SH波绕界面孔的散射

用波函数展开方法研究了SH波绕界面孔的散射问题。由入射、反射和透射波组成的自由波场与孔的散射场叠加成总波场。按照一定方式将两个半平面散射波场延拓于全平面，通过Hankel-Fourier展开方法求得了任意形状孔散射场的级数解。以椭圆形孔为例计算了孔边缘的动应力集中系数。

Scattering of SH-wave by an interface cavity

SH-wave scattering and dynamic concentration by an arbitrary cavity which is located at the interface between two elastic mediums are investigated in the paper. The total wave field is obtained by superposition of a free field and scattering fields. The free one is composed of incident, reflection and refraction waves and the correspondent exact solutions are known. The scattering fields in different mediums must be expressed respectively. The solution for each scattering fields can be expanded into Hankel-Fourier series with unknown coefficients on the basis of the theory of wave functions expansion. According to the boundary conditions of the total wave field on the interface and around the cavity, the non-orthogonal Hankel-Fourier integral is carried out. As a result, an infinite system of algebraic equations containing the unknown coefficients of the series is gotten. The non-orthogonality comes from the following factors: (1) the geometric boundary of the cavity is non-orthogonal for the polar coordinates; (2) two scattering wave functions are define in one's own hail plane respectively; (3) the arguments (kir and k2r) of the two wave function the interface are different because the wave numbers for the two mediums are unequal. The non-orthogonality makes the system of equations for the unknown coefficients infinite. Another key point is to extend each scattering field from its half-plane domains into the full plane domain by the certain way keeping the total wave field unchanged for the non-orthogonal integrals around tJ cavity. Finally, taking ellipse cavities with different ratio between long and short axis as example the calculation is completed. Some numerical results about the distribution of coefficients dynamic stress concentration around the cavities are presented in this paper.