Repositório UFAL: Força e torque de radiação sobre uma partícula viscoelástica em um fluido ideal

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❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❆❧❛❣♦❛s

■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛

❏♦sé P❡r❡✐r❛ ▲❡ã♦ ◆❡t♦

❋♦rç❛ ❡ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛

✈✐s❝♦❡❧ást✐❝❛ ❡♠ ✉♠ ✢✉✐❞♦ ✐❞❡❛❧

4 2 0 2 4

4 2 0 2 4

kx

ky

1 2 3 4 5 [nJ]

❋♦rç❛ ❞❡ r❛❞✐❛çã♦ tr❛♥s✈❡rs❛❧ ❞❡ ✉♠ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ❡♠ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ ♣♦❧✐❡t✐❧❡♥♦✳

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❏♦sé P❡r❡✐r❛ ▲❡ã♦ ◆❡t♦

❋♦rç❛ ❡ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛

✈✐s❝♦❡❧ást✐❝❛ ❡♠ ✉♠ ✢✉✐❞♦ ✐❞❡❛❧

❚❡s❡ ❛♣r❡s❡♥t❛❞❛ ♥♦ ■♥st✐t✉t♦ ❞❡ ❋í✲ s✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❆❧❛❣♦❛s✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♥❡❝❡ssár✐♦ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❋ís✐❝❛✳

❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ●❧❛✉❜❡r ❚✳ ❙✐❧✈❛

▼❛❝❡✐ó ✲ ❇r❛s✐❧ ❙❡t❡♠❜r♦ ✲ ✷✵✶✺

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❈❛t❛❧♦❣❛çã♦ ♥❛ ❢♦♥t❡

❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❆❧❛❣♦❛s

❇✐❜❧✐♦t❡❝❛ ❈❡♥tr❛❧

❉✐✈✐sã♦ ❞❡ ❚r❛t❛♠❡♥t♦ ❚é❝♥✐❝♦

❇✐❜❧✐♦t❡❝ár✐♦ ❘❡s♣♦♥sá✈❡❧✿ ❱❛❧t❡r ❞♦s ❙❛♥t♦s ❆♥❞r❛❞❡

▲✹✸✼❢ ▲❡ã♦ ◆❡t♦✱ ❏♦sé P❡r❡✐r❛✳

❋♦rç❛ ❡ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ ✈✐s❝♦❡❧ást✐❝❛ ❡♠ ✉♠ ✢✉✐❞♦ ✐❞❡❛❧ ✴ ❏♦sé P❡r❡✐r❛ ▲❡ã♦ ◆❡t♦✳ ✕ ✷✵✶✺✳

✾✽ ❢✳✿ ✐❧✳

❖r✐❡♥t❛❞♦r✿ ●❧❛✉❜❡r ❚✳ ❙✐❧✈❛✳

❚❡s❡ ✭❞♦✉t♦r❛❞♦ ❡♠ ❋ís✐❝❛✮ ✕ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❆❧❛❣♦❛s✳ ■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛✳ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛✳ ▼❛❝❡✐ó✱ ✷✵✶✺✳

❇✐❜❧✐♦❣r❛✜❛✿ ❢✳ ✾✵ ✕ ✾✽✳

✶✳ ❋♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛✳ ✷✳ ❚♦rq✉❡ ❞❡ r❛❞✐❛çã♦✳ ✸✳ ❆❝úst✐❝❛✳ ✹✳ ❊s♣❛❧❤❛♠❡♥t♦ ❛❝úst✐❝♦✳ ✺✳ ❱✐s❝♦❡❧❛st✐❝✐❞❛❞❡✳ ✻✳ ▼❛♥✐♣✉❧❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s✳ ■✳ ❚ít✉❧♦✳

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❆❣r❛❞❡❝✐♠❡♥t♦s

❆ ❉❡✉s ♣♦r t❡r s✐❞♦ ♠✐♥❤❛ ❢♦rt❛❧❡③❛ ❡ s✉st❡♥t♦ ♥❛s ❤♦r❛s ❞✐❢í❝❡✐s ❞✉r❛♥t❡ ❡st❛ ❡t❛♣❛ ❞❛ ♠✐♥❤❛ ✈✐❞❛✳

❆ ♠✐♥❤❛ ❡s♣♦s❛ ▲✐❞✐❛♥❡ ❖♠❡♥❛✱ ♣♦r ❡st❛r ❛♦ ♠❡✉ ❧❛❞♦ ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s ♠❡ ✐♥❝❡♥t✐✈❛♥❞♦✱ ♣❡❧♦ ♦ s❡✉ ❛♠♦r ✐♥❝♦♥❞✐❝✐♦♥❛❧ ❡ ♣♦r t♦❞❛ ❛ s✉❛ ♣❛❝✐ê♥❝✐❛ ❡ ❝♦♠♣r❡❡♥sã♦ ♥❡st❛ ❡t❛♣❛ tã♦ ❞✐❢í❝✐❧✳

❆♦s ♠❡✉s ♣❛✐s ■❧s♦♥ ❡ ❋át✐♠❛✱ ♣♦r t♦❞♦ ♦ s❛❝r✐❢í❝✐♦✱ ❞❡❞✐❝❛çã♦✱ ❡ ♣♦r ❛❜❞✐❝❛r❡♠ ❞❡ ♣r♦❥❡t♦s ♣❡ss♦❛✐s ♣❛r❛ q✉❡ ❡✉ t✐✈❡ss❡ ❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❡st✉❞❛r✳ ❊♥✜♠✱ ♦❜r✐❣❛❞♦ ♣♦r t❡r ♠❡ ❞❛❞♦ ❛ ❡❞✉❝❛çã♦ ❡ ❞✐r❡❝✐♦♥❛♠❡♥t♦ q✉❡ ❢♦r❛♠ ✐♠♣r❡s❝✐♥❞í✈❡✐s ♣❛r❛ ❛ ♠✐♥❤❛ ❢♦r♠❛çã♦✳ ❆♦s ♠❡✉s ✐r♠ã♦s ■❧s♦♥ ❏r✱ ■❡❧s♦♥ ▲❡ã♦✱ ■✈❡♥s ▲❡ã♦ ❡ ■❧③❛ ❋❡r♥❛♥❞❛ ♣♦r t♦❞♦ ❝♦♠♣❛✲ ♥❤❡✐r✐s♠♦✱ ✜❞❡❧✐❞❛❞❡ ❡ ♣♦r s❡♠♣r❡ s❡r❡♠ ❡①❡♠♣❧♦s ❞❡ ❞❡t❡r♠✐♥❛çã♦ ❡ ✉♥✐ã♦ ♥❛ ♠✐♥❤❛ ✈✐❞❛✳

❆ ●r❛♥❞❡ ❢❛♠í❧✐❛✿ ❉✳ ❈❧❛✉❞❡t❡✱ ❉✳ ❙♦❝♦rr♦✱ ▲✐❞②❛♥❡ ■❣♥á❝✐♦✱ ■r✐s ▲✐♠❛✱ ●❛❜r✐❡❧❛ ❆③❡✈❡❞♦✱ ❘❡❣✐♥❛ ❚♦❧❡❞♦ ❡ ▼❛r❝♦s ❆♥❞ré ♣♦r t♦❞❛ ❛ ✉♥✐ã♦✱ ❛♣♦✐♦ ❡ ✐♥❝❡♥t✐✈♦✳ ❆❧é♠ ❞❛s ❞❛t❛s ✐♠♣♦rt❛♥t❡s✱ ♠♦♠❡♥t♦s ❡s♣❡❝✐❛✐s✱ q✉❡ ❡st❛♠♦s t♦❞♦s ❥✉♥t♦s ❢❛③❡♥❞♦ s❡♠♣r❡ ❜♦❛s ❝♦♥❢r❛t❡r♥✐③❛çõ❡s✱ ❝♦♠ ❜♦❛s ❝♦♥✈❡rs❛s ❡ r✐s❛❞❛s✳ ◆ã♦ ♣♦❞❡r✐❛ ❞❡✐①❛r ❞❡ ❛❣r❛❞❡❝❡r ❛♦s ♠❡✉s s♦❜r✐♥❤♦s✿ ▲❡♦♥❛r❞♦ ■❣♥á❝✐♦✱ ▼❛r✐❛ ▲ét✐❝✐❛ ❡ ■❛♥ ❘❛❢❛❡❧ ♣❡❧❛ ❛❧❡❣r✐❛ ❡ ❡♥❡r❣✐❛ ❞❡ s❡♠♣r❡✳

❆ t♦❞♦s ♠❡✉s ❢❛♠✐❧✐❛r❡s q✉❡ ❡st✐✈❡r❛♠ ♣r❡s❡♥t❡s ❞✉r❛♥t❡ ❛ ♠✐♥❤❛ ❢♦r♠❛çã♦✳

❆♦ Pr♦❢✳ ●❧❛✉❜❡r ❚✳ ❙✐❧✈❛ ♣♦r ❛❝r❡❞✐t❛r ♥♦ ♠❡✉ tr❛❜❛❧❤♦✱ ♣❡❧♦ s❡✉ ❛♣♦✐♦✱ ❞❡❞✐❝❛çã♦ ❡ ❞✐s♣♦s✐çã♦ ❡♠ ❛❥✉❞❛r✳ ❉✐s♣♦♥❞♦ ❞❡ ❤♦r❛s ❞❡ ♦r✐❡♥t❛çã♦ ♣❛r❛ ❛ ❝♦♥❝r❡t✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳

❆♦ ❣r✉♣♦ t✉❝❛♥♦ ❛③✉❧✱ q✉❡ ❥á sã♦ ♠✐♥❤❛ ❢❛♠í❧✐❛✿ ❆♥❞ré ▼♦✉r❛ ✭●❛❜❡❤✮✱ ❊♠♠❛♥✉❡❧❧❡ ❙❛t✐❦♦✱ ❍❡♥r✐q✉❡ ▲♦♣❡s ✭●❛❧♦ ❈❡❣♦✮ ❡ ❚❛♠✐r②s ▼❛❝❡❞♦✳ P❡❧♦s ♠♦♠❡♥t♦s ❞❡ ❞❡s❝♦♥tr❛çã♦✱ q✉❡ ♥ã♦ ❢♦r❛♠ ♣♦✉❝♦s✱ ♣❡❧❛ ❛♠✐③❛❞❡ ❞❡ ❝❛❞❛ ✉♠ ❞❡ ✈♦❝ês✳ P♦r ❡st❛r❡♠ s❡♠♣r❡ ♣r❡s❡♥t❡s✱ ✐♥❞❡♣❡♥❞❡♥t❡ ❞♦ ♠♦♠❡♥t♦ q✉❡ ❝❛❞❛ ✉♠ ❡st❛ ♣❛ss❛♥❞♦✳

❆♦s ❛♠✐❣♦s ❋r❡❞❡r✐❝♦ P❛ss♦s✱ ❆❧❡① ❈♦st❛ ❡ ❆♥❞❡rs♦♥ ❇❛♥❞❡✐r❛ ♣♦r ❡st❛r❡♠ s❡♠♣r❡ ❞✐s♣♦st♦s ❛ ❛❥✉❞❛r✱ ♣♦r t❡r ❛♣r❡♥❞✐❞♦ ♠✉✐t♦ ❝♦♠ ✈♦❝ês ❡ ♣❡❧♦s ✐♥❝❡♥t✐✈♦s ❞❛❞♦s ❞✉r❛♥t❡ t♦❞❛ ❛ ♠✐♥❤❛ ❢♦r♠❛çã♦✳

❆♦s ❛♠✐❣♦s ▲✉✐③ ❊❞✉❛r❞♦✱ ❱❛❧♠✐r♦ ❍♦r❛ ❡ ❘♦❣ér✐♦ ▼❛t✐❛s q✉❡ t✐✈❡ ❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❝♦♥✈✐✈❡r ❡ ❛♣r❡♥❞❡r ♠✉✐t♦✳

❆♦s ❛♠✐❣♦s Pr♦❢✳ ❲❛♥❞❡❛r❧❡② ❉✐❛s ❡ Pr♦❢❛✳ ❙♦❝♦rr♦ ❙❡✐①❛s ♣❡❧♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦✱

♣❡❧❛s ❜♦❛s ❝♦♥✈❡rs❛s ❡ ♣❡❧♦s ✐♥❝❡♥t✐✈♦s q✉❡ ❢♦r❛♠ ❡ss❡♥❝✐❛✐s ♥❡st❛ ❡t❛♣❛✳

❆♦s ❛♠✐❣♦s ❞♦ ●❆❋✱ ❡♠ ❡s♣❡❝✐❛❧ ❛♦ Pr♦❢✳ ❆♥❞ré ❇❛❣❣✐♦ ♣♦r t♦❞❛ ❝♦❧❛❜♦r❛çã♦✳ ❆♦s ♣r♦❢❡ss♦r❡s ❞❛ ❜❛♥❝❛✱ ♣♦r ❛❝❡✐t❛r ♣❛rt✐❝✐♣❛r ❞❡st❡ ♠♦♠❡♥t♦ ✐♠♣♦rt❛♥t❡ ♥❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❡ ❝♦♥tr✐❜✉✐r ❝♦♠ ❡st❡ tr❛❜❛❧❤♦✳

