                                                                                                      ◆♦ q✉❡ r❡s♣❡✐t❛ à tan δ✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦s ✈ér✐♦s ♠ét♦❞♦s ❛♣r❡s❡♥t❛♠ r❡s✉❧t❛❞♦s s❡♠❡❧❤❛♥t❡s✱ s❡♥❞♦ ♦s ♦❜t✐❞♦s ♥✉♠❡r✐❝❛♠❡♥t❡ ♦s ❞❡ ♠❡♥♦r ✈❛❧♦r✳

                                                                                                      P❡❧❛ ❛♥á❧✐s❡ ❞❛ ❋✐❣✉r❛ ✹✳✸✺ é ♣♦ssí✈❡❧ ❛✜r♠❛r q✉❡ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ ✐♥❝❧✐♥❛çã♦ ❞♦ t❡rr❡♥♦✱ ❛ H

                                                                                                      C2,tan δ

                                                                                                      s❡♠❡❧❤❛♥ç❛ ❡♥tr❡ ❛s ❜❛♥❞❛s ❞❡ ♣♦♥t♦s ♣❧ást✐❝♦s ❡ ❛s s✉♣❡r❢í❝✐❡s ❞❡✜♥✐❞❛s ♣♦r β C2,I a ❡ β s❡ ♠❛♥té♠✱ s❡♥❞♦ ❛s ú❧t✐♠❛s ❝♦✐♥❝✐❞❡♥t❡s ❡♥tr❡ s✐✳ ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣♦r ❇❛r❣❤♦✉t❤✐ sã♦ s❡♠❡❧❤❛♥t❡s ❛♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥✉♠❡r✐❝❛♠❡♥t❡✳

                                                                                                      ❈❛♣ít✉❧♦ ✺

                                                                                                    ❈♦♥❝❧✉sõ❡s ❡ ❢✉t✉r♦s ❞❡s❡♥✈♦❧✈✐♠❡♥t♦s

                                                                                                    ✺✳✶ ❈♦♥❝❧✉sõ❡s

                                                                                                      ■❞❡♥t✐✜❝❛r❛♠✲s❡ três ♠ét♦❞♦s ♣❛r❛ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s ❞❡ t❡rr❛s s♦❜r❡ ♠✉r♦s ❞❡ s✉♣♦rt❡ ❡♠ ❝♦♥s♦❧❛✿ ✉♠ ♠ét♦❞♦ ✲ q✉❡ ❢♦✐✱ ♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✱ ✐❞❡♥t✐✜❝❛❞♦ ♣♦r ♠ét♦❞♦ R ✲ ❜❛s❡❛❞♦ ♥❛ t❡♦r✐❛ ❞❡ ❘❛♥❦✐♥❡✱ ✉♠ ♠ét♦❞♦ ✲ ✐❞❡♥t✐✜❝❛❞♦ ♣♦r C

                                                                                                      1 ✲ ❜❛s❡❛❞♦ ♥❛ ♠♦❜✐❧✐③❛çã♦ ❞♦s ✐♠♣✉❧s♦s ♥✉♠❛

                                                                                                      s✉♣❡r❢í❝✐❡ ✈✐rt✉❛❧ s✐♠♣❧✐✜❝❛❞❛ ❡ ♥❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜ ❡✱ ✜♥❛❧♠❡♥t❡✱ ✉♠ ♠ét♦❞♦ ✲ ✐❞❡♥t✐✜❝❛❞♦ ♣♦r C

                                                                                                      2 ✲ t❛♠❜é♠ ❜❛s❡❛❞♦ ♥♦ ♠ét♦❞♦ ❞❡ ❈♦✉❧♦♠❜ ❡ q✉❡ ❝♦♥s✐st❡ ♥❛ ❜✉s❝❛ ❞❛ s✉♣❡r❢í❝✐❡

                                                                                                      ✈✐rt✉❛❧ q✉❡ ❝♦♥❞✉③ ❛♦ ♠❛✐♦r ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ♦✉ à ❝♦♥❞✐çã♦ ❞❡ ❡st❛❜✐❧✐❞❛❞❡ ❞♦ ♠✉r♦ ♠❛✐s ❞❡s❢❛✈♦rá✈❡❧✳

