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Hrmo n ic pressure nd longitudinl plne wve diffrction

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roidal and cylindrical surfaces under time-harmo

n

ic pressure and longitudinal plane wave diffraction. The formulas are derived for the calculations of wave scattering amplitudes and cross-sections in the far zone in terms of BIEs solutions. The influence of spheroidal crack curvature on the scattering a

mplitudes are studied for different  time-harmonic perturbations.

\par }{\b\lang1033 \tab Keywords}{\lang1033 : infinite elastic solid, spatial crack, time-harmonic elastic waves, dynamic stress intensity factors, wave scattering amplitudes, boundary integral equation method.

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???C?o?m?p?O?b?j?????????????????????????????????????????????????????#???%???ÿÿÿÿ????????????????????????????????????3???f?????????O?b?j?I?n?f?o?????????????????????????????????????????????????????ÿÿÿÿ&???ÿÿÿÿ????????????????????????????????????5???????????E?q?u?a?t?i?o?n? ?N?a?t?i?v?e??????????????????????????????????? ???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????6???‰???????_?1?2?0?9?8?8?3?9?9?5???????????????????????????????????????????????????;???)????Î??????À??????F????Pdœ¥¸~Æ?Pdœ¥¸~Æ?????????????‚)??†+??

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????‚(??ˆ2??†Å"?ˆ2??ˆ2??ˆ4??ˆ0??†?"?ˆ3??‚,??ˆ1??ˆ4??†Å"?‚(??ˆ1??ˆ4??ˆ0??†+??ˆ5??ˆ6??ˆ0??‚)??‚)????? ???ˆ2???

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????ŠÁ—???????¿??ÜÆ??????????

??ƒa????? ??‚m??‚i??‚n????

?†=??ƒa??†?"?ˆ0??‚,??ˆ0??ˆ1??†Å"?ƒL??†=??ˆ5??ˆ2??ˆ9??†?"?ˆ0??‚.??ˆ0??ˆ1??‚*??ˆ2??ˆ2??ˆ4??ˆ0??†=??ˆ5??ˆ0??ˆ7??ƒ<??ƒ<??????????????????O?l?e?????????????????????????????????????????????????????????

???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????A?????????????C?o?m?p?O?b?j?????????????????????????????????????????????????????(???*???ÿÿÿÿ????????????????????????????????????B???f?????????O?b?j?I?n?f?o?????????????????????????????????????????????????????ÿÿÿÿ+???ÿÿÿÿ????????????????????????????????????D???????????E?q?u?a?t?i?o?n? ?N?a?t?i?v?e??????????????????????????????????? ???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????E???³???????_?1?2?0?9?8?8?4?3?6?5???????????????????????????????????????????????ÿÿÿÿÿÿÿÿ.????Î??????À??????F????Pdœ¥¸~Æ?Pdœ¥¸~Æ???????????????O?l?e?????????????????????????????????????????????????????????

???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????H?????????????C?o?m?p?O?b?j?????????????????????????????????????????????????????-???/???ÿÿÿÿ????????????????????????????????????I???f?????????O?b?j?I?n?f?o?????????????????????????????????????????????????????ÿÿÿÿ0???ÿÿÿÿ????????????????????????????????????K?????????????????????????????????????????????????????????????????????????????þÿ?

??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????ŠÁç???????xÄ??$ ??????????

??ƒL????? ??ˆ1????

???? ???ˆ0???

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????ŠÁ:????????µ??Œ»??????????

???????ƒL????? ??ˆ1?????

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???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????W?????????????C?o?m?p?O?b?j?????????????????????????????????????????????????????7???9???ÿÿÿÿ????????????????????????????????????X???f?????????O?b?j?I?n?f?o?????????????????????????????????????????????????????ÿÿÿÿ:???ÿÿÿÿ????????????????????????????????????Z???????????E?q?u?a?t?i?o?n? ?N?a?t?i?v?e??????????????????????????????????? ???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????[???¹???????_?1?2?0?9?8?8?4?8?5?9???????????????????????????????????????????????1???E???=????Î??????À??????F????Pdœ¥¸~Æ?Pdœ¥¸~Æ???????????????þÿ?