❆ t♦❞♦s ♦s ❛♠✐❣♦s ❞♦ ■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛✱ ❡♠ ❡s♣❡❝✐❛❧✱ ❛♦s ❛♠✐❣♦s ❞❛ ❇❛t❝❛✈❡r♥❛✳ ❆ t♦❞♦ ❝♦r♣♦ ❞♦❝❡♥t❡ ❞♦ ■❋✱ ♣♦r ❝♦♥tr✐❜✉í❞♦ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♥❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❛❝❛❞ê♠✐❝❛✳ ❊♠ ❡s♣❡❝✐❛❧ ❛♦s ♣r♦❢❡ss♦r❡s✱ ❈r✐só❣♦♥♦ ❙✐❧✈❛ ❡ ❑❧é❜❡r ❙❡rr❛✳

❆ ❈❆P❊❙ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦ ❞✉r❛♥t❡ ♦ ❉♦✉t♦r❛❞♦✳

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❘❡s✉♠♦

❖ ❡st✉❞♦ ❞♦s ❢❡♥ô♠❡♥♦s ❞❡ ❢♦rç❛ ❡ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦ t❡♠ ❛tr❛í❞♦ ✉♠ ❡♥♦r♠❡ ✐♥t❡r❡ss❡ ❞❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛✱ ❞❡✈✐❞♦ ❛ ❛♣❧✐❝❛çõ❡s ❞❡ss❡s ❢❡♥ô♠❡♥♦s ❡♠ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s s❡♠ ❝♦♥t❛t♦✳ ◆❡st❡ tr❛❜❛❧❤♦✱ r❡❛❧✐③❛♠♦s ✉♠❛ ❛♥á❧✐s❡ t❡ór✐❝❛ ❞❛ ❢♦rç❛ ❡ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦ ❡①❡r❝✐❞♦ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ ✈✐s❝♦❡❧ást✐❝❛ ❤♦♠♦❣ê♥❡❛ ♥♦ ❧✐♠✐t❡ ❞♦ ❡s♣❛❧❤❛♠❡♥t♦ ❞❡ ❘❛②❧❡✐❣❤ ✭♦ r❛✐♦ ❞❛ ♣❛rtí❝✉❧❛ é ♠✉✐t♦ ♠❡♥♦r q✉❡ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ✐♥❝✐❞❡♥t❡✮ ♣♦r ✉♠❛ ♦♥❞❛ ❝♦♠ ❣❡♦♠❡tr✐❛ ❛r❜✐trár✐❛✳ ◆♦ss♦ ❡st✉❞♦ ❜❛s❡✐❛✲s❡ ♥❛ ❡①♣❛♥sã♦ ❞❡ ♦♥❞❛s ♣❛r❝✐❛✐s ❡♠ ❝♦♦r❞❡♥❛❞❛s ❡s❢ér✐❝❛s ❞❛s ♦♥❞❛s ✐♥❝✐❞❡♥t❡ ❡ ❡s♣❛❧❤❛❞❛✳ ◆❡ss❡ ❝♦♥t❡①t♦✱ ❛ ❢♦rç❛ ❡ ♦ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ sã♦ ♦❜t✐❞♦s ❛♥❛❧✐t✐❝❛♠❡♥t❡ ❡♠ t❡r♠♦s ❞❡ ✉♠❛ sér✐❡ ✐♥✜♥✐t❛ q✉❡ ❡♥✈♦❧✈❡ ♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ ❡①♣❛♥sã♦ ❞❛s ♦♥❞❛s ❡s♣❛❧❤❛❞❛ ❡ ✐♥❝✐❞❡♥t❡✳ ❆ss✉♠✐♠♦s q✉❡ ❛ ♣❛rtí❝✉❧❛ s❡ ❝♦♠♣♦rt❛ ❝♦♠♦ ✉♠ só❧✐❞♦ ✈✐s❝♦❡❧ást✐❝♦ ❧✐♥❡❛r✱ q✉❡ ♦❜❡❞❡❝❡ ♦ ♠♦❞❡❧♦ ❞❡ ❑❡❧✈✐♥✲❱♦✐❣t ❢r❛❝✐♦♥ár✐♦✳ ❋ór♠✉❧❛s ❛♥❛❧ít✐❝❛s ♣❛r❛ ❛ ❢♦rç❛ ❡ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ sã♦ ♦❜t✐❞❛s ❝♦♥s✐❞❡r❛♥❞♦ ✉♠❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ❜❛✐①❛ ❡ ❞❡ ❛❧t❛ ❢r❡q✉ê♥❝✐❛ ♥♦ ♠♦❞❡❧♦ ✈✐s❝♦❡❧ást✐❝♦✳ ❆ t❡♦r✐❛ ❞❡s❡♥✈♦❧✈✐❞❛ é ✉s❛❞❛ ♣❛r❛ ❞❡s❝r❡✈❡r ❛ ✐♥t❡r❛çã♦ ❞❡ ♦♥❞❛s ❛❝úst✐❝❛s ✭♦♥❞❛ ♣❧❛♥❛ ♣r♦❣r❡ss✐✈❛✱ ♦♥❞❛ ♣❧❛♥❛ ❡st❛❝✐♦♥ár✐❛✱ ❢❡✐①❡s ❞❡ ❇❡ss❡❧ ❞❡ ♦r❞❡♠ ③❡r♦ ❡ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✮ ❝♦♠ ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✐❡t✐❧❡♥♦ ❞❡ ❜❛✐①❛ ❡ ❞❡ ❛❧t❛ ❞❡♥s✐❞❛❞❡✳ ❖s ♥♦ss♦s r❡s✉❧t❛❞♦s ♠♦str❛♠ q✉❡ ❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ❛①✐❛❧ ♣♦❞❡ s❡r ♥❡❣❛t✐✈❛ ✭✐st♦ é✱ ❡♠ ♦♣♦s✐çã♦ à ❞✐r❡çã♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞❛ ♦♥❞❛✮ q✉❛♥❞♦ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❝♦♥❞✐çã♦ ❡♥✈♦❧✈❡♥❞♦ ♦s ♣❛râ♠❡tr♦s ❢ís✐❝♦s ❞❛ ♣❛rtí❝✉❧❛ é s❛t✐s❢❡✐t❛✳ ❚♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦ ♥❡❣❛t✐✈♦ ❞❡✈✐❞♦ ❛ ✉♠ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ t❛♠❜é♠ ♣♦❞❡ ♦❝♦rr❡r q✉❛♥❞♦ ❛ ♠❡s♠❛ ❝♦♥❞✐çã♦ ❞❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ♥❡❣❛t✐✈❛ ❢♦r ❛t❡♥❞✐❞❛✳ ◆♦t❛✈❡❧♠❡♥t❡✱ ❡st❛ é ❛ ♣r✐♠❡✐r❛ ✈❡③ q✉❡ ❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ♥❡❣❛t✐✈❛ é ♣r❡✈✐st❛ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ ❤♦♠♦❣ê♥❡❛ ♥♦ r❡❣✐♠❡ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛②❧❡✐❣❤✳ ❆❧é♠ ❞✐ss♦✱ ❛ ❡st❛❜✐❧✐❞❛❞❡ tr❛♥s✈❡rs❛❧ ❞❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ❣❡r❛❞❛ ♣❡❧♦ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ t❛♠❜é♠ é ✐♥✈❡st✐❣❛❞❛✳ ▼♦str❛♠♦s q✉❡ ✉♠ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ tr❛t♦r ✸❉ ❝♦♠♣❧❡t♦ ❛t✉❛ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ ♣♦❧✐❡t✐❧❡♥♦ ❞❡ ❛❧t❛ ❞❡♥s✐❞❛❞❡ ✭P❊❆❉✮✳ ◆❛ ❛♥á❧✐s❡ ❞❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ❣❡r❛❞❛ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ ✈✐s❝♦❡❧ást✐❝❛ ♣♦r ✉♠❛ ♦♥❞❛ ♣❧❛♥❛ ❡st❛❝✐♦♥ár✐❛✱ ❞❡s✈✐♦s r❡❧❡✈❛♥t❡s s✉r❣✐r❛♠ ❡♠ ❝♦♠♣❛r❛çã♦ ❝♦♠ ♣❛rtí❝✉❧❛ só❧✐❞❛ ❡❧ást✐❝❛✳ ❆ ❛♠♣❧✐t✉❞❡ ❞❛ ❢♦rç❛ ❡ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ s♦❜r❡ ✉♠❛ P❊❆❉ ❞❡s❝r✐t❛ ♣❡❧♦ ♠♦❞❡❧♦ ✈✐s❝♦❡❧ást✐❝♦ ❛♣r❡s❡♥t❛ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❞✐❢❡r❡♥t❡ ✭❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ♥❡❣❛t✐✈❛✮ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦s ♦✉tr♦s ♠❛t❡r✐❛✐s ✭só❧✐❞❛ ❡❧ást✐❝❛ ❡ ✢✉✐❞❛ ❝♦♠ ❛❜s♦rçã♦ ❧♦♥❣✐t✉❞✐♥❛❧✮ ❞❡✈✐❞♦ ❛ ♦♥❞❛ ♣❧❛♥❛ ♣r♦❣r❡ss✐✈❛ ❡ ❢❡✐①❡s ❞❡ ❇❡ss❡❧✳ P♦r ✜♠✱ ❛❝r❡❞✐t❛♠♦s q✉❡ ❡st❡ ❡st✉❞♦ ♣♦❞❡ ❛❥✉❞❛r ❛ ♠❡❧❤♦r❛r ❛✐♥❞❛ ♠❛✐s ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❞✐s♣♦s✐t✐✈♦s ❞❡ ❧❡✈✐t❛çã♦ ❛❝úst✐❝❛✱ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❡♠ ❛❝✉st♦✢✉í❞✐❝❛ ❡ ♣✐♥ç❛s ❛❝úst✐❝❛s✳

P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❋♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛✱ ❚♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦✱ ❊s♣❛❧❤❛✲ ♠❡♥t♦ ❛❝úst✐❝♦✱ ❱✐s❝♦❡❧❛st✐❝✐❞❛❞❡✱ ▼❛♥✐♣✉❧❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s✳