                                                                                                      ❉❡s❡♥✈♦❧✈❡r❛♠✲s❡ ❡①♣r❡ssõ❡s ♣❛r❛✱ ♣❛r❛ ❝❛❞❛ ♠ét♦❞♦✱ ❞❡t❡r♠✐♥❛r ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ♣❡❧♦ ♣❡s♦ ✈♦❧ú♠✐❝♦ ❞♦ s♦❧♦ ❡ ♣❡❧❛ ❛❧t✉r❛ ❞♦ ♠✉r♦✳ ❉❡s❡♥✈♦❧✈❡r❛♠✲s❡ ✐❣✉❛❧♠❡♥t❡ ❡①♣r❡ssõ❡s q✉❡✱ ♣❛r❛ ❝❛❞❛ ♠ét♦❞♦✱ ❞❡✜♥❡♠ ❛ r❡❧❛çã♦ ❡♥tr❡ ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ❡ ❛ r❡s✉❧t❛♥t❡ ❞❛s ❝❛r❣❛s ✈❡rt✐❝❛✐s✳ ❊st❛ r❡❧❛çã♦ tr❛❞✉③ ❛ t❛♥❣❡♥t❡ ❞♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ s♦❧♦✲❜❛s❡ ♥❡❝❡ssár✐♦ ♣❛r❛ ❛ ✈❡r✐✜❝❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❞♦ ♠✉r♦✳ ❈♦♥st❛t♦✉✲s❡ q✉❡✱ ♣❛r❛ ❛❧é♠ ❞❡ ❞❡♣❡♥❞❡♥t❡s ❞❛s ♣r♦♣r✐❡❞❛❞❡s s♦ s♦❧♦ s✉♣♦rt❛❞♦✱ ❛s r❡❢❡r✐❞❛s ❡①♣r❡ssõ❡s ❞❡♣❡♥❞❡♠ ❞❡ ♣❛râ♠❡tr♦s ❣❡♦♠étr✐❝♦s ❞♦ ♠✉r♦✳ ◆ã♦ ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞❛s✱ ♥❡st❛s ❡①♣r❡ssõ❡s✱ q✉❛✐sq✉❡r s♦❜r❡❝❛r❣❛s ❛♣❧✐❝❛❞❛s à s✉♣❡r❢í❝✐❡ ❞♦ t❡rr❡♥♦✳ ❈♦♠♣❛r❛r❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❛r❛ ❛♠❜❛s ❛s ❣r❛♥❞❡③❛s ✲ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❡ t❛♥❣❡♥t❡ ❞♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ s♦❧♦✲❜❛s❡ ✭❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦✮✳

                                                                                                      ❊♠ r❡❧❛çã♦ ❛♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ✈❡r✐✜❝❛✲s❡ q✉❡✿ ❼ ♦ ♠ét♦❞♦ R ❝♦♥❞✉③✱ ♥♦r♠❛❧♠❡♥t❡✱ ❛ ✈❛❧♦r❡s ❞♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ s✉✲

                                                                                                      ♣❡r✐♦r❡s ❛♦s r❡st❛♥t❡s ♠ét♦❞♦s✳ ❆s ❡①❝❡♣çõ❡s ✈❡r✐✜❝❛♠✲s❡ ♣❛r❛ ✐♥❝❧✐♥❛çõ❡s ❞♦ t❡rr❡♥♦ s✉♣❡r✐♦r❡s ❛♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ s♦❧♦✲♣❛r❛♠❡♥t♦❀ ♣❛r❛ ❡st❡s ❝❛s♦s✱ ♦ ♠ét♦❞♦ C

                                                                                                      2 ❛♣r❡s❡♥t❛ ✈❛❧♦r❡s ❧✐❣❡✐r❛♠❡♥t❡

                                                                                                      s✉♣❡r✐♦r❡s❀ ❼ ❡①✐st❡ ✉♠❛ ❣❛♠❛ ❞❡ ✈❛❧♦r❡s ❞❛ ❧❛r❣✉r❛ ❞♦ ♠✉r♦ ♣❛r❛ ♦s q✉❛✐s ♦s r❡s✉❧t❛❞♦s ❞♦s ♠ét♦❞♦s R ❡ C

                                                                                                      1

                                                                                                      sã♦ ♣r❛t✐❝❛♠❡♥t❡ ✐❣✉❛✐s❀ ❼ ♦ ♠ét♦❞♦ C

                                                                                                      1 ❛❢❛st❛✲s❡ ❞♦s r❡st❛♥t❡s ♣❛r❛ ❧❛r❣✉r❛s ❞♦ ♠✉r♦ ❡❧❡✈❛❞❛s✳

                                                                                                      ✶✵✷ ❈❆P❮❚❯▲❖ ✺✳ ❈❖◆❈▲❯❙Õ❊❙ ❊ ❋❯❚❯❘❖❙ ❉❊❙❊◆❱❖▲❱■▼❊◆❚❖❙

                                                                                                      2

                                                                                                      ❼ ♣❛r❛ ❧❛r❣✉r❛s ❞♦ ♠✉r♦ ♣❡q✉❡♥❛s✱ ♦s r❡s✉❧t❛❞♦s ❞♦ ♠ét♦❞♦ C sã♦ ✐♥❢❡r✐♦r❡s ❛♦s ❞♦ ♠ét♦❞♦ R q✉❛♥❞♦ i < δ❀ sã♦ ✐❣✉❛✐s q✉❛♥❞♦ i = δ❀ sã♦ s✉♣❡r✐♦r❡s q✉❛♥❞♦ i > δ❀ ❼ ♣❛r❛ ❧❛r❣✉r❛s ❞♦ ♠✉r♦ ❣r❛♥❞❡s✱ ❡①✐st❡ ❣r❛♥❞❡ s❡♠❡❧❤❛♥ç❛ ❡♥tr❡ ♦s ♠ét♦❞♦s R ❡ C