??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????ŠÁ???????pŒ??Ԍ??????????

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Eq??O?l?e?????????????????????????????????????????????????????????

???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????^?????????????C?o?m?p?O?b?j?????????????????????????????????????????????????????<???>???ÿÿÿÿ????????????????????????????????????_???f?????????O?b?j?I?n?f?o?????????????????????????????????????????????????????ÿÿÿÿ????ÿÿÿÿ????????????????????????????????????a???????????E?q?u?a?t?i?o?n? ?N?a?t?i?v?e??????????????????????????????????? ???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????b???)???????uation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????ŠÁ

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????¤Á/????????¶??„Ç??????????

??ƒC????? ??ƒL????

?†=??ˆ0??‚,_?1?2?0?9?9?1?1?9?5?0???????????????????????????????????????????????ÿÿÿÿÿÿÿÿB????Î??????À??????F????Pdœ¥¸~Æ?Pdœ¥¸~Æ???????????????O?l?e?????????????????????????????????????????????????????????

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???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????i?????????????C?o?m?p?O?b?j?????????????????????????????????????????????????????F???H???ÿÿÿÿ????????????????????????????????????j???f?????????ˆ8??ˆ6??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????þÿ?

??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????¤Á)???????èn??ä`??????????

??…”??ƒT??†=??ˆ3??‚.??ˆ1??ƒH??ƒ<????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????O?b?j?I?n?f?o?????????????????????????????????????????????????????ÿÿÿÿI???ÿÿÿÿ????????????????????????????????????l???????????E?q?u?a?t?i?o?n? ?N?a?t?i?v?e??????????????????????????????????? ???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????m???E???????_?1?2?0?9?9?1?2?2?5?2???????????????????????????????????????????????ÿÿÿÿÿÿÿÿL????Î??????À??????F????Pdœ¥¸~Æ?Pdœ¥¸~Æ???????????????O?l?e?????????????????????????????????????????????????????????

???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????o?????????????C?o?m?p?O?b?j?????????????????????????????????????????????????????K???M???ÿÿÿÿ????????????????????????????????????p???f?????????O?b?j?I?n?f?o?????????????????????????????????????????????????????ÿÿÿÿN???ÿÿÿÿ????????????????????????????????????r???????????E?q?u?a?t?i?o?n? ?N?a?t?i?v?e??????????????????????????????????? ???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????s???Ë???????_?1?2?0?9?9?1?2?7?0?4???????????????????????????????????????????????'???w???Q????Î??????À??????F????Pdœ¥¸~Æ?Pdœ¥¸~Æ???????????????þÿ?

??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????¤Á¯???????°®??”f??????????

??…”??ƒN??†=??ˆ0??‚,??ˆ0??ˆ0??ˆ0??ˆ1??†Å"?…”??ƒT??†Å"?ƒn????? ??ƒ1????

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????¤Á)???????°À??„Ç??????????

??ƒN????? ??ƒ4????