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❆❜str❛❝t

❚❤❡ st✉❞② ♦❢ ❛❝♦✉st✐❝ r❛❞✐❛t✐♦♥ ❢♦r❝❡ ❛♥❞ t♦rq✉❡ ♣❤❡♥♦♠❡♥❛ ❤❛s ❛ttr❛❝t❡❞ ❛♥ ❡♥♦r♠♦✉s ✐♥t❡r❡st ♦❢ t❤❡ s❝✐❡♥t✐✜❝ ❝♦♠♠✉♥✐t②✱ ❞✉❡ t♦ ❛♣♣❧✐❝❛t✐♦♥s ♦❢ t❤❡s❡ ♣❤❡♥♦♠❡♥❛ ✐♥ ♥♦♥❝♦♥✲ t❛❝t ♣❛rt✐❝❧❡s ♠❛♥✐♣✉❧❛t✐♦♥✳ ■♥ t❤✐s ✇♦r❦✱ ✇❡ ♣❡r❢♦r♠ ❛ t❤❡♦r❡t✐❝❛❧ ❛♥❛❧②s✐s ♦❢ ❛❝♦✉st✐❝ r❛❞✐❛t✐♦♥ ❢♦r❝❡ ❛♥❞ t♦rq✉❡ ❡①❡rt❡❞ ♦♥ ❛ ❤♦♠♦❣❡♥❡♦✉s ✈✐s❝♦❡❧❛st✐❝ ♣❛rt✐❝❧❡ ✐♥ t❤❡ ❘❛②❧❡✐❣❤ s❝❛tt❡r✐♥❣ ❧✐♠✐t ✭t❤❡ ♣❛rt✐❝❧❡ r❛❞✐✉s ✐s ♠✉❝❤ s♠❛❧❧❡r t❤❛♥ t❤❡ ✐♥❝✐❞❡♥t ✇❛✈❡❧❡♥❣t❤✮ ❜② ❛ ✇❛✈❡ ✇✐t❤ ❛r❜✐tr❛r② ❣❡♦♠❡tr②✳ ❖✉r st✉❞② ✐s ❜❛s❡❞ ♦♥ t❤❡ ♣❛rt✐❛❧✲✇❛✈❡ ❡①♣❛♥s✐♦♥ ✐♥ s♣❤❡✲ r✐❝❛❧ ❝♦♦r❞✐♥❛t❡s ♦❢ t❤❡ ✐♥❝✐❞❡♥t ❛♥❞ s❝❛tt❡r❡❞ ✇❛✈❡s✳ ■♥ t❤✐s ❝♦♥t❡①t✱ t❤❡ r❛❞✐❛t✐♦♥ ❢♦r❝❡ ❛♥❞ t♦rq✉❡ ❛r❡ ♦❜t❛✐♥❡❞ ❛♥❛❧②t✐❝❛❧❧② ✐♥ t❡r♠s ♦❢ ❛♥ ✐♥✜♥✐t❡ s❡r✐❡s ✇❤✐❝❤ ✐♥✈♦❧✈❡s t❤❡ s❝❛t✲ t❡r✐♥❣ ❛♥❞ ✐♥❝✐❞❡♥t ❡①♣❛♥s✐♦♥ ❝♦❡✣❝✐❡♥ts✳ ❲❡ ❛ss✉♠❡ t❤❛t t❤❡ ♣❛rt✐❝❧❡ ❜❡❤❛✈❡s ❛s ❛ ❧✐♥❡❛r ✈✐s❝♦❡❧❛st✐❝ s♦❧✐❞✱ ✇❤✐❝❤ ♦❜❡②s t❤❡ ❢r❛❝t✐♦♥❛❧ ❑❡❧✈✐♥✲❱♦✐❣t ♠♦❞❡❧✳ ❆♥❛❧②t✐❝❛❧ ❡①♣r❡ss✐♦♥s ❢♦r t❤❡ r❛❞✐❛t✐♦♥ ❢♦r❝❡ ❛♥❞ t♦rq✉❡ ❛r❡ ♦❜t❛✐♥❡❞ ❝♦♥s✐❞❡r✐♥❣ t❤❡ ❧♦✇✲ ❛♥❞ ❤✐❣❤✲❢r❡q✉❡♥❝② ❛♣♣r♦①✐♠❛t✐♦♥ ✐♥ t❤❡ ✈✐s❝♦❡❧❛st✐❝ ♠♦❞❡❧✳ ❚❤❡ ❞❡✈❡❧♦♣❡❞ t❤❡♦r② ✐s ✉s❡❞ t♦ ❞❡s❝r✐❜❡ t❤❡ ✐♥t❡r❛❝t✐♦♥ ♦❢ ❛❝♦✉st✐❝ ✇❛✈❡s ✭tr❛✈❡❧✐♥❣ ❛♥❞ st❛♥❞✐♥❣ ♣❧❛♥❡ ✇❛✈❡s✱ ❛♥❞ ③❡r♦ ❛♥❞ ✜rst✲♦r❞❡r ❇❡ss❡❧ ❜❡❛♠s✮ ✇✐t❤ ❛ ❧♦✇✲❛♥❞ ❤✐❣❤✲❞❡♥s✐t② ♣♦❧②❡t❤②❧❡♥❡ ♣❛rt✐❝❧❡✳ ❖✉r r❡s✉❧ts s❤♦✇ t❤❛t t❤❡ ❛①✐❛❧ ❛❝♦✉st✐❝ r❛❞✐❛t✐♦♥ ❢♦r❝❡ ♠✐❣❤t ❜❡❝♦♠❡ ♥❡❣❛t✐✈❡ ✭✐✳❡✳ ✐♥ ♦♣♣♦s✐t✐♦♥ t♦ t❤❡ ✇❛✈❡ ♣r♦♣❛❣❛t✐♦♥ ❞✐r❡❝t✐♦♥✮ ✇❤❡♥ ❛ ❝❡rt❛✐♥ ❝♦♥❞✐t✐♦♥ ✐♥✈♦❧✈✐♥❣ t❤❡ ♣❤②s✐❝❛❧ ♣❛r❛♠❡t❡rs ♦❢ t❤❡ ♣❛rt✐❝❧❡ ✐s s❛t✐s✜❡❞✳ ◆❡❣❛t✐✈❡ ❛❝♦✉st✐❝ r❛❞✐❛t✐♦♥ t♦rq✉❡ ❞✉❡ ❛ ❜❡❛♠ ♦❢ ✜rst✲♦r❞❡r ❇❡ss❡❧ ♠❛② ❛❧s♦ ♦❝❝✉r ✇❤❡♥ t❤❡ s❛♠❡ ❝♦♥❞✐t✐♦♥ ♦❢ ♥❡❣❛t✐✈❡ r❛❞✐❛t✐♦♥ ❢♦r❝❡ ✐s ♠❡t✳ ❘❡♠❛r❦❛❜❧②✱ t❤✐s ✐s t❤❡ ✜rst t✐♠❡ t❤❛t ♥❡❣❛t✐✈❡ r❛❞✐❛t✐♦♥ ❢♦r❝❡ ✐s ♣r❡❞✐❝t❡❞ ♦♥ ❛ ❤♦♠♦❣❡♥❡♦✉s ♣❛rt✐❝❧❡ ✐♥ t❤❡ ❘❛②❧❡✐❣❤ s❝❛tt❡r✐♥❣ r❡❣✐♠❡✳ ❋✉rt❤❡r♠♦r❡✱ t❤❡ st❛❜✐❧✐t② ♦❢ t❤❡ tr❛♥s✈❡rs❡ ❛❝♦✉st✐❝ r❛❞✐❛t✐♦♥ ❢♦r❝❡ ❣❡♥❡r❛t❡❞ ❜② ❛ ❇❡ss❡❧ ❜❡❛♠ ✐s ❛❧s♦ ✐♥✈❡st✐❣❛t❡❞✳ ❲❡ s❤♦✇ ❛ ❢✉❧❧ ✸❉ tr❛❝t♦r ❇❡ss❡❧ ✈♦rt❡① ❜❡❛♠ ❛❝t✐♥❣ ♦♥ t❤❡ ❤✐❣❤✲❞❡♥s✐t② ♣♦❧②❡t❤②❧❡♥❡ ✭❍❉P❊✮✳ ■♥ t❤❡ ❛♥❛❧②s✐s ♦❢ ❛❝♦✉st✐❝ r❛❞✐❛t✐♦♥ ❢♦r❝❡ ❣❡♥❡r❛t❡❞ ♦♥ ❛ ✈✐s❝♦❡❧❛st✐❝ ♣❛rt✐❝❧❡ ❜② ❛ st❛♥❞✐♥❣ ♣❧❛♥❡ ✇❛✈❡✱ r❡❧❡✈❛♥t ❞❡✈✐❛t✐♦♥s ❛r♦s❡ ✐♥ ❝♦♠♣❛r✐s♦♥ ✇✐t❤ t❤❡ s♦❧✐❞ ❡❧❛st✐❝ ♠♦❞❡❧ ❢♦r t❤❡ ♣❛rt✐❝❧❡s✳ ❚❤❡ ♠❛❣♥✐t✉❞❡ ♦❢ t❤❡ r❛❞✐❛t✐♦♥ ❢♦r❝❡ ❛♥❞ t♦rq✉❡ ♦♥ ❛ ❍❉P❊ ❞❡s❝r✐❜❡❞ ❜② t❤❡ ✈✐s❝♦❡❧❛st✐❝ ♠♦❞❡❧ ❜❡❤❛✈❡s ❞✐✛❡r❡♥t❧② ✭♥❡❣❛t✐✈❡ r❛❞✐❛t✐♦♥ ❢♦r❝❡✮ ❝♦♠♣❛r❡❞ ✇✐t❤ ♦t❤❡r ♠❛t❡r✐❛❧s ✭s♦❧✐❞ ❡❧❛st✐❝ ❛♥❞ ❝♦♠♣r❡ss✐❜❧❡ ✢✉✐❞ ♣❛rt✐❝❧❡✮ ❞✉❡ t♦ tr❛✈❡❧✐♥❣ ♣❧❛♥❡ ✇❛✈❡ ❛♥❞ ❇❡ss❡❧ ❜❡❛♠s✳ ❋✐♥❛❧❧②✱ ✇❡ ❜❡❧✐❡✈❡ t❤❛t t❤✐s st✉❞② ♠❛② ❤❡❧♣ ❢✉rt❤❡r ❡♥❤❛♥❝❡ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❛❝♦✉st✐❝ ❧❡✈✐t❛t✐♦♥✱ ♣❛rt✐❝❧❡ ❤❛♥❞❧✐♥❣ ✐♥ ❛❝♦✉st♦✢✉✐❞s✱ ❛♥❞ ❛❝♦✉st✐❝❛❧ t✇❡❡③❡rs ❞❡✈✐❝❡s✳

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▲✐st❛ ❞❡ sí♠❜♦❧♦s

❙í♠❜♦❧♦ ◆♦♠❡ ❯♥✐❞❛❞❡s✭❙✳■✳✮

ρ0 ❞❡♥s✐❞❛❞❡ ❞♦ ✢✉✐❞♦ ✐❞❡❛❧ kg·m−3

ρ ❞❡♥s✐❞❛❞❡ kg·m−3

m ♠❛ss❛ kg

c0 ✈❡❧♦❝✐❞❛❞❡ ❞♦ s♦♠ ♥♦ ✢✉✐❞♦ ✐❞❡❛❧ m/s

cℓ ✈❡❧♦❝✐❞❛❞❡ ❞♦ s♦♠ ❧♦♥❣✐t✉❞✐♥❛❧ m/s

cs ✈❡❧♦❝✐❞❛❞❡ ❞♦ s♦♠ ❞❡ ❝✐s❛❧❤❛♠❡♥t♦ m/s

τℓ t❡♠♣♦ ❞❡ r❡❧❛①❛çã♦ ❧♦♥❣✐t✉❞✐♥❛❧ s

τs t❡♠♣♦ ❞❡ r❡❧❛①❛çã♦ ❞❡ ❝✐s❛❧❤❛♠❡♥t♦ s

a r❛✐♦ ❞❛ ♣❛rtí❝✉❧❛ m

w ✈❡t♦r ❞❡s❧♦❝❛♠❡♥t♦ m

v ✈❡❧♦❝✐❞❛❞❡ ❞❛ ♣❛rtí❝✉❧❛ m/s

ǫ t❡♥s♦r ❞❡❢♦r♠❛çã♦

σ t❡♥s♦r ❞❡ t❡♥sõ❡s ❡♠ só❧✐❞♦s

♣ ♣r❡ssã♦ ❛❝úst✐❝❛ Pa

L ❞❡♥s✐❞❛❞❡ ▲❛❣r❛♥❣✐❛♥❛ ❛❝úst✐❝❛ J/m3

φ ♣♦t❡♥❝✐❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡ m2/s

ψ1,s✱ψ2,s ♣♦t❡♥❝✐❛✐s ❡s❝❛❧❛r❡s ❞❡ ❉❡❜②❡ m2/s

ω ❢r❡q✉ê♥❝✐❛ ❛♥❣✉❧❛r s−1

λ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ m−1

❦ ♥ú♠❡r♦ ❞❡ ♦♥❞❛ m−1

❦ℓ ♥ú♠❡r♦ ❞❡ ♦♥❞❛ ❧♦♥❣✐t✉❞✐♥❛❧ m−1

❦s ♥ú♠❡r♦ ❞❡ ♦♥❞❛ ❞❡ ❝✐s❛❧❤❛♠❡♥t♦ m−1

anm ❝♦❡✜❝✐❡♥t❡ ❢♦r♠❛ ❞♦ ❢❡✐①❡

sn ❝♦❡✜❝✐❡♥t❡ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❡s❝❛❧❛r

bn✱cn✱dn ❝♦❡✜❝✐❡♥t❡s ❞❡ ❡①♣❛♥sã♦

ε ♣❛râ♠❡tr♦ ❞❡ ❡s❝❛❧❛ ❡♠ t❡r♠♦s ❞♦ t❛♠❛♥❤♦ ❞❛ ♣❛rtí❝✉❧❛

εj ♣❛râ♠❡tr♦ ❞❡ ❡s❝❛❧❛ ❡♠ t❡r♠♦s t❡♠♣♦ ❞❡ r❡❧❛①❛çã♦

ϕ â♥❣✉❧♦ ❛③✐♠✉t❛❧

θ â♥❣✉❧♦ r❛❞✐❛❧

jn ❢✉♥çã♦ ❞❡ ❇❡ss❡❧ ❡s❢ér✐❝❛ ❞❡ ♦r❞❡♠ ♥

h(1)n ❢✉♥çã♦ ❞❡ ❍❛♥❦❡❧ ❡s❢ér✐❝❛ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ♥

h(2)n ❢✉♥çã♦ ❞❡ ❍❛♥❦❡❧ ❡s❢ér✐❝❛ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ♥

Ym

n ❤❛r♠ô♥✐❝♦s ❡s❢ér✐❝♦s

Pm

n ❢✉♥çõ❡s ❛ss♦❝✐❛❞❛s ❞❡ ▲❡❣❡♥❞r❡ ❞❡ ♦r❞❡♠ ♥

Fr❛❞ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ N

Yx, Yy, Yz ❝♦♠♣♦♥❡♥t❡s ❛❞✐♠❡♥s✐♦♥❛✐s ❞❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦

Nr❛❞ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦ N·m

Nx, Ny, Nz ❝♦♠♣♦♥❡♥t❡s ❛❞✐♠❡♥s✐♦♥❛✐s ❞♦ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦

∇ ♦♣❡r❛❞♦r ❣r❛❞✐❡♥t❡ m−1

∇· ♦♣❡r❛❞♦r ❞✐✈❡r❣❡♥t❡ m−1

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∇× ♦♣❡r❛❞♦r r♦t❛❝✐♦♥❛❧ m−1

∇2 ♦♣❡r❛❞♦r ▲❛♣❧❛❝✐❛♥♦ m−2

r ✈❡t♦r ♣♦s✐çã♦ ♠

(x, y, z) ❝♦♦r❞❡♥❛❞❛s ❝❛rt❡s✐❛♥❛s (r, θ, φ) ❝♦♦r❞❡♥❛❞❛s ❡s❢ér✐❝❛s

(ex,ey,ez) ❝♦♠♣♦♥❡♥t❡s ❝❛rt❡s✐❛♥❛s ✉♥✐trát✐❛s

n ✈❡t♦r ♥♦r♠❛❧ à s✉♣❡r❢í❝✐❡

n í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦ ❝♦♠♣❧❡①♦

nR í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦ ❞♦ ♠❛t❡r✐❛❧

˜

α ❢✉♥çã♦ ❞❡ ❛❜s♦rçã♦ ❛❞✐♠❡♥s✐♦♥❛❧

❘❡ ♣❛rt❡ r❡❛❧

■♠ ♣❛rt❡ ✐♠❛❣✐♥ár✐❛

(12)