                                                                                                      2 ✳

                                                                                                      ❆♣❧✐❝♦✉✲s❡ ♦ ♠ét♦❞♦ ❞♦s ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ✉s❛♥❞♦ ✉♠ ♠♦❞❡❧♦ ❡❧ást✐❝♦✲♣❡r❢❡✐t❛♠❡♥t❡ ♣❧ást✐❝♦ ❝♦♠ ❧❡✐ ❞❡ ✢✉①♦ ❛ss♦❝✐❛❞❛ à ❞❡t❡r♠✐♥❛çã♦ ♥✉♠ér✐❝❛ ❞♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s s♦❜r❡ ♠✉r♦s ❞❡ s✉♣♦rt❡ ❡♠ ❝♦♥s♦❧❛✳

                                                                                                      ❖ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❢♦✐ ♠♦❜✐❧✐③❛❞♦ ❛♣❧✐❝❛♥❞♦ ❛♦s ❡❧❡♠❡♥t♦s q✉❡ s✐♠✉❧❛♠ ♦ ♠✉r♦ ❞❡ s✉♣♦rt❡ ✉♠ ❞❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧ ♥♦ s❡♥t✐❞♦ ❝♦♥trár✐♦ ❛♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦✳ ❆❞♠✐t✐✉✲s❡ t❡r ❛t✐♥❣✐❞♦ ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ q✉❛♥❞♦ ❛ ❢♦rç❛ ❤♦r✐③♦♥t❛❧ t♦t❛❧ ❛♣❧✐❝❛❞❛ ♣❡❧♦ s♦❧♦ ❛♦ ♠✉r♦ ❡st❛❜✐❧✐③♦✉✳ ❉♦s ❝á❧❝✉❧♦s r❡❛❧✐③❛❞♦s✱ r❡t✐r❛r❛♠✲s❡ ♦s ✐♠♣✉❧s♦s ❤♦r✐③♦♥t❛✐s✱ ❛s ❝❛r❣❛s ✈❡rt✐❝❛✐s ♥❛ ❜❛s❡ ❡ ❛ ❧♦❝❛❧✐③❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s✳ Pr♦❝❡❞❡✉✲s❡ ❛ ❛♥á❧✐s❡s ♣❛r❛♠étr✐❝❛s r❡❧❛t✐✈❛s à r✉❣♦s✐❞❛❞❡ ❞♦ ❝♦♥t❛❝t♦ ❡♥tr❡ ♦ ♠✉r♦ ❡ ♦ s♦❧♦ s✉♣♦rt❛❞♦✱ ❛♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦ s✉♣♦rt❛❞♦✱ à ❧❛r❣✉r❛ ❞❛ ❜❛s❡ ❞♦ ♠✉r♦ ❡ à ✐♥❝❧✐♥❛çã♦ ❞♦ t❡rr❡♥♦✳ ❈♦♠♣❛r❛r❛♠✲s❡ ♦s ✈❛❧♦r❡s ❞♦s ✐♠♣✉❧s♦s ❛❝t✐✈♦s ❤♦r✐③♦♥t❛✐s ❡ ♦s ✈❛❧♦r❡s ❞❛ t❛♥❣❡♥t❡ ❞♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ s♦❧♦✲❜❛s❡ ♥❡❝❡ssár✐♦ ♣❛r❛ ❛ ✈❡r✐✜❝❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❞❡s❧✐③❛♠❡♥t♦ ❝♦♠ ♦s ♦❜t✐❞♦s ❛♥t❡r✐♦r♠❡♥t❡ ❛tr❛✈és ❞♦s ♠ét♦❞♦s R✱ C