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?†=??‚(??ˆ3??‚.??ˆ8??ˆ3??†Å"?ˆ0??‚,??ˆ8??ˆ6??†Å"?ˆ1??†+??ˆ0??‚,??ˆ8??ˆ7??†+??ˆ0??‚.??ˆ3??ˆ5??‚)??†Å"?ˆ0??‚.??ˆ6??ˆ8??†=??ˆ2??‚.??ˆ8??ˆ3??ƒ:??ƒ???þÿÿÿþÿÿÿƒ???þÿÿÿþÿÿÿ†???‡???þÿÿÿþÿÿÿŠ???þÿÿÿþÿÿÿ???þÿÿÿþÿÿÿ???þÿÿÿþÿÿÿ“???”???þÿÿÿþÿÿÿ—???þÿÿÿþÿÿÿþÿÿÿþÿÿÿœ???þÿÿÿþÿÿÿŸ??? ???¡???¢???£???¤???þÿÿÿþÿÿÿ§???þÿÿÿþÿÿÿª???«???¬???þÿÿÿþÿÿÿ¯???þÿÿÿþÿÿÿ²???³???´???µ???¶???·???¸???þÿÿÿþÿÿÿ»???þÿÿÿþÿÿÿ¾???¿???À???Á???þÿÿÿþÿÿÿÄ???þÿÿÿþÿÿÿÇ???È???É???þÿÿÿþÿÿÿÌ???þÿÿÿþÿÿÿþÿÿÿþÿÿÿÑ???þÿÿÿþÿÿÿþÿÿÿþÿÿÿÖ???þÿÿÿþÿÿÿÙ???Ú???þÿÿÿþÿÿÿÝ???þÿÿÿþÿÿÿà???þÿÿÿþÿÿÿã???þÿÿÿþÿÿÿæ???þÿÿÿþÿÿÿé???þÿÿÿþÿÿÿì???þÿÿÿþÿÿÿï???þÿÿÿþÿÿÿþÿÿÿþÿÿÿô???þÿÿÿþÿÿÿ÷???þÿÿÿþÿÿÿú???þÿÿÿþÿÿÿý???þ???ÿ???????ƒB????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????þÿ?

??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????¤Á+????????É??lÀ??????????

??ƒC????? ??ƒz????

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Eq??O?b?j?I?n?f?o?????????????????????????????????????????????????????ÿÿÿÿ]???ÿÿÿÿ????????????????????????????????????‹???????????E?q?u?a?t?i?o?n? ?N?a?t?i?v?e??????????????????????????????????? ???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????Œ???G???????_?1?2?0?9?9?1?3?1?4?7???????????????????????????????????????????????ÿÿÿÿÿÿÿÿ`????Î??????À??????F????Pdœ¥¸~Æ?Pdœ¥¸~Æ???????????????O?l?e?????????????????????????????????????????????????????????

???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????Ž?????????????C?o?m?p?O?b?j?????????????????????????????????????????????????????_???a???ÿÿÿÿ???????????????????????????????????????f?????????O?b?j?I?n?f?o?????????????????????????????????????????????????????ÿÿÿÿb???ÿÿÿÿ????????????????????????????????????‘???????????E?q?u?a?t?i?o?n? ?N?a?t?i?v?e??????????????????????????????????? ???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????’???…???????_?1?2?0?9?9?1?3?1?5?9???????????????????????????????????????????????Y???m???e????Î??????À??????F????Pdœ¥¸~Æ?Pdœ¥¸~Æ?????????????uation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????¤Ái???????ˆ¼??„Ç??????????

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????¤Á9???????°X??<ý??????????

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????¤Áš???????X²??¤ ??????????

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Eq??O?b?j?I?n?f?o?????????????????????????????????????????????????????ÿÿÿÿÕ???ÿÿÿÿ????????????????????????????????????:???????????E?q?u?a?t?i?o?n? ?N?a?t?i?v?e??????????????????????????????????? ???ÿÿÿÿÿÿÿÿÿÿÿÿ????????????????????????????????????;???¶???????_?1?2?0?9?9?2?0?5?7?1???????????????????????????????????????????????Û???ÿÿÿÿØ????Î??????À??????F????P՞¥¸~Æ?P՞¥¸~Æ???????????????O?l?e?????????????????????????????????????????????????????????

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????O?l?e?????????????????????????????????????????????????????????

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????¤Á+???????Xø??„,??????????

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????¤Á????????ø¸??D·??????????

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
???DS Equation? ???Equation.3?ô9²q????????????????????????????????????????????????????????????????????????????????????????????????????????????¤ÁL????????²??Ô.??????????

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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
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??ÿÿÿÿ?Î??????À??????F????Microsoft Equation 3.0?
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