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✸✳✶ ❈♦❡✜❝✐❡♥t❡s ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❞❛❞♦s ♥❛ ❊q✳ ✭✸✳✸✼✮ sã♦ ♦❜t✐❞♦s r❡s♦❧✈❡♥❞♦ ♦ s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s ❧✐♥❡❛r❡s ♣❛r❛ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ♥❛ s✉♣❡r❢í❝✐❡ ❞❛ ♣❛rtí❝✉❧❛✳ ❖s ❊❧❡♠❡♥t♦s ❞❛ ♠❛tr✐③ ❞❡ss❛ ❡q✉❛çã♦ sã♦ ❞❛❞♦s ❛q✉✐✳ ✳ ✳ ✳ ✳ ✳ ✺✶

✺✳✶ P❛râ♠❡tr♦s ❡ ♠❡❞✐❞❛s ❞❛ q✉❛❧✐❞❛❞❡ ❞♦ ❛❥✉st❡ ♣❛r❛ ❛ ❢✉♥çã♦ ❞❡ ❛❜s♦rçã♦ ♥❛ ❊q✳ ✭✺✳✷✺✮ ❡ ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❞❡ ❛❜s♦rçã♦ ❧♦♥❣✐t✉❞✐♥❛❧ ❡ ❞❡ ❝✐s❛❧❤❛♠❡♥t♦ ❡①tr❛í❞♦s ❞❛s ❋✐❣✳ ✹ ❡ ✺ ❞❛ ❘❡❢✳ ❬✶✵✾❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✺✳✷ Pr♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ❡ ♦s ♣❛râ♠❡tr♦s ❞❡ ❛❥✉st❡s ❞❛ ♣❛rtí❝✉❧❛ ❞❡ ♣♦❧✐❡t✐❧❡♥♦

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▲✐st❛ ❞❡ ❋✐❣✉r❛s

✶✳✶ ▲❡✈✐t❛çã♦ ❛❝úst✐❝❛ ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✐❡st✐r❡♥♦ ♣❛r❛ três ❝♦♥✜❣✉r❛çõ❡s ❞✐❢❡r❡♥t❡s ❞♦ ❧❡✈✐t❛❞♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✷✳✶ ❋♦rç❛s ❛t✉❛♥❞♦ s♦❜r❡ ❛s ♣❛rtí❝✉❧❛s ❞❡ ♠❛ss❛mi ❡ ✈❡❧♦❝✐❞❛❞❡vi q✉❡ ♦❝✉♣❛♠ ✉♠

❡❧❡♠❡♥t♦ ❞❡ ✢✉✐❞♦ ❞❡ ✈♦❧✉♠❡ V0(t)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

✷✳✷ ❈♦♦r❞❡♥❛❞❛s ❡s❢ér✐❝❛s(r, θ, ϕ)✿ r é ❛ ❞✐stâ♥❝✐❛ r❛❞✐❛❧✱θ é ♦ â♥❣✉❧♦ ♣♦❧❛r ❡ϕé ♦ â♥❣✉❧♦ ❛③✐♠✉t❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✸ ❉❡❢♦r♠❛çã♦ ❞❡ ✉♠ ♠❡✐♦ ❝♦♥tí♥✉♦ ❞❡ ✈♦❧✉♠❡V0 ❡ s✉♣❡r❢í❝✐❡S0 ♣❛r❛ ♦ ✈♦❧✉♠❡V0′

❡ s✉♣❡r❢í❝✐❡S′

0✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

✷✳✹ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ✈❡t♦r tr❛çã♦q ❞❡ ✉♠ ♠❡✐♦ ❝♦♥tí♥✉♦ ❞❡ ✈♦❧✉♠❡ V0 ❡ s✉♣❡r❢í❝✐❡

S0 ❞❡✈✐❞♦ ❛ ❢♦rç❛s ❡①t❡r♥❛sfi(i= 1,2,3)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

✸✳✶ ❯♠ ❢❡✐①❡ ✐♥❝✐❞❡♥t❡ ✭❜❛rr❛s ✈❡rt✐❝❛✐s ✈❡r❞❡✲❡s❝✉r♦✮✱ ❝♦♠ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛λ❡ r❡♣r❡s❡♥t❛❞♦ ♣❡❧❛ ❛♠♣❧✐t✉❞❡ ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡φ✐♥✱ ❛t✐♥❣❡ ✉♠❛ ♣❡q✉❡♥❛ ♣❛rtí❝✉❧❛ ✈✐s❝♦❡❧ást✐❝❛ ✭❝ír❝✉❧♦ ✈❡r♠❡❧❤♦✮ ❞❡ r❛✐♦ a s✉s♣❡♥s♦ ♥✉♠ ✢✉✐❞♦✱ ❝♦♠ ❞❡♥s✐❞❛❞❡ ρ0 ❡ ❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ s♦♠ c0✳ ❯♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❝❛rt❡s✐❛♥❛

❡stá s✐t✉❛❞♦ ♥♦ ❝❡♥tr♦ ❞❛ ♣❛rtí❝✉❧❛ ❝♦♠ ✉♠ ♣♦♥t♦ ❞❡ ♦❜s❡r✈❛çã♦ ❞❡s✐❣♥❛❞♦ ♣♦r r = (x, y, z)✳ ❈♦♦r❞❡♥❛❞❛s ❡s❢ér✐❝❛s (r, θ, ϕ) t❛♠❜é♠ sã♦ ✐❧✉str❛❞♦s✳ ❆s ♦♥❞❛s ❡s♣❛❧❤❛❞❛s ✭❛r❝♦s ✈❡r❞❡ ❝❧❛r♦✮ sã♦ r❡♣r❡s❡♥t❛❞♦s ♣❡❧❛ ❛♠♣❧✐t✉❞❡ ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡φs❝✳ ❙❡t❛s ♣r❡t❛s ✐♥❞✐❝❛♠ ❛s ❞✐r❡çõ❡s ❞❡ ♣r♦♣❛❣❛çã♦ ❞❛ ♦♥❞❛✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✶ ■❧✉str❛çã♦ ❞❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ❛ ♦♥❞❛ ✐♥❝✐❞❡♥t❡ φ✐♥✭❜❛rr❛s ✈❡rt✐❝❛✐s ✈❡r❞❡✲❡s❝✉r♦✮

❞❡ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛λ❡ ❛ ♣❛rtí❝✉❧❛ ✈✐s❝♦❡❧ást✐❝❛ ✭❝ír❝✉❧♦ ✈❡r♠❡❧❤♦✮ ❞❡ r❛✐♦a s✉s♣❡♥s❛ ❡♠ ✉♠ ✢✉✐❞♦ ✐❞❡❛❧✳ ❆ ♦♥❞❛ ❡s♣❛❧❤❛❞❛ ❞❡✈✐❞♦ ❡ss❛ ✐♥t❡r❛çã♦ é ❞❡♥♦t❛❞❛ ♣♦r φs❝✭❛r❝♦s ✈❡r❞❡ ❝❧❛r♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✷ ❙✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ♣❛r❛ ❝♦♠♣✉t❛r ❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ❡♠ ✉♠❛

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▲■❙❚❆ ❉❊ ❋■●❯❘❆❙

✺✳✶ ❋❡✐①❡ ❞❡ ❇❡ss❡❧ r❡♣r❡s❡♥t❛❞♦ ♣♦r ✉♠❛ s✉♣❡r♣♦s✐çã♦ ❞❡ ♦♥❞❛s ♣❧❛♥❛s ❝♦♠β s❡♥❞♦ ♦ â♥❣✉❧♦ ❞❡ ♠❡✐♦ ❝♦♥❡✳ ❖ ❝✐r❝✉❧♦ ✈❡r♠❡❧❤♦ r❡♣r❡s❡♥t❛ ❛ ♣❛rtí❝✉❧❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✺✳✷ ❆❥✉st❡ ❞❛ ❢✉♥çã♦ ❞❡ ❛❜s♦rçã♦ ❞❛ ❊q✳ ✭✺✳✷✺✮ ❞♦s ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❞❡ ❛❜s♦rçã♦ ❧♦♥❣✐t✉❞✐♥❛❧ ✭❛✮ ❡ ❞❡ ❝✐s❛❧❤❛♠❡♥t♦ ✭❜✮ ❡①tr❛í❞♦s ❞❛s ❋✐❣✳ ✹ ❡ ✺ ❞❛ ❘❡❢✳ ❬✶✵✾❪ ♣❛r❛ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ P♦❧✐❡t✐❧❡♥♦ ❞❡ ❛❧t❛ ❞❡♥s✐❞❛❞❡ ✭P❊❆❉✮✳ ▲❡❣❡♥❞❛✿ ❧✐♥❤❛ só❧✐❞❛ ❛③✉❧ r❡♣r❡s❡♥t❛ ♦ ❛❥✉st❡ ❞❛ ❢✉♥çã♦ ❞❡ ❛❜s♦rçã♦ ❞❛❞❛ ♥❛ ❊q✳ ✭✺✳✷✺✮✱ ♣♦♥t♦s ✈❡r♠❡❧❤♦s r❡♣r❡s❡♥t❛♠ ♦s ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❞❛❞♦ ♥❛s ❋✐❣✳ ✹ ❡ ✺ ❞❛ ❘❡❢✳ ❬✶✵✾❪✳ ✼✻ ✺✳✸ ❆❥✉st❡ ❞❛ ❢✉♥çã♦ ❞❡ ❛❜s♦rçã♦ ❞❛ ❊q✳ ✭✺✳✷✺✮ ❞♦s ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❞❡ ❛❜s♦rçã♦

❧♦♥❣✐t✉❞✐♥❛❧ ✭❛✮ ❡ ❞❡ ❝✐s❛❧❤❛♠❡♥t♦ ✭❜✮ ❡①tr❛í❞♦s ❞❛s ❋✐❣✳ ✹ ❡ ✺ ❞❛ ❘❡❢✳ ❬✶✵✾❪ ♣❛r❛ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ P♦❧✐❡t✐❧❡♥♦ ❞❡ ❜❛✐①❛ ❞❡♥s✐❞❛❞❡ ✭P❊❇❉✮✳ ▲❡❣❡♥❞❛✿ ❧✐♥❤❛ só❧✐❞❛ ❛③✉❧ r❡♣r❡s❡♥t❛ ♦ ❛❥✉st❡ ❞❛ ❢✉♥çã♦ ❞❡ ❛❜s♦rçã♦ ❞❛❞❛ ♥❛ ❊q✳ ✭✺✳✷✺✮✱ ♣♦♥t♦s ✈❡r♠❡❧❤♦s r❡♣r❡s❡♥t❛♠ ♦s ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❞❛❞♦ ♥❛s ❋✐❣✳ ✹ ❡ ✺ ❞❛ ❘❡❢✳ ❬✶✵✾❪✳ ✼✼ ✺✳✹ ❋♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ✈❡rs✉s ❢r❡q✉ê♥❝✐❛ ❡①❡r❝✐❞❛ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡

♣♦❧✐❡t✐❧❡♥♦ ❞❡ ❛❧t❛ ❞❡♥s✐❞❛❞❡ ✭P❊❆❉✮ ❡ ❞❡ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ ♣♦❧✐❡t✐❧❡♥♦ ❞❡ ❜❛✐①❛ ❞❡♥s✐❞❛❞❡ ✭P❊❇❉✮✳ ❆s ❝♦♥✜❣✉r❛çõ❡s sã♦✿ ✉♠❛ ♦♥❞❛ ♣❧❛♥❛ ♣r♦❣r❡ss✐✈❛ ❛❣✐♥❞♦ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ ✭❛✮ ❞❡ P❊❆❉ ❡ ✭❜✮ ❞❡ P❊❇❉✳ ❆s ♣❛rtí❝✉❧❛s ❞❡ P❊❆❉ ❡ P❊❇❉ sã♦ s✉s♣❡♥s❛ ❡♠ á❣✉❛ ❡ t❡♠ r❛✐♦ ❞❡ a= 1.0,0.01 mm✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❖s ♣❛râ♠❡tr♦s ❢ís✐❝♦s ❞❛s ♣❛rtí❝✉❧❛s sã♦ ❞❛❞♦s ♥❛ ❚❛❜❡❧❛ ✺✳✷✳ ❖s ❢❡✐①❡s ✐♥❝✐❞❡♥t❡s tê♠ ♣✐❝♦ ❞❡ ✐♥t❡♥s✐❞❛❞❡ ❞❡I0= 30kW/m2✳ ▲❡❣❡♥❞❛✿ ❧✐♥❤❛ só❧✐❞❛ ❛③✉❧ r❡♣r❡s❡♥t❛

❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛✈❛❧✐❛❞❛ ♥❛ ❛♣r♦①✐♠❛çã♦ ♠♦♥♦♣♦❧♦✲❞✐♣♦❧♦ ❞❛❞❛ ♥❛ ❊q✳ ✭✹✳✹✶✮✱ ❧✐♥❤❛ ✈❡r♠❡❧❤❛ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ♥♦s r❡❣✐♠❡s ❞❡ ❜❛✐①❛ ❡ ❛❧t❛ ❢r❡q✉ê♥❝✐❛ ❛tr❛✈és ❞❛ ❊qs✳ ✭✺✳✺✮ ♣❛r❛ ♦♥❞❛ ♣❧❛♥❛ ♣r♦❣r❡ss✐✈❛✳ ❖s ✐♥s❡rt❡s ♠♦str❛♠ ♦ ❡rr♦ r❡❧❛t✐✈♦ ❡♥tr❡ ❛ ❢ór♠✉❧❛s ❞❡ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦✳ ❆ ❧✐♥❤❛ ✈❡rt✐❝❛❧ ♣♦♥t✐❧❤❛❞❛ ❞❡❧✐♠✐t❛ ❛ r❡❣✐ã♦ ❞❛ ❛♣r♦①✐♠❛çã♦ ❘❛②❧❡✐❣❤✱ ε <0.3✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✺✳✺ ❋♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ✈❡rs✉s ❢r❡q✉ê♥❝✐❛ ❡①❡r❝✐❞❛ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ ♣♦✲