                                                                                                      1 ❡ C 2 ✳

                                                                                                      ❘❡❧❛t✐✈❛♠❡♥t❡ à r✉❣♦s✐❞❛❞❡ ❞♦ ❝♦♥t❛❝t♦ ❡♥tr❡ ♦ ♠✉r♦ ❡ ♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦✱ ✈❡r✐✜❝♦✉✲s❡ q✉❡ s❡ tr❛t❛ ❞❡ ✉♠ ♣❛râ♠❡tr♦ q✉❡✱ ♣❡❧♦ ♠❡♥♦s ♣❛r❛ ❛ ❣❡♦♠❡tr✐❛ ❡st✉❞❛❞❛✱ ♥ã♦ é r❡❧❡✈❛♥t❡✱ ❞❛❞♦ q✉❡ ♥❡♠ ♦ ✐♠♣✉❧s♦ ❛❝t✐✈♦ ❤♦r✐③♦♥t❛❧ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ♥❡♠ ❛ t❛♥❣❡♥t❡ ❞♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ s♦❧♦✲❜❛s❡ ❛♣r❡s❡♥t❛♠ ✈❛r✐❛çõ❡s s✐❣♥✐✜❝❛t✐✈❛s ❝♦♠ ❡ss❛ r✉❣♦s✐❞❛❞❡✳

                                                                                                      ◆❛ ❛♥á❧✐s❡ ♣❛r❛♠étr✐❝❛ r❡❧❛t✐✈❛ ❛♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦ s✉♣♦rt❛❞♦ ❢♦✐ t❛♠❜é♠ ❛♣❡♥❛s ❝♦♥s✐❞❡r❛❞❛ ✉♠❛ ❣❡♦♠❡tr✐❛ ❞♦ ♠✉r♦✳ P❛r❛ ❡ss❡ ❝❛s♦ ✈❡r✐✜❝♦✉✲s❡ ✉♠❛ q✉❛s❡ ❝♦✐♥❝✐❞ê♥❝✐❛ ❡♥tr❡ ♦s r❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ❡ ♦s ♠ét♦❞♦s R✱ C

                                                                                                      1 ❡ C 2 ✱ t❛♥t♦ ♥♦ q✉❡ r❡s♣❡✐t❛ ❛♦ ✐♠♣✉❧s♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦

                                                                                                      ❝♦♠♦ ♥♦ q✉❡ r❡s♣❡✐t❛ à t❛♥❣❡♥t❡ ❞♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ s♦❧♦✲❜❛s❡✳ ❆ ❛♥á❧✐s❡ ♣❛r❛♠étr✐❝❛ r❡❧❛t✐✈❛ à ❧❛r❣✉r❛ ❞❛ ❜❛s❡ ❢♦✐ r❡❛❧✐③❛❞❛ ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ❛ ❛♥á❧✐s❡ ♣❛r❛♠étr✐❝❛

                                                                                                      ❞❛ ✐♥❝❧✐♥❛çã♦ ❞♦ t❡rr❡♥♦ s✉♣♦rt❛❞♦ ❡ ♦s r❡s✉❧t❛❞♦s ♠♦str❛♠ ♣r♦①✐♠✐❞❛❞❡ ❡♥tr❡ ♦ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ❡ ♦ ♠ét♦❞♦ C

                                                                                                      2 ✳

                                                                                                      ❋✐♥❛❧♠❡♥t❡✱ r❡❢❡r❡✲s❡ q✉❡ ❡①✐st❡ ✉♠❛ ♥♦tór✐❛ s❡♠❡❧❤❛♥ç❛ ❡♥tr❡ ❛s ❜❛♥❞❛s ❞❡✜♥✐❞❛s ♣❡❧❛ ❧♦❝❛❧✐③❛çã♦ ❞♦s ♣♦♥t♦s ♣❧ást✐❝♦s r❡s✉❧t❛♥t❡s ❞♦s ❝á❧❝✉❧♦s ♥✉♠ér✐❝♦s ❡ ❛s s✉♣❡r❢í❝✐❡s ♦❜t✐❞❛s ♣♦r ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ H C

                                                                                                      

                                                                                                    2 ✱ ❞❡✜♥✐❞❛s ♣♦r β ❡ β C2,tan δ ✱ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞♦ ❝❛s♦ ❛♥❛❧✐s❛❞♦✳ ■❣✉❛❧♠❡♥t❡✱ ❛s ❜❛♥❞❛s ❞❡

                                                                                                    C2,I a

                                                                                                      ♣♦♥t♦s ♣❧ást✐❝♦s q✉❡ ❞❡✜♥❡♠ ❛ ✐♥❝❧✐♥❛çã♦ ❞❛ ❝✉♥❤❛ ❞❡ s♦❧♦ sã♦ s❡♠❡❧❤❛♥t❡s às s✉♣❡r❢í❝✐❡s ❞❡✜♥✐❞❛s ♣♦r ❇❛r❣❤♦✉t❤✐ ✭✶✾✾✵✮✳

