含有脱胶的椭圆夹杂及圆夹杂对SH波的散射

Scattering of SH waves with a partially degummed elliptical inclusion and a circular inclusion

为了求解半空间内含有部分脱胶的椭圆夹杂与圆形夹杂对SH波的散射影响问题,本文将复变函数法、Green函数法与保角映射技术相结合,根据保角映射的原理,将椭圆夹杂映射为圆夹杂,求出散射波的位移及应力场。结合Green函数法在脱胶部分"虚设点源",根据椭圆夹杂以及圆形夹杂周围应力及位移连续的边界条件,求出位移及应力的基本解。在脱胶部分通过施加大小相等、方向相反的力构造"脱胶模型",得到在半空间内含有部分脱胶的椭圆夹杂以及圆形夹杂对SH波散射的总位移场。通过数值算例表明:得到不同的介质参数对动应力集中系数的影响不同,其中,SH波入射的角度、入射频率、波数比、介质参数、埋深、缺陷之间距离、脱胶角度等对动应力集中系数都有影响。

The complex function method, Green function method, and conformal mapping are combined to solve the problem of SH-wave scattering in a half-space with a partially degummed elliptical inclusion and circular inclusion. First, the elliptical inclusion is mapped into circular inclusions to derive the displacement and stress field of scattered waves in accordance with the principle of conformal mapping. The virtual point source of the degummed component is derived in accordance with the Green function method, and the basic solutions of displacement and stress are obtained under the continuous boundary conditions of peripheral stress and displacement with elliptical and circular inclusions. Furthermore, the degumming model is structured by applying forces that are equal in strength and opposite in direction on the degumming component to obtain the total displacement field of the SH-wave scattering in the half-space with partially degummed elliptical and circular inclusions. Numerical examples show that different medium parameters, including the SH-wave incident angle, incident frequency, wave-number ratio, medium parameter, embedded depth, distance between defects, and degumming angle, have different influences on the dynamic stress coefficient.