❧✐❡t✐❧❡♥♦ ❞❡ ❛❧t❛ ❞❡♥s✐❞❛❞❡ ✭P❊❆❉✮ ❡ ❞❡ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ ♣♦❧✐❡t✐❧❡♥♦ ❞❡ ❜❛✐①❛ ❞❡♥s✐❞❛❞❡ ✭P❊❇❉✮✳ ❆s ❝♦♥✜❣✉r❛çõ❡s sã♦✿ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ❝♦♠ n= 1❡β = 45◦❛❣✐♥❞♦ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ ✭❛✮ P❊❆❉ ❡ ✭❜✮ ❞❡ P❊❇❉✳ ❆s ♣❛r✲

tí❝✉❧❛s ❞❡ P❊❆❉ ❡ P❊❇❉ sã♦ s✉s♣❡♥s❛ ❡♠ á❣✉❛ ❡ t❡♠ r❛✐♦ ❞❡ a= 1.0,0.01 mm✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❖s ♣❛râ♠❡tr♦s ❢ís✐❝♦s ❞❛s ♣❛rtí❝✉❧❛s sã♦ ❞❛❞♦s ♥❛ ❚❛❜❡❧❛ ✺✳✷✳ ❖s ❢❡✐①❡s ✐♥❝✐❞❡♥t❡s tê♠ ♣✐❝♦ ❞❡ ✐♥t❡♥s✐❞❛❞❡ ❞❡ I0= 30 kW/m2✳ ▲❡❣❡♥❞❛✿ ❧✐♥❤❛

só❧✐❞❛ ❛③✉❧ r❡♣r❡s❡♥t❛ ❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛✈❛❧✐❛❞❛ ♥❛ ❛♣r♦①✐♠❛çã♦ ♠♦♥♦♣♦❧♦✲ ❞✐♣♦❧♦ ❞❛❞❛ ♥❛ ❊q✳ ✭✹✳✹✶✮✱ ❧✐♥❤❛ ✈❡r♠❡❧❤❛ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ❛ ❢♦rç❛ ❞❡ r❛❞✐✲ ❛çã♦ ♥♦s r❡❣✐♠❡s ❞❡ ❜❛✐①❛ ❡ ❛❧t❛ ❢r❡q✉ê♥❝✐❛ ❛tr❛✈és ❞❛ ❊q✳ ✭✺✳✶✻✮ ♣❛r❛ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✳ ❖s ✐♥s❡rt❡s ♠♦str❛♠ ♦ ❡rr♦ r❡❧❛t✐✈♦ ❡♥tr❡ ❛ ❢ór♠✉❧❛s ❞❡ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦✳ ❆ ❧✐♥❤❛ ✈❡rt✐❝❛❧ ♣♦♥t✐❧❤❛❞❛ ❞❡❧✐♠✐t❛ ❛ r❡❣✐ã♦ ❞❛ ❛♣r♦①✐♠❛çã♦ ❘❛②❧❡✐❣❤✱ ε <0.3✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶

(15)

▲■❙❚❆ ❉❊ ❋■●❯❘❆❙

✺✳✻ ❈❛♠♣♦ ✈❡t♦r✐❛❧ ✭s❡t❛s✮ ❞❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ tr❛♥s✈❡rs❛❧ ♥♦ ♣❧❛♥♦ xy✱ ❡①❡r❝✐❞♦ s♦❜r❡ ❛ ♣❛rtí❝✉❧❛ ❞❡ P❊❆❉ ❝♦♠ r❛✐♦ a= 1 mm ♥❛ á❣✉❛✳ ❖ ❣rá✜❝♦ ❞❡ ❝♦♥t♦r♥♦ ❝♦rr❡s♣♦♥❞❡ ❛ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ U1 ❞❛❞❛ ♥❛ ❊q✳ ✭✺✳✶✼✮✳

❖s ♣❛râ♠❡tr♦s ❞♦ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ sã♦ ♦s ♠❡s♠♦s ❞❡s❝r✐t♦s ♥❛ ❧❡❣❡♥❞❛ ❞❛ ❋✐❣✳ ✺✳✺✳ ◆♦ ❡♥t❛♥t♦✱ ❛q✉✐ ✜①❛♠♦s ❛ ❢r❡q✉ê♥❝✐❛ ♣❛r❛ 50 kHz✳ ❖ ❝❛♠♣♦ ✈❡t♦r✐❛❧ ❞❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ é ❝❛❧❝✉❧❛❞♦ ❛tr❛✈és ❞❛ ❊q✳ ✭✺✳✷✵✮✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✺✳✼ ❋♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ♣r♦❞✉③✐❞❛ ♣♦r ✉♠❛ ♦♥❞❛ ♣❧❛♥❛ ❡st❛❝✐♦♥ár✐❛ ❛♦ ❧♦♥❣♦

❞♦ ❡✐①♦ z ❡♠ ✭❛✮ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ P❊❆❉ ♣❛r❛ 50 kHz ❡ ✭❜✮ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ P❊❇❉ ♣❛r❛2 MHz✱ ✐♠❡rs♦ ❡♠ á❣✉❛✳ ❖s ♣❛râ♠❡tr♦s ❢ís✐❝♦s ❞❛ ♣❛rtí❝✉❧❛ sã♦ ❞❛❞♦s ♥❛ ❚❛❜❡❧❛ ✺✳✷✳ ❆ ♦♥❞❛ ♣❧❛♥❛ ❡st❛❝✐♦♥ár✐❛ t❡♠ ♣✐❝♦ ❞❡ ♣r❡ssã♦ ❞❡ 0.3 MPa✳ ❆ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❢♦✐ ❝♦♠♣✉t❛❞❛ ✉s❛♥❞♦ ❛ ❊q✳ ✭✺✳✽✮✳ P❛r❛ ♦ ♠♦❞❡❧♦ ❡❧ást✐❝♦ ❡♠ ♣❡r❞❛s✱ ❛ss✉♠✐♠♦s q✉❡ f0✭❘✮=f0✭❊✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✺✳✽ ❚♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦ ✈❡rs✉s ❢r❡q✉ê♥❝✐❛ ❡①❡r❝✐❞♦ ♣♦r ✉♠ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ ❞❡

♣r✐♠❡✐r❛ ♦r❞❡♠ s♦❜r❡ ✭❛✮ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ P❊❆❉ ❡ ✭❜✮ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ P❊❇❉ ❞❡ r❛✐♦ a = 1.0,0.01 mm✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ✐♠❡rs♦ ❡♠ á❣✉❛✳ ❖s ♣❛râ♠❡tr♦s ❢ís✐❝♦s ❞❛s ♣❛rtí❝✉❧❛s sã♦ ❞❛❞♦s ♥❛ ❚❛❜❡❧❛ ✺✳✷✳ ❖ ❢❡✐①❡ ✐♥❝✐❞❡♥t❡ t❡♠ s❡✉ ♣✐❝♦ ❞❡ ✐♥t❡♥s✐❞❛❞❡ ❞❡ I0 = 30 kW/m2✳ ▲❡❣❡♥❞❛✿ ❧✐♥❤❛ só❧✐❞❛ ❛③✉❧ é ♦ t♦rq✉❡ ❞❡

r❛❞✐❛çã♦ ❛✈❛❧✐❛❞♦ ♥❛ ❛♣r♦①✐♠❛çã♦ ♠♦♥♦♣♦❧♦✲❞✐♣♦❧♦ ❞❛❞♦ ♥❛ ❊q✳ ✭✹✳✻✷✮✱ ❧✐♥❤❛ ✈❡r♠❡❧❤❛ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ♥♦s r❡❣✐♠❡s ❞❡ ❜❛✐①❛ ❡ ❛❧t❛ ❢r❡q✉ê♥❝✐❛ ❛tr❛✈és ❞❛ ❊q✳ ✭✺✳✷✹✮✳ ❖s ✐♥s❡rt❡s ♠♦str❛♠ ♦ ❡rr♦ r❡❧❛t✐✈♦ ❡♥tr❡ ❛s ❢ór♠✉❧❛s ❞❡ t♦rq✉❡✳ ❆ ❧✐♥❤❛ ✈❡rt✐❝❛❧ ♣♦♥t✐❧❤❛❞❛ ❞❡❧✐♠✐t❛ ❛ r❡❣✐ã♦ ❞❛ ❛♣r♦①✐♠❛çã♦ ❘❛②❧❡✐❣❤ε <0.3✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✺✳✾ ❋♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ♣r♦❞✉③✐❞❛ ♣♦r ✉♠❛ ♦♥❞❛ ♣❧❛♥❛ ♣r♦❣r❡ss✐✈❛✱ ❢❡✐①❡ ❞❡

❇❡ss❡❧ ❞❡ ♦r❞❡♠ ③❡r♦ ❡ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ❡①❡r❝✐❞❛ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ ❞❡ ✭❛✮ P❊❆❉ ❡ ✭❜✮ P❊❇❉ ❞❡ r❛✐♦s a= 1.0,0.01 mm✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❖s ❢❡✐①❡s ✐♥❝✐❞❡♥t❡s t❡♠ ❢r❡q✉ê♥❝✐❛ ❞❡ ✭❛✮2MHz❡ ✭❜✮50kHz✱ ♣✐❝♦ ❞❡ ✐♥t❡♥s✐❞❛❞❡

I0 = 30 kW/m2✱ ❡ â♥❣✉❧♦ ❞❡ ♠❡✐♦ ❝♦♥❡ β = 45◦✳ ❖s ✈❛❧♦r❡s ❞❛s ❛♠♣❧✐t✉❞❡s ❞❛s

(16)

❙✉♠ár✐♦

✶ ■♥tr♦❞✉çã♦ ✶✻

✶✳✶ ❘❡✈✐sã♦ ❍✐stór✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✶✳✶✳✶ ❋♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✶✳✶✳✷ ❚♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✶✳✷ ❆♣❧✐❝❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✶✳✷✳✶ ▲❡✈✐t❛çã♦ ❛❝úst✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✶✳✷✳✷ P✐♥ç❛ ❛❝úst✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✶✳✷✳✸ ❆❝✉st♦✢✉í❞✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✶✳✸ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✶✳✹ ❆rt✐❣♦s ❡ ♣✉❜❧✐❝❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✳✺ ❆♣r❡s❡♥t❛çã♦ ❣❡r❛❧ ❞♦ tr❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷

✷ ❊q✉❛çõ❡s ❞♦ ♠♦❞❡❧♦ ✷✹

(17)

❙❯▼➪❘■❖

✸ ❊s♣❛❧❤❛♠❡♥t♦ ❛❝úst✐❝♦ ♥♦ ❧✐♠✐t❡ ❞❡ ❘❛②❧❡✐❣❤ ✹✹

✸✳✶ ❊s♣❛❧❤❛♠❡♥t♦ ♣♦r ✉♠❛ ❡s❢❡r❛ ✈✐s❝♦❡❧ást✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✷ ▲✐♠✐t❡ ❞❡ ❘❛②❧❡✐❣❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

✹ ❋♦rç❛ ❡ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦ ♥♦ ❧✐♠✐t❡ ❞❡ ❘❛②❧❡✐❣❤ ✺✸

✹✳✶ ❊❢❡✐t♦s ♥❡❣❧✐❣❡♥❝✐❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✷ ❋♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ♥♦ ❧✐♠✐t❡ ❞❡ ❘❛②❧❡✐❣❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✷✳✶ ❚❡♥s♦r t❡♥sã♦ ❞❡ r❛❞✐❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✷✳✷ ▼ét♦❞♦ ❞❡ ❝❛♠♣♦ ❞✐st❛♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✸ ❚♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦ ♥♦ ❧✐♠✐t❡ ❞❡ ❘❛②❧❡✐❣❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✸✳✶ ❋❧✉①♦ ❞♦ ♠♦♠❡♥t♦ ❛♥❣✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✸✳✷ ▼ét♦❞♦ ❞❡ ❝❛♠♣♦ ❞✐st❛♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✹ ❊①♣❛♥sã♦ ❛ss✐♥tót✐❝❛ ❞♦ í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦ ❝♦♠♣❧❡①♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✹✳✶ ❘❡❣✐♠❡ ❞❡ ❜❛✐①❛ ❢r❡q✉ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✹✳✷ ❘❡❣✐♠❡ ❞❡ ❛❧t❛ ❢r❡q✉ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻

✺ ❘❡s✉❧t❛❞♦s ❡ ❞✐s❝✉ssõ❡s ✻✽

✺✳✶ ❊①❡♠♣❧♦s ❞❡ ♦♥❞❛s ❛❝úst✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✺✳✶✳✶ ❖♥❞❛ ♣❧❛♥❛ ♣r♦❣r❡ss✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✺✳✶✳✷ ❖♥❞❛ ♣❧❛♥❛ ❡st❛❝✐♦♥ár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✺✳✶✳✸ ❋❡✐①❡ ❞❡ ❇❡ss❡❧ ❛❝úst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✺✳✷ ❘❡s✉❧t❛❞♦s ❡ ❞✐s❝✉ssõ❡s ♣❛r❛ ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✐❡t✐❧❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✺✳✷✳✶ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♣♦❧✐❡t✐❧❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✺✳✷✳✷ ❆♥á❧✐s❡ ❞♦s ♣❛râ♠❡tr♦s ❞❡ ❡s❝❛❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✺✳✷✳✸ ❖♥❞❛s ♣r♦❣r❡ss✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✺✳✷✳✹ ❋❡✐①❡ ❞❡ ❇❡ss❡❧ tr❛t♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✺✳✷✳✺ ❖♥❞❛ ♣❧❛♥❛ ❡st❛❝✐♦♥ár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✺✳✷✳✻ ❚♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ♣♦r ✉♠ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✺✳✷✳✼ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♣❛rtí❝✉❧❛s s❡♠ ❛❜s♦rçã♦ ❞❡ ❝✐s❛❧❤❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✽✹