                                                                                                      ❈♦♠♣❛r❛♥❞♦ ♦s ❞✐✈❡rs♦s ♠ét♦❞♦s ❝♦♠ ❛s ❛♥á❧✐s❡s ♥✉♠ér✐❝❛s ❡ ❛ss✉♠✐♥❞♦ ❡st❛s ❝♦♠♦ r✐❣♦r♦s❛s✱ ❝♦♥❝❧✉✐✲s❡ q✉❡ ♦ ♠ét♦❞♦ R é s❡♠♣r❡ ❛❞❡q✉❛❞♦ ♣❛r❛ ♠✉r♦s ❝♦♠ s❛♣❛t❛s ❧♦♥❣❛s ❡ t❛♠❜é♠ ♣❛r❛ s❛♣❛t❛s ❝✉rt❛s q✉❛♥❞♦ i ≤ δ✳ P❛r❛ i > δ✱ ♦ ♠ét♦❞♦ C

                                                                                                      2 ❢♦r♥❡❝❡ r❡s✉❧t❛❞♦s ♠❛✐s ❛❞❡q✉❛❞♦s✳

                                                                                                      2 P❛r❛ ✉♠❛ ❡st✐♠❛t✐✈❛ ❛❞❡q✉❛❞❛ ❞♦ ✐♠♣✉❧s♦ ❤♦r✐③♦♥t❛❧✱ ♦ ♠ét♦❞♦ C ♣❛r❡❝❡ s❡r ♦ ♠❛✐s ❛❞❡q✉❛❞♦✱

                                                                                                      ♣❛r❛ ✉♠❛ ❣❛♠❛ ❞❡ ❣❡♦♠❡tr✐❛ ♠❛✐s ❛❧❛r❣❛❞❛✳ ◆♦ ❡♥t❛♥t♦✱ ❢❛③✲s❡ ♥♦t❛r q✉❡ ♦ ♠ét♦❞♦ R é✱ ♥❛ ❣❡♥❡✲ r❛❧✐❞❛❞❡✱ ❝♦♥s❡r✈❛t✐✈♦✳ P❛r❛ ❡❢❡✐t♦s ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❛♦ ❞❡s❧✐③❛♠❡♥t♦✱ ♦ ♠ét♦❞♦ C

                                                                                                      2 ❢♦r♥❡❝❡ ❜♦♥s

                                                                                                      r❡s✉❧t❛❞♦s✱ ♠❛s ♥ã♦ s✉❜st❛♥❝✐❛❧♠❡♥t❡ ♠❡❧❤♦r❡s ❞♦ q✉❡ ♦ ♠ét♦❞♦ R✱ q✉❡ ♣❛r❡❝❡ r❡✈❡❧❛r✲s❡ ♣❡r❢❡✐t❛♠❡♥t❡ ❛❞❡q✉❛❞♦✳

                                                                                                      ✺✳✷✳ ❋❯❚❯❘❖❙ ❉❊❙❊◆❱❖▲❱■▼❊◆❚❖❙ ✶✵✸

                                                                                                      ❉❡ ❢♦r♠❛ ❝♦♠♣❧❡♠❡♥t❛r✱ ❛ ❝♦♥s✐❞❡r❛çã♦ ❞❡ ♦✉tr♦s ♠♦❞♦s ❞❡ r♦t✉r❛ ❞❛ ❡str✉t✉r❛✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ r♦t✉r❛ ❞❛ ❢✉♥❞❛çã♦✱ ❞❡rr✉❜❛♠❡♥t♦ ♦✉ r♦t✉r❛ ❡str✉t✉r❛❧✱ ❞❡♠♦♥str❛✲s❡ ✐❣✉❛❧♠❡♥t❡ r❡❧❡✈❛♥t❡✳ ❉❡✈❡ ✐❣✉❛❧♠❡♥t❡ ♣r♦❝✉r❛r ❛♥❛❧✐s❛r✲s❡✱ ❡♠ ♠❛✐♦r ❞❡t❛❧❤❡ ❞♦ q✉❡ ♦ q✉❡ ❢♦✐ ♣♦ssí✈❡❧ ♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✱ ❛ ✐♥✢✉ê♥❝✐❛ ❞❛ r✉❣♦s✐❞❛❞❡ s♦❧♦✲♣❛r❛♠❡♥t♦ ♥♦s r❡s✉❧t❛❞♦s ❞♦ ✐♠♣✉❧s♦ ❤♦r✐③♦♥t❛❧ ❡ ❞❛ ❝♦♥❞✐çã♦

                                                                                                      ❞❡ ❞❡s❧✐③❛♠❡♥t♦✳ ❘❡❢❡r❡✲s❡✱ ✜♥❛❧♠❡♥t❡✱ q✉❡ ♦s ❝❛s♦s ❞❡ ❜❛s❡s ❞❡ ♣❡q✉❡♥❛ ❞✐♠❡♥sã♦ ✭❡♠ q✉❡ ❛ s✉♣❡r❢í❝✐❡ ✈✐rt✉❛❧