✻ ❈♦♥❝❧✉sõ❡s ❡ tr❛❜❛❧❤♦s ❢✉t✉r♦s ✽✽

(18)

1

■♥tr♦❞✉çã♦

❖♥❞❛s ❛❝úst✐❝❛s ❝♦♥s✐st❡♠ ❡♠ ♣❡rt✉r❜❛çõ❡s q✉❡ tr❛♥s♣♦rt❛♠ ❡♥❡r❣✐❛ ❡ ♠♦♠❡♥t♦✳ ❖ ♠♦♠❡♥t♦ ❞❛ ♦♥❞❛ ✐♥❝✐❞❡♥t❡ ♣♦❞❡ s❡r tr❛♥s❢❡r✐❞♦ ♣❛r❛ ♦❜❥❡t♦s s✉s♣❡♥s♦s✳ ❊st❛ tr❛♥s❢❡rê♥✲ ❝✐❛ ❞♦ ♠♦♠❡♥t♦ ❧✐♥❡❛r ❡ ❛♥❣✉❧❛r ❞❛ ♦♥❞❛ ❛❝úst✐❝❛ ❤❛r♠ô♥✐❝❛ ♣❛r❛ ✉♠ ♦❜❥❡t♦ s✉s♣❡♥s♦ ♣♦❞❡ ❞❛r ♦r✐❣❡♠ ❛♦s ❢❡♥ô♠❡♥♦s ❞❡ ❢♦rç❛ ❡ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❬✶✱ ✷❪✳

◗✉❛♥❞♦ ✉♠ ❝❛♠♣♦ ❛❝úst✐❝♦ é ❛♣❧✐❝❛❞♦ ❡♠ ✉♠ ✢✉✐❞♦ ❝♦♥t❡♥❞♦ ♣❛rtí❝✉❧❛s s✉s♣❡♥s❛s✱ ❡ss❛s ♣❛rtí❝✉❧❛s s❡rã♦ ❛❢❡t❛❞❛s ❞❡✈✐❞♦ ❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛✳ ❆ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♣♦r ✉❧tr❛ss♦♠ ✉t✐❧✐③❛ ❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ♣❛r❛ ❢♦r♥❡❝❡r ✉♠ ♠ét♦❞♦ ❞❡ ♠❛♥✐♣✉✲ ❧❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s s❡♠ ❝♦♥t❛t♦✳ ❊st❡ ♠ét♦❞♦ t♦r♥♦✉✲s❡ ♣r♦♠✐ss♦r ♥❛ ár❡❛ ❞❡ ❜✐♦t❡❝♥♦❧♦✲ ❣✐❛ ❡ ♣❡r♠✐t❡ ❛ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ❞✐✈❡rs❛s ♣❛rtí❝✉❧❛s✱ ✐♥❝❧✉✐♥❞♦ ❝é❧✉❧❛s ❜✐♦❧ó❣✐❝❛s ❡ ♦✉tr♦s ♠✐❝r♦r❣❛♥✐s♠♦s ❬✸❪✕❬✶✺❪ ❡ ❧❡✈✐t❛çã♦ ❛❝úst✐❝❛ ♥♦ ❛r ❬✶✻❪✕❬✶✾❪✳ ❊st❡s ♠ét♦❞♦s ❞❡♣❡♥❞❡♠ s♦♠❡♥t❡ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ♠❡❝â♥✐❝❛s ❞❛ ♣❛rtí❝✉❧❛ ❡ ❞♦ ✢✉✐❞♦✳ ❆❧é♠ ❞❡ s❡r tr❛♥s❧❛❞❛❞❛ ♦✉ ❛♣r✐s✐♦♥❛❞❛✱ ✉♠❛ ♣❛rtí❝✉❧❛ ♣♦❞❡ s❡r ❛❥✉st❛❞❛ ♣❛r❛ ❣✐r❛r ❞❡✈✐❞♦ ❛♦ t♦rq✉❡ ❞❡ r❛❞✐❛✲ çã♦ ❛❝úst✐❝♦ ❬✷✵❪✕❬✷✷❪✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ✉♠ ❣r❛✉ ❞❡ ❧✐❜❡r❞❛❞❡ ❞❡ r♦t❛çã♦ t❛♠❜é♠ é ❛✈❛❧✐❛❞♦ ♥❛ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❝♦♠ ❜❛s❡ ❡♠ ♠ét♦❞♦s ❛❝úst✐❝♦s✳

◆❡st❡ ❝❛♣ít✉❧♦ ❢❛r❡♠♦s ✉♠❛ r❡✈✐sã♦ ❤✐stór✐❝❛ ❞♦s ❢❡♥ô♠❡♥♦s ❞❡ ❢♦rç❛ ❡ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦ ❣❡r❛❞♦s ♣♦r ♠❡✐♦ ❞❛ ✐♥t❡r❛çã♦ ❞❡ ✉♠❛ ♦♥❞❛ ❛❝úst✐❝❛ ❝♦♠ ✉♠ ♦❜❥❡t♦✳ ❆❧é♠ ❞✐ss♦✱ ✐r❡♠♦s ❛❜♦r❞❛r ❛❧❣✉♠❛s ❛♣❧✐❝❛çõ❡s t❡❝♥♦❧ó❣✐❝❛s ❡ ❛♣r❡s❡♥t❛r ❛ ♠♦t✐✈❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳

✶✳✶ ❘❡✈✐sã♦ ❍✐stór✐❝❛

✶✳✶✳✶ ❋♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛

❖ ❡st✉❞♦ ❞❡ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ❡♠ ♣❛rtí❝✉❧❛s ❡s❢ér✐❝❛s t❡✈❡ ✐♥í❝✐♦ ❡♠ ✶✾✸✹ ❬✷✸❪✳ ◆❡ss❡ tr❛❜❛❧❤♦ ♣✐♦♥❡✐r♦✱ ❑✐♥❣ ♦❜t❡✈❡ ✉♠❛ ❡①♣r❡ssã♦ ❣❡r❛❧ ♣❛r❛ ❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ❛♣❧✐❝❛❞❛ ❛ ✉♠❛ ❡s❢❡r❛ rí❣✐❞❛ ✭t❛♠❛♥❤♦ ❛r❜✐trár✐♦✮ s✉s♣❡♥s❛ ❡♠ ✉♠ ✢✉✐❞♦ ✐❞❡❛❧ ❞❡✈✐❞♦ ❛ ✉♠❛ ♦♥❞❛ ♣❧❛♥❛ ♣r♦❣r❡ss✐✈❛ ❡ ✉♠❛ ♦♥❞❛ ♣❧❛♥❛ ❡st❛❝✐♦♥ár✐❛✳ ❆ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❢♦✐ ❡①♣r❡ss❛ ❡♠ t❡r♠♦s ❞❡ ✉♠❛ sér✐❡ ✐♥✜♥✐t❛✱ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❡①♣❛♥sã♦ ❞❡ ♦♥❞❛s ♣❛r❝✐❛✐s✳ ❯♠❛ ❡①t❡♥sã♦ ❞♦ tr❛❜❛❧❤♦ ❞❡ ❑✐♥❣ ❝♦♥s✐❞❡r❛♥❞♦ ✉♠❛ ♦♥❞❛ ❡s❢ér✐❝❛ ✐♥❝✐❞❡♥t❡ ❢♦✐ ♣r♦♣♦st♦ ♣♦r ❊♠❜❧❡t♦♥ ❬✷✹❪✳ P❡r❝❡❜❡✉✲s❡ q✉❡ ❛ ♣❛rtí❝✉❧❛ ♣♦❞❡ s❡r t❛♥t♦ ❛tr❛í❞❛ ❝♦♠♦ r❡♣❡❧✐❞❛

(19)

✶✳✶ ❘❡✈✐sã♦ ❍✐stór✐❝❛ ✶✼

(20)

✶✳✶ ❘❡✈✐sã♦ ❍✐stór✐❝❛ ✶✽

❡①♣r❡ssã♦ ❞❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ é ♦❜t✐❞❛ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ ❢♦r♠❛ ❞♦ ❢❡✐①❡ ❞❡ ✉♠❛ ♦♥❞❛ ✐♥❝✐❞❡♥t❡ ❡ ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ ❡s♣❛❧❤❛♠❡♥t♦✳ P♦st❡r✐♦r♠❡♥t❡✱ ❩❤❛♥❣ ❡ ▼❛rst♦♥ ❬✹✷❪ ❞❡s❡♥✈♦❧✈❡r❛♠ ✉♠❛ ✐♥t❡r♣r❡t❛çã♦ ❣❡♦♠étr✐❝❛ ❞❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❡①❡r❝✐❞❛ ♣❡❧♦ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ ❞❡ ♦r❞❡♠ ③❡r♦ ❡♠ ✉♠❛ ❡s❢❡r❛ ♥♦ ❡✐①♦ ❡♠ t❡r♠♦s ❞❛s s❡çõ❡s tr❛♥s✈❡rs❛✐s ❞❡ ❛❜s♦rçã♦✱ ❡s♣❛❧❤❛♠❡♥t♦ ❡ ❞❛ ♣♦tê♥❝✐❛ ❡①tr❛í❞❛ ❞♦ ❢❡✐①❡✳ ❯♠ ❡st✉❞♦ s❡♠❡❧❤❛♥t❡ s♦❜r❡ ✉♠❛ ❝❧❛ss❡ ♠❛✐s ❛♠♣❧❛ ❞❡ ❢❡✐①❡s ❛❝úst✐❝♦s ❢♦✐ t❛♠❜é♠ r❡❛❧✐③❛❞♦ ♣♦r ❡st❡ ❣r✉♣♦ ❬✹✸✱ ✹✹❪✳ ❆③❛r♣❡②✈❛♥❞ ❬✹✺❪ r❡❛❧✐③♦✉ ✉♠ ❡st✉❞♦ t❡ór✐❝♦ s♦❜r❡ ❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❡①❡r❝✐❞❛ s♦❜r❡ ✉♠❛ ❡s❢❡r❛ ♣♦r♦s❛ ❞❡ ❛❧✉♠í♥✐♦ ♥♦ ❡✐①♦✳ ◆❡st❡ ❝❛s♦✱ ♦ ❛✉♠❡♥t♦ ❞❛ ♣♦r♦s✐❞❛❞❡ ❞❡❣r❛❞❛ ❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ ♣❡q✉❡♥❛✳ ❊❧❡ t❛♠❜é♠ ❛♣r❡s❡♥t♦✉ ✉♠ ❡st✉❞♦ s♦❜r❡ ❛ ♠❛♥✐♣✉❧❛çã♦ ❛❝úst✐❝❛ ❞❡ ❝❛s❝❛s ❡s❢ér✐❝❛s ♣♦r♦s❛s ❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ✐♥❞✐❝❛♠ q✉❡ ❛ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ❝❛s❝❛s ❞❡ ❜❛✐①❛ ♣♦r♦s✐❞❛❞❡ é ♣♦ssí✈❡❧ ✉s❛♥❞♦ ❢❡✐①❡s ❞❡ ❇❡ss❡❧ ❝♦♠ ❣r❛♥❞❡s â♥❣✉❧♦s ❝ô♥✐❝♦s ❬✹✻❪✳ ❆ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❞❡ ✉♠ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ ❡①❡r❝✐❞♦ s♦❜r❡ ✉♠❛ ♣❡q✉❡♥❛ ♣❛rtí❝✉❧❛ ❢♦✐ ✐♥✈❡st✐❣❛❞♦ ♣♦r ❇❛r❡s❝❤ ❡ ❝♦❧❛❜♦r❛❞♦r❡s ❬✹✼✱ ✹✽❪✳ ❆❧é♠ ❞✐ss♦✱ ❙❛♣♦③❤♥✐❦♦✈ ❬✹✾❪ ❞❡s❡♥✈♦❧✈❡✉ ✉♠❛ ❛❜♦r❞❛❣❡♠ t❡ór✐❝❛ ♣❛r❛ ❝❛❧❝✉❧❛r ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❞❡ ✉♠ ❢❡✐①❡ ❛❝úst✐❝♦ ❛r❜✐trár✐♦ s♦❜r❡ ✉♠❛ ❡s❢❡r❛ ❡❧ást✐❝❛ ❞❡♥tr♦ ❞❡ ✉♠ ❧íq✉✐❞♦ ♦✉ ❣ás✳ ❋ór♠✉❧❛s ❡①❛t❛s ❞❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ❡①❡r❝✐❞❛ ♣♦r ✉♠❛ ♦♥❞❛ ❤❛r♠ô♥✐❝❛ ❛r❜✐trár✐❛ s♦❜r❡ ✉♠❛ ♣❡q✉❡♥❛ ♣❛rtí❝✉❧❛ ❝♦♠♣r❡ssí✈❡❧ ❛❜s♦r✈❡❞♦r❛✱ s✉s♣❡♥s❛ ♥✉♠ ✢✉✐❞♦ ✐❞❡❛❧✱ ❢♦✐ ♣r♦♣♦st❛ ♣♦r ❙✐❧✈❛ ❬✺✵❪✳

❆ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ❡♥tr❡ ❞✉❛s ♦✉ ♠❛✐s ♣❛rtí❝✉❧❛s ♥ã♦ ❛❜s♦r✈❡❞♦r❛s t❛♠❜é♠ tê♠ s✐❞❛ ❛♥❛❧✐s❛❞❛ ❬✺✶❪✕❬✺✼❪✳ ❆❧❣✉♥s ❡s❢♦rç♦s tê♠ s✐❞♦ ❞❡❞✐❝❛❞♦ ❛ ❝♦♠♣r❡❡♥❞❡r ❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❣✐♥❞♦ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ r❡✈❡st✐❞❛ ♣♦r ✉♠❛ ❝❛♠❛❞❛ ✈✐s❝♦❡❧ást✐❝❛ ❬✺✽❪✕❬✻✵❪✳ ❱❡r✐✜❝♦✉✲s❡ q✉❡✱ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠❛ ❝❛♠❛❞❛ ✈✐s❝♦❡❧ást✐❝❛✱ ❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛①✐❛❧ ♣♦r ♦♥❞❛s ♣r♦❣r❡ss✐✈❛s ♣♦❞❡ t♦r♥❛r✲s❡ ♥❡❣❛t✐✈❛✱ ♦ q✉❡ s✐❣♥✐✜❝❛ q✉❡ ❛ ❢♦rç❛ ❡ ❛ ❞✐r❡çã♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞❛ ♦♥❞❛ sã♦ ❝♦♥trár✐❛s ❬✻✶❪✳

✶✳✶✳✷ ❚♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦

❯♠❛ ♦♥❞❛ ❛❝úst✐❝❛ ♣♦❞❡ tr❛♥s♣♦rt❛r ♠♦♠❡♥t♦ ❛♥❣✉❧❛r✱ ❡ ❡st❡ ♣♦❞❡ s❡r tr❛♥s❢❡r✐❞♦ ♣❛r❛ ✉♠ ♦❜❥❡t♦ s✉s♣❡♥s♦✳ ❊ss❛ ✐♥t❡r❛çã♦ ❞❛ ♦♥❞❛ ❛❝úst✐❝❛ ❝♦♠ ✉♠ ♦❜❥❡t♦ s✉s♣❡♥s♦ ♥✉♠ ✢✉✐❞♦ ♣♦❞❡ ❣❡r❛r ✉♠ t♦rq✉❡ ♠é❞✐♦✱ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦✳ ❯♠❛ ❞❛s ♣r✐♠❡✐r❛s ♦❜s❡r✈❛çõ❡s ❛ r❡s♣❡✐t♦ ❞❡s❞❡ ❢❡♥ô♠❡♥♦ ❢♦✐ r❡❧❛t❛❞❛ ♣♦r ❘❛②❧❡✐❣❤ ❬✻✷❪✳ ❖ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❘❛②❧❡✐❣❤ é ♣r♦✈♦❝❛❞♦ ♣❡❧♦ ♠♦♠❡♥t♦ ❞♦ ❡str❡ss❡ ❞❡ r❛❞✐❛çã♦ ❛❣✐♥❞♦ s♦❜r❡ ✉♠ ♦❜❥❡t♦ ❛ss✐♠étr✐❝♦✳ ❯♠ tr❛❜❛❧❤♦ ♣✐♦♥❡✐r♦ ❛ r❡s♣❡✐t♦ ❞❡st❡ ❢❡♥ô♠❡♥♦ ❢♦✐ ♣r♦♣♦st♦ ♣♦r ▼❛✐❞❛♥✐❦ ❬✻✸❪✳ ◆❡st❡ tr❛❜❛❧❤♦ ❡❧❡ ❞❡r✐✈♦✉ ✉♠❛ ❡①♣r❡ssã♦ ♣❛r❛ ♦ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ s♦❜r❡ ✉♠ ♦❜❥❡t♦ ❞❡ ❢♦r♠❛ ❛r❜✐trár✐❛ ❞❡✈✐❞♦ ❛ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ ❢❛③❡♥❞♦ ♦ ✉s♦ ❞♦ t❡♦r❡♠❛ ❞♦ ♠♦♠❡♥t♦ ❛♥❣✉❧❛r✳ ❯♠❛ ❢ór♠✉❧❛ ❛❧t❡r♥❛t✐✈❛ ♣❛r❛ ♦ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ q✉❡ ❞❡♣❡♥❞❡ ❞❡ ✈❛r✐❛çõ❡s ♥❛ ❛♠♣❧✐t✉❞❡ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ♣❛r❛ ♠✉❞❛♥ç❛s ♥❛ ♦r✐❡♥t❛çã♦ ❞❛ ♦♥❞❛ ♣❧❛♥❛ ✐♥❝✐❞❡♥t❡ ❢♦✐ ♦❜t✐❞♦ ♣♦r ❙♠✐t❤ ❬✻✹❪ ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ❣❡♥❡r❛❧✐③❛çã♦ ❞♦ t❡♦r❡♠❛ ót✐❝♦✳ ❍❡❢♥❡r ❡ ▼❛rst♦♥ ❬✻✺❪ ♠♦str❛r❛♠ q✉❡ ✉♠ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛①✐❛❧ ♣♦❞❡ s❡r ❞❡s❡♥✈♦❧✈✐❞♦ ❡♠ ✉♠ ♦❜❥❡t♦ ❛❜s♦r✈❡❞♦r ♣♦r ✉♠ ❢❡✐①❡ ❞❡ ✈♦rt✐❝✐❞❛❞❡ ♣❛r❛①✐❛❧✳ ❋❛♥ ❡ ❝♦❧❛❜♦r❛❞♦r❡s ❬✻✻❪ ❡st❛❜❡❧❡❝❡r❛♠ ✉♠❛ t❡♦r✐❛ ♣❛r❛ ❝❛❧❝✉❧❛r ♦ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ s♦❜r❡ ✉♠ ❡s♣❛❧❤❛❞♦r ❞❡ ❢♦r♠❛ ❛r❜✐trár✐❛ ♣❛r❛ ✉♠❛ ♦♥❞❛ ❛❝úst✐❝❛ ❛r❜✐trár✐❛✳ ❊ss❡ ❡st✉❞♦ é ❧✐♠✐t❛❞♦✱ ♣♦✐s ♦ ❡s♣❛❧❤❛❞♦r t❡♠ q✉❡ s❡r ♣❡q✉❡♥♦ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ ❛♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛✳ ❩❤❛♥❣ ❡ ▼❛rst♦♥ ❬✻✼❪

(21)

✶✳✷ ❆♣❧✐❝❛çõ❡s ✶✾

❡st✉❞❛r❛♠ t❡♦r✐❝❛♠❡♥t❡ ♦ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛①✐❛❧ s♦❜r❡ ✉♠ ♦❜❥❡t♦ ❝♦♠ s✐♠❡tr✐❛ ❛①✐❛❧ s✉s♣❡♥s♦ ♥✉♠ ✢✉✐❞♦ ✐❞❡❛❧ ✳ ❊❧❡s t❛♠❜é♠ ❡①♣r❡ss❛r❛♠ ♦ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❝♦♠♦ ❛ ✐♥t❡❣r❛❧ ❞♦ ✢✉①♦ ❞♦ ♠♦♠❡♥t♦ ❛♥❣✉❧❛r ♠é❞✐♦ s♦❜r❡ ✉♠❛ s✉♣❡r❢í❝✐❡ ❡s❢ér✐❝❛ ❞✐st❛♥t❡ ❞♦ ♦❜❥❡t♦ ❡s♣❛❧❤❛❞♦r ❬✻✽❪✳ ❙✐❧✈❛ ❡ ❝♦❧❛❜♦r❛❞♦r❡s ❬✻✾❪ ❢♦r♥❡❝❡r❛♠ ✉♠❛ ❡①♣r❡ssã♦ ❣❡r❛❧ ♣❛r❛ ♦ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ tr✐❞✐♠❡♥s✐♦♥❛❧ ❡①❡r❝✐❞♦ ♣♦r ✉♠ ❢❡✐①❡ ❛❝úst✐❝♦ ❞❡ ❢r❡♥t❡ ❞❡ ♦♥❞❛ ❛r❜✐trár✐❛ s♦❜r❡ ✉♠ ♦❜❥❡t♦ ❞❡ q✉❛❧q✉❡r ❢♦r♠❛ ❣❡♦♠étr✐❝❛ ❡♠ t❡r♠♦s ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ ❢♦r♠❛ ❞♦ ❢❡✐①❡ ❡ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦✳ ❆❧é♠ ❞✐ss♦✱ ❙✐❧✈❛ ❞❡s❡♥✈♦❧✈❡✉ ✉♠❛ ❡①♣r❡ssã♦ ♣❛r❛ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦ s♦❜r❡ ✉♠❛ ♣❡q✉❡♥❛ ♣❛rtí❝✉❧❛ ✢✉✐❞❛ ♣❛r❛ ❝❛♠♣♦ ❛❝úst✐❝♦ ❛r❜✐trár✐♦ ❬✺✵❪✳ ❯♠ ❡st✉❞♦ s♦❜r❡ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛①✐❛❧ ❞❡ ✉♠ ❢❡✐①❡ ❞❡ ❇❡ss❡❧ ♣r♦❣r❡ss✐✈♦ ❡ ❡st❛❝✐♦♥ár✐♦ s♦❜r❡ ✉♠❛ ❝❛s❝❛ ❡s❢ér✐❝❛ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ▼✐tr✐ ❬✼✵❪✳ ❆♥❤❛✉s❡r ❡ ❝♦❧❛❜♦r❛❞♦r❡s ❬✷✶❪ ❛♣r❡s❡♥t❛r❛♠ ♦ ♣r✐♠❡✐r♦ t❡st❡ q✉❛♥t✐t❛t✐✈♦ ❞❡ tr❛♥s❢❡rê♥❝✐❛ ❞♦ ♠♦♠❡♥t♦ ❛♥❣✉❧❛r ♣❛r❛ ✉♠ ♦❜❥❡t♦ ❛❜s♦r✈❡❞♦r ✐♠❡rs♦ ❡♠ ✉♠ ❧✐q✉✐❞♦ ✈✐s❝♦s♦✳ ◆❛ ❡①♣❡r✐ê♥❝✐❛ r❡❛❧✐③❛❞❛✱ ❡❧❡ ♦❜s❡r✈♦✉ q✉❡ é ♣♦ssí✈❡❧ ❣✐r❛r ✉♠ ❞✐s❝♦ ❞❡ t❛♠❛♥❤♦ ♠✐❧✐♠étr✐❝♦ ✉t✐❧✐③❛♥❞♦ ❢❡✐①❡ ❣❡r❛❞♦ ♣♦r ✉♠ tr❛♥s❞✉t♦r ❡s❢ér✐❝♦✳ ❙❝❤✇❛r③ ❡ ❝♦❧❛❜♦r❛❞♦r❡s ❬✷✷❪ ✜③❡r❛♠ ✉♠❛ ❛♥á❧✐s❡ t❡ór✐❝❛ ❞♦ t♦rq✉❡ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝♦ ❡ r❡❛❧✐③❛r❛♠ ✉♠ ❡①♣❡r✐♠❡♥t♦ q✉❡ é ❝❛♣❛③ ❞❡ r♦t❛❝✐♦♥❛r ♣❛rtí❝✉❧❛s ♥ã♦ ❡s❢ér✐❝❛s ❞❡ ❢♦r♠❛ ❝♦♥tr♦❧❛❞❛ ♣♦r ♠❡✐♦ ❞❡ ♦♥❞❛s ❛❝úst✐❝❛s ❡st❛❝✐♦♥ár✐❛s✳

✶✳✷ ❆♣❧✐❝❛çõ❡s

❖ ✐♥t❡r❡ss❡ ❡♠ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❛❝úst✐❝❛ t❡♠ ❝r❡s❝✐❞♦ ♥❛s ú❧t✐♠❛s ❞é❝❛❞❛s ❞❡✈✐❞♦ ❛ ❛♣❧✐❝❛çõ❡s ❡♠ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s s❡♠ ❝♦♥t❛t♦s s✉s♣❡♥s❛ ❡♠ ✉♠ ✢✉✐❞♦✳ ❉✐❢❡r❡♥✲ t❡s ❛♣❧✐❝❛çõ❡s ❜✐♦t❡❝♥♦❧ó❣✐❝❛s s✉r❣✐r❛♠✱ ✐♥❝❧✉✐♥❞♦ ❧❡✈✐t❛çã♦ ❛❝úst✐❝❛✱ ♣✐♥ç❛s ❛❝úst✐❝❛s ❡ ♠✐❝r♦✢✉í❞✐❝❛ ✭❧❛❜✲♦♥✲❛✲❝❤✐♣✮✳

✶✳✷✳✶ ▲❡✈✐t❛çã♦ ❛❝úst✐❝❛

❆ ❧❡✈✐t❛çã♦ é ✉♠ ♣r♦❝❡ss♦ ♥♦ q✉❛❧ ✉♠ ♦❜❥❡t♦ é s✉s♣❡♥s♦ ❡♠ ✉♠❛ ♣♦s✐çã♦ ❡stá✈❡❧ s❡♠ ❝♦♥t❛t♦✳ ❯♠ s✐st❡♠❛ ❞❡ ❧❡✈✐t❛çã♦ ❛❝úst✐❝❛ é ❝♦♠♣♦st♦ ♣♦r ✉♠ tr❛♥s❞✉t♦r✱ s✉♣❡r❢í❝✐❡ ❝♦♠ ✈✐❜r❛çã♦ ❤❛r♠ô♥✐❝❛ ❝❛♣❛③ ❞❡ ♣r♦❞✉③✐r ✉♠❛ ♦♥❞❛ s♦♥♦r❛ ❞❡ ❢r❡q✉ê♥❝✐❛ ❞❡✜♥✐❞❛ ❡ ✉♠ r❡✢❡t♦r✳ ❉❡st❛ ❢♦r♠❛✱ ✉♠❛ ♦♥❞❛ ❡st❛❝✐♦♥ár✐❛ é ❣❡r❛❞❛ ❞❡✈✐❞♦ ❛ r❡✢❡①õ❡s ❡♥tr❡ ♦ tr❛♥s❞✉t♦r ❡ ✉♠ r❡✢❡t♦r✳ ❆ ❧❡✈✐t❛çã♦ ❛❝úst✐❝❛ é ✉♠❛ ❞❛s ❛♣❧✐❝❛çõ❡s q✉❡ ✉t✐❧✐③❛ ♦♥❞❛ ❡st❛❝✐♦♥ár✐❛✳