                                                                                                      ✐♥t❡rs❡❝t❛ ♦ ♣❛r❛♠❡♥t♦✮ sã♦ ♦s q✉❡ ♠❡r❡❝❡♠ ♠❛✐♦r ❛t❡♥çã♦✱ ♥❛ ♠❡❞✐❞❛ ❡♠ q✉❡ ♦s r❡st❛♥t❡s ♣❛r❡❝❡♠ r❡s♦❧✈✐❞♦s✳

                                                                                                      ✶✵✹ ❈❆P❮❚❯▲❖ ✺✳ ❈❖◆❈▲❯❙Õ❊❙ ❊ ❋❯❚❯❘❖❙ ❉❊❙❊◆❱❖▲❱■▼❊◆❚❖❙

                                                                                                      ❇✐❜❧✐♦❣r❛✜❛

                                                                                                      ❆❣✉✐❛r✱ ▼✳ ❆✳ ❡ ▼❛rt✐♥s✱ ❏✳ ●✳ ✭✷✵✵✺✮✳ ❊str✉t✉r❛s ✲ ❈♦♥t❡♥çã♦ ❧❛t❡r❛❧ ❞❡ s♦❧♦s✳ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡r♥❛♥❞♦ P❡ss♦❛✱ P♦rt♦✱ ✶➟ ❡❞✐çã♦✳

                                                                                                      ❇❛r❣❤♦✉t❤✐✱ ❆✳ ❋✳ ✭✶✾✾✵✮✳ ❆❝t✐✈❡ ❡❛rt❤ ♣r❡ss✉r❡ ♦♥ ✇❛❧❧s ✇✐t❤ ❜❛s❡ ♣r♦❥❡❝t✐♦♥✳ ❆❙❈❊ ❏♦✉r♥❛❧ ♦❢ ●❡♦t❡❝❤♥✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣✱ ✶✶✻✭✶✵✮✿✶✺✼✵✕✶✺✼✺✳

                                                                                                      ❇r✐♥❦❣r❡✈❡✱ ❘✳ ❇✳ ❏✳✱ ❇r♦❡r❡✱ ❲✳✱ ❡ ❲❛t❡r♠❛♥✱ ❉✳ ✭✷✵✵✹✮✳ P▲❆❳■❙✿ ❋✐♥✐t❡ ❊❧❡♠❡♥t ❈♦❞❡ ❢♦r ❙♦✐❧ ❛♥❞ ❘♦❝❦ ❆♥❛❧②s❡s ✭✷❉ ✲ ❱❡rs✐♦♥ ✽✮✳

                                                                                                      ❇❙ ✽✵✷✷✿✶✾✾✹ ✭✷✵✵✷✮✳ ❈♦❞❡ ♦❢ ♣r❛❝t✐❝❡ ❢♦r ❡❛rt❤ r❡t❛✐♥✐♥❣ ✇❛❧❧s✳ ❇r✐t✐s❤ ❙t❛♥❞❛r❞✳ ❈❡r♥✐❝❛✱ ❏✳ ◆✳ ✭✶✾✾✹✮✳ ❋♦✉♥❞❛t✐♦♥ ❞❡s✐❣♥✳ ❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✱ ■♥❝✳ ❉♦♠✐♥❣✉❡s✱ P✳ ❈✳ ✭✶✾✾✼✮✳ ■♥❞✐❝❛çõ❡s ♣❛r❛ ♣r♦❥❡❝t♦ ❞❡ ♠✉r♦s ❞❡ ❛rr✐♠♦ ❡♠ ❝♦♥❝r❡t♦ ❛r♠❛❞♦✳ ❉✐ss❡r✲ t❛çã♦ ❞❡ ▼❡str❛❞♦✱ ❊s❝♦❧❛ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞❡ ❙ã♦ ❈❛r❧♦s✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❇r❛s✐❧✳ ❊▼ ✶✶✶✵✲✷✲✷✺✵✷ ✭✶✾✽✾✮✳ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❞❡s✐❣♥ ✲ r❡t❛✐♥✐♥❣ ❛♥❞ ✢♦♦❞ ✇❛❧❧s✳ ❯✳ ❙✳ ❆r♠② ❈♦r♣s ♦❢

                                                                                                      ❊♥❣✐♥❡❡rs✳ ❊◆ ✶✾✾✷✲✶ ✭✷✵✵✶✮✳ ❊✉r♦❝♦❞❡ ✷✱ ❉❡s✐❣♥ ♦❢ ❝♦♥❝r❡t❡ str✉❝t✉r❡s✱ ♣❛rt ✶✿ ●❡♥❡r❛❧ r✉❧❡s ❛♥❞ r✉❧❡s ❢♦r