❊♠ ✶✾✽✺✱ ❚r✐♥❤ ❬✶✻❪ ✉t✐❧✐③♦✉ ♦ ♠ét♦❞♦ ❞❡ ♦♥❞❛ ❡st❛❝✐♦♥ár✐❛ ♣❛r❛ ❧❡✈✐t❛r ❛♠♦str❛s ❝♦♠ ❞✐♠❡♥sõ❡s tí♣✐❝❛s q✉❡ ✈❛r✐❛♠ ❞❡ 100µm ❛ 5 mm ❡ t❡♠♣❡r❛t✉r❛s ❡♥tr❡ 40◦C ❡ 500◦C✳

●❛♠♠❡❧ ❡ ❝♦❧❛❜♦r❛❞♦r❡s ❬✼✶❪ ✉t✐❧✐③❛r❛♠ ✉♠❛ s✐r❡♥❡ ♦♣❡r❛♥❞♦ ❛ 3260 Hz ❡ ✉♠ r❡✢❡t♦r

❛♣r♦♣r✐❛❞♦ ♣❛r❛ ♠♦str❛r q✉❡ é ♣♦ssí✈❡❧ ❧❡✈✐t❛r ❧✐✈r❡♠❡♥t❡ ✉♠❛ ❜♦❧❛ ❞❡ ❛ç♦ ❞❡ 1 cm ❞❡

❞✐â♠❡tr♦✳ ❳✐❡ ❡ ❲❡✐ ❬✼✷❪ ♥♦t❛r❛♠ ✉♠ ❛✉♠❡♥t♦ ♥♦tá✈❡❧ ❞❛ ❢♦rç❛ ❞❡ ❧❡✈✐t❛çã♦ ♣r♦❥❡t❛♥❞♦ ❛❞❡q✉❛❞❛♠❡♥t❡ ❛ ❢♦r♠❛ ❞♦ r❡✢❡t♦r✳ ■st♦ ♣❡r♠✐t✐✉ ❧❡✈✐t❛r ❜♦❧❛s ❞❡ t✉♥❣stê♥✐♦ ❞❡ ❛❧t❛ ❞❡♥s✐❞❛❞❡ 18,9 g/cm3✳ ❇r❛♥❞t ❬✶✼❪ ♠♦str♦✉ q✉❡ ♦♥❞❛s ❞❡ ✉❧tr❛ss♦♠ ♣♦❞❡ ❧❡✈✐t❛r ❜♦❧❛s

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✶✳✷ ❆♣❧✐❝❛çõ❡s ✷✵

✐♥❝❧✉✐♥❞♦ ♠♦✈✐♠❡♥t♦ ♦r❜✐t❛❧ ♦✉ r♦t❛çã♦ ❞❛ ❣♦tí❝✉❧❛s ❡ ♣❛rtí❝✉❧❛s ♥♦ ❛r✳ ❆♥❞r❛❞❡ ❡ ❝♦❧❛❜♦✲ r❛❞♦r❡s ❬✶✾❪ ✜③❡r❛♠ ✉♠❛ ❛♥á❧✐s❡ ❞❡ ✉♠ ❧❡✈✐t❛❞♦r ❛❝úst✐❝♦ ❢♦r♠❛❞♦ ♣♦r ✉♠ tr❛♥s❞✉t♦r ❞❡ ✉❧tr❛ss♦♠ ❡ ✉♠ r❡✢❡t♦r ❝ô♥❝❛✈♦✳ ❊♠ ❝♦♥tr❛st❡ ❝♦♠ ❧❡✈✐t❛❞♦r❡s tr❛❞✐❝✐♦♥❛✐s✱ ❛ ❣❡♦♠❡tr✐❛ ❛♣r❡s❡♥t❛❞❛ ♥❡st❡ tr❛❜❛❧❤♦ ♥ã♦ ♥❡❝❡ss✐t❛ q✉❡ ❛ ❞✐stâ♥❝✐❛ ❞❡ s❡♣❛r❛çã♦ ❡♥tr❡ ♦ tr❛♥s❞✉t♦r ❡ ♦ r❡✢❡t♦r s❡❥❛ ♠ú❧t✐♣❧❛ ❞❡ ♠❡✐♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛✳ ❆❧é♠ ❞✐ss♦✱ ❡❧❡s ❞❡♠♦♥str❛r❛♠ q✉❡ ❛s ♣❛rtí❝✉❧❛s ❞❡ ❧❡✈✐t❛çã♦ ♣♦❞❡♠ s❡r❡♠ ♠❛♥✐♣✉❧❛❞❛s ❛tr❛✈és ❞♦ ❝♦♥tr♦❧❡ ❞❛ ♣♦s✐çã♦ ❞♦ r❡✢❡t♦r✱ ♠❛♥t❡♥❞♦ ♦ tr❛♥s❞✉t♦r ♥✉♠❛ ♣♦s✐çã♦ ✜①❛✱ ❋✐❣✳ ✭✶✳✶✮✳

❋✐❣✉r❛ ✶✳✶✿ ▲❡✈✐t❛çã♦ ❛❝úst✐❝❛ ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✐❡st✐r❡♥♦ ♣❛r❛ três ❝♦♥✜❣✉r❛çõ❡s ❞✐❢❡r❡♥t❡s ❞♦ ❧❡✈✐t❛❞♦r✳

❋♦♥t❡✿ ▼❛r❝♦ ❆♥❞r❛❞❡ ❡ ❝♦❧❛❜♦r❛❞♦r❡s✱ ✷✵✶✺ ❬✶✾❪✳

✶✳✷✳✷ P✐♥ç❛ ❛❝úst✐❝❛

❯♠❛ ❞❛s ♣r✐♠❡✐r❛s ❛♣❧✐❝❛çõ❡s ❞❛ ❢♦rç❛ ❞❡ r❛❞✐❛çã♦ ❢♦✐ ❞❡♥♦♠✐♥❛❞❛ ♣✐♥ç❛ ❛❝úst✐❝❛✱ q✉❡ é ✉♠❛ té❝♥✐❝❛ ♣❛r❛ ❛♣r✐s✐♦♥❛♠❡♥t♦ ❞❡ ♣❛rtí❝✉❧❛s q✉❡ ✉t✐❧✐③❛ ❢❡✐①❡s ❛❝úst✐❝♦s✳ ❉✉❛s ❛❜♦r❞❛❣❡♥s ❞✐❢❡r❡♥t❡s tê♠ s✐❞♦ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛♣r✐s✐♦♥❛♠❡♥t♦ ❞❡ ♠✐❝r♦♣❛rtí❝✉❧❛s ❞❡♥♦♠✐✲ ♥❛❞❛s ❞❡ ♦♥❞❛ ❡st❛❝✐♦♥ár✐❛ ❡ ♠ét♦❞♦ ❞❡ ❢❡✐①❡ ú♥✐❝♦✳ ❖ ♣r✐♠❡✐r♦ s✐st❡♠❛ ❞❡ ♣✐♥ç❛ ❛❝úst✐❝♦ ❢♦✐ ♣r♦♣♦st♦ ♣♦r ❲✉ ❝♦♠ ✉♠ ❞✐s♣♦s✐t✐✈♦ ❝❛♣❛③ ❞❡ ❛♣r✐s✐♦♥❛r ❡st❛✈❡❧♠❡♥t❡ ♣❛rtí❝✉❧❛s ❞❡ ❧❛t❡① ❡ ♦✈♦s ❞❡ rã ❞❡ 270µm ❞❡ ❞✐â♠❡tr♦ ❡♠ á❣✉❛ ❬✸❪✳ ❊ss❡ ❞✐s♣♦s✐t✐✈♦ é ❝♦♠♣♦st♦ ♣♦r

❞♦✐s ❢❡✐①❡s ❢♦❝❛❧✐③❛❞♦s ❝♦♥tr❛♣r♦♣❛❣❛♥t❡s ♣❛r❛ ❢♦r♠❛r ✉♠❛ ♦♥❞❛ ❡st❛❝✐♦♥ár✐❛ ❞❡3.5 MHz

❝❛♣❛③ ❞❡ ❛♣r✐s✐♦♥❛r ♠✐❝r♦♣❛rtí❝✉❧❛s✳ ❑♦③✉❦❛ ❡ ❝♦❧❛❜♦r❛❞♦r❡s ❬✹❪ ❛♣r❡s❡♥t❛r❛♠ ✉♠ ♠ét♦❞♦ ❞❡ ♣✐♥ç❛ ❛❝úst✐❝❛ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ♦♥❞❛ ❡st❛❝✐♦♥ár✐❛ ❞❡2.1 MHz❣❡r❛❞❛ ♣♦r ✉♠ tr❛♥s❞✉t♦r

❢♦❝❛❧✐③❛❞♦ ❡ ✉♠ r❡✢❡t♦r ❝❛♣❛③ ❞❡ ❛♣r✐s✐♦♥❛r ♠✐❝r♦♣❛rtí❝✉❧❛s ❞❡ ❛❧✉♠í♥✐♦ ❝♦♠ ❞✐â♠❡tr♦ ♠é❞✐♦ ❞❡16µm✳ ❖♥❞❛s ❡st❛❝✐♦♥ár✐❛s ✐♥❝❧✐♥❛❞❛s sã♦ ♣r♦❞✉③✐❞❛s ♣♦r ✉♠❛ ❝♦♥✜❣✉r❛çã♦ ❞❡

três tr❛♥s❞✉t♦r❡s ♦♣❡r❛♥❞♦ ❛ 1.67 MHz ❢♦r❛♠ ✉s❛❞❛s ♣❛r❛ ❛♣r✐s✐♦♥❛r ❡ tr❛♥s♣♦rt❛r ❣♦t❛s

❞❡ sí❧✐❝❛ ❞❡100µm❞❡ ❞✐â♠❡tr♦ ❬✼✹❪✳

P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ❛❜♦r❞❛❣❡♠ ❞❡ ♣✐♥ç❛s ❛❝úst✐❝❛s ❛tr❛✈és ❞♦ ♠ét♦❞♦ ❞❡ ❢❡✐①❡ ú♥✐❝♦ ✉t✐✲ ❧✐③❛ tr❛♥s❞✉t♦r❡s ❜❡♠ ❢♦❝❛❧✐③❛❞♦s ♣❛r❛ ❛♣r✐s✐♦♥❛r ♣❛rtí❝✉❧❛s ♥♦ ♣♦♥t♦ ❢♦❝❛❧ ❞♦ ❞✐s♣♦s✐t✐✈♦✳ ▲❡❡ ❡ ❝♦❧❛❜♦r❛❞♦r❡s ❬✻❪ ❞❡s❡♥✈♦❧✈❡r❛♠ ✉♠ ❞✐s♣♦s✐t✐✈♦ ❛❝úst✐❝♦ ❞❡ ❢❡✐①❡ ú♥✐❝♦ ✉t✐❧✐③❛♥❞♦ ✉♠ tr❛♥s❞✉t♦r ❞❡ 30 MHz ❝❛♣❛③ ❞❡ ❛♣r✐s✐♦♥❛r ❣♦tí❝✉❧❛s ❞❡ ❧✐♣í❞✐♦s ❞❡ 126µm ❞❡ ❞✐â♠❡tr♦s✳

❚r❛♥s❞✉t♦r❡s ❝♦♠ ❢r❡q✉ê♥❝✐❛s ♠❛✐s ❛❧t❛s q✉❡ ♦♣❡r❛♠ ❛ 200 MHz ❢♦r❛♠ ♣r♦❥❡t❛❞♦s ♣❛r❛

✐♠♦❜✐❧✐③❛r ❡ tr❛♥s❧❛❞❛r ✉♠❛ ❝é❧✉❧❛ ❞❡ ❧❡✉❝❡♠✐❛ ❞❡10µm ❬✼✺❪ ❡ ♠✐❝r♦❡s❢❡r❛s ❬✼✻❪✳ ❈❤♦❡ ❡

❝♦❧❛❜♦r❛❞♦r❡s ❬✶✸❪ ❞❡s❝r❡✈❡r❛♠ ✉♠ ❛♣r✐s✐♦♥❛♠❡♥t♦ ❛❝úst✐❝♦ ❞❡ ♠✐❝r♦❡s❢❡r❛s ✈❛r✐❛♥❞♦ ❞❡ ❞✐â♠❡tr♦ ❡♥tr❡70 ❛ 90µm ✉t✐❧✐③❛♥❞♦ ✉♠ tr❛♥s❞✉t♦r ❡q✉✐♣❛❞♦ ❝♦♠ ✉♠❛ ❧❡♥t❡ ❞❡ ❋r❡s♥❡❧

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