                                                                                                      ❜✉✐❧❞✐♥❣s✳ ❈❊◆✱ ❊✉r♦♣❡❛♥ ❈♦♠♠✐tt❡❡ ❢♦r ❙t❛♥❞❛r❞✐③❛t✐♦♥✱ ❇r✉ss❡❧s✳ ●❡rs❝♦✈✐❝❤✱ ❉✳ ▼✳ ❙✳ ✭✷✵✵✻✮✳ ❊str✉t✉r❛s ❞❡ ❝♦♥t❡♥çã♦✳ ❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ✲ ❯♥✐✈❡rs✐❞❛❞❡ ❞♦

                                                                                                      ❘✐♦ ❞❡ ❏❛♥❡✐r♦✳ ●r❡❝♦✱ ❱✳ ❘✳ ✭✶✾✾✷✮✳ ❉✐s❝✉ss✐♦♥ t♦ ❛❝t✐✈❡ ❡❛rt❤ ♣r❡ss✉r❡ ♦♥ ✇❛❧❧s ✇✐t❤ ❜❛s❡ ♣r♦❥❡❝t✐♦♥✳ ❆❙❈❊ ❏♦✉r♥❛❧

                                                                                                      ♦❢ ●❡♦t❡❝❤♥✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ❉✐✈✐s✐♦♥✱ ✶✶✽✭✺✮✿✽✷✺✕✽✷✼✳ ●r❡❝♦✱ ❱✳ ❘✳ ✭✶✾✾✾✮✳ ❆❝t✐✈❡ ❡❛rt❤ t❤r✉sts ♦♥ ❝❛♥t✐❧❡✈❡r ✇❛❧❧s ✐♥ ❣❡♥❡r❛❧ ❝♦♥❞✐t✐♦♥s✳ ❙♦✐❧s ❛♥❞ ❋♦✉♥✲

                                                                                                      ❞❛t✐♦♥s✱ ✸✾✭✻✮✿✻✺✕✼✽✳ ●r❡❝♦✱ ❱✳ ❘✳ ✭✷✵✵✶✮✳ ❆❝t✐✈❡ ❡❛rt❤ t❤r✉st ♦♥ ❝❛♥t✐❧❡✈❡r ✇❛❧❧s ✇✐t❤ s❤♦rt ❤❡❡❧✳ ❈❛♥❛❞✐❛♥ ●❡♦t❡❝❤♥✐❝❛❧

                                                                                                      ❏♦✉r♥❛❧✱ ✸✽✭✷✮✿✹✵✶✕✹✵✾✳ ▼❛❝❝❛❢❡rr✐ ✭✷✵✵✸✮✳ ❘♦❛❞ ✇♦r❦s✱ Pr♦❜❧❡♠s ❛♥❞ s♦❧✉t✐♦♥s ✲ ●r❛✈✐t② ❡❛rt❤ r❡t❛✐♥✐♥❣ str✉❝t✉r❡s✳ ▼❛❝❝❛❢❡rr✐

                                                                                                      ✲ ❊♥✈✐r♦♥♠❡♥t❛❧ s♦❧✉t✐♦♥s✳

                                                                                                      ✶✵✻ ❇■❇▲■❖●❘❆❋■❆

                                                                                                      ▼❛t♦s ❋❡r♥❛♥❞❡s✱ ❆✳ ▼✳✱ ▼❛t❡✉s ❞❡ ❇r✐t♦✱ ❏✳✱ ❙✐❧✈❛ ❈❛r❞♦s♦✱ ❆✳✱ ❡ ❱✐❡✐r❛✱ ❈✳ ❋✳ ❙✳ ✭✶✾✾✼✮✳ ❊str✉t✉r❛s ❞❡ s✉♣♦rt❡✳ ❊♠ ✷✺ ❆♥♦s ❙♦❝✐❡❞❛❞❡ P♦rt✉❣✉❡s❛ ❞❡ ●❡♦t❡❝♥✐❛ ✲ ❊✉r♦❝ó❞✐❣♦ ✼✿ Pr♦❥❡❝t♦ ●❡♦té❝♥✐❝♦✱ ♣á❣✐♥❛s ■❱✕✶ ✕ ■❱✕✺✸✳ ▲◆❊❈✳

                                                                                                      ▼✐♥❡✐r♦✱ ❆✳ ❏✳ ❈✳ ✭✶✾✼✽✮✳ ▼❡❝â♥✐❝❛ ❞♦s s♦❧♦s ❡ ❢✉♥❞❛çõ❡s ✲ ■♠♣✉❧s♦s ❞❡ t❡rr❛s✳ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛✳

                                                                                                      ▼♦❧✐t❡r♥♦✱ ❆✳ ✭✶✾✽✵✮✳ ❈❛❞❡r♥♦ ❞❡ ♠✉r♦s ❞❡ ❛rr✐♠♦✳ ❊❞❣❛r❞ ❇❧✉❝❤❡r✱ ❙ã♦ P❛✉❧♦✱ ❇r❛s✐❧✱ ✷➟ ❡❞✐çã♦✳ ✭♥ã♦ ❝♦♥s✉❧t❛❞♦ ❞✐r❡❝t❛♠❡♥t❡✮✳

                                                                                                      ❘♦❝❤❛✱ ❆✳ ▼✳ ✭✶✾✼✹✮✳ ◆♦✈♦ ❝✉rs♦ ♣rát✐❝♦ ❞❡ ❝♦♥❝r❡t♦ ❛r♠❛❞♦✱ ✈♦❧✉♠❡ ✸✳ ❈✐❡♥tí✜❝❛✱ ❘✐♦ ❞❡ ❏❛♥❡✐r♦✱ ❇r❛s✐❧✳ ✭♥ã♦ ❝♦♥s✉❧t❛❞♦ ❞✐r❡❝t❛♠❡♥t❡✮✳

                                                                                                      ❚❡r③❛❣❤✐✱ ❑✳✱ P❡❝❦✱ ❘✳ ❇✳✱ ❡ ▼❡sr✐✱ ●✳ ✭✶✾✹✽✮✳ ❙♦✐❧ ♠❡❝❤❛♥✐❝s ✐♥ ❡♥❣✐♥❡❡r✐♥❣ ♣r❛❝t✐❝❡✳ ❏♦❤♥ ❲✐❧❡② ❛♥❞ ❙♦♥s✱ ◆❡✇ ❨♦r❦✱ ✸➟ ❡❞✐çã♦✳

Novo documento

Tags

Documento similar

Avaliação da extracção e recuperação de betumes modificados com polímeros em misturas betuminosas
0
0
125
UNIVERSIDADE NOVA DE LISBOA Faculdade de Ciências e Tecnologia Departamento de Engenharia Civil Adaptive glass pane using shape-memory alloys
0
0
109
Dissertação para obtenção do Grau de Mestre em Engenharia Civil – Perfil de Estruturas
0
0
152
Engenharia Civil - Perfil de Estruturas
0
0
139
Dissertação para obtenção do Grau de Doutor em Engenharia Civil, Especialidade Estruturas Orientador: Jorge Manuel Gonçalves Branco, Professor Auxiliar, Escola de Engenharia UMinho Co-orientador: Luís Armando Canhoto Neves, Professor Auxiliar, FCTUNL
0
8
364
Dissertação para obtenção do Grau de Mestre em Engenharia Civil – Perfil de Construção Orientador: Fionn McGregor, Post doctoral, École Nationale des Travaux Publics de l’État Co-orientador: Mª Paulina Faria Rodrigues, Professora Associada, Faculdade de C
0
0
102
Contributo para a sua conservação Dissertação para obtenção do Grau de Mestre em Engenharia Civil – Perfil de Construção Orientadora: Professora Doutora Paulina Faria Professora Associada, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa
0
2
187
Dissertação para obtenção do Grau de Mestre em Engenharia Civil – Perfil de Construção
0
0
109
Orientador: Professor Doutor João Pacheco de Almeida, Investigador Pós-Doutorado, EPFL Co-orientador: Professor Doutor Corneliu Cismasiu, Professor Associado, FCTUNL
0
0
106
Dissertação para obtenção do Grau de Mestre em Engenharia Civil – Perfil Construção Orientador: Luís Gonçalo Correia Baltazar, Professor Auxiliar Convidado, Faculdade de Ciências e Tecnologias da Universidade Nova de Lisboa
0
0
91
Dissertação para obtenção do Grau de Mestre em Engenharia Civil – Perfil de Construção Orientadora: Maria Paulina Faria Rodrigues, Professora Associada, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa Coorientador: António Santos Silva,
0
0
153
Avaliação do Comportamento Visco-Plástico de Misturas Betuminosas
0
0
128
Dissertação para obtenção do Grau de Mestre em Engenharia Civil – Perfil de Construção Orientadora: Maria Paulina Faria Rodrigues, Professora Associada, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa
0
0
118
Efeitos estruturais das sobrecargas rodoviárias definidas nas normas mais utilizadas pela engenharia portuguesa em tabuleiros de betão de nervura única e em caixão
0
0
174
Dissertação para obtenção do Grau de Mestre em Engenharia Civil – Ramo de Estruturas e Geotecnia Orientadora: Doutora Simona Fontul, Professora Auxiliar Convidada
0
0
105
Show more