The present problem aims to study the scattering behavior of SH-waves by a circular cavity near two symmetrically permeable interface cracks in the piezoelectric bi-material half-space. The steady-state response of the problem is obtained, with the aid of the Green’s function method and the complex function method. Above all, the essential expression of Green’s function is constructed by the mirror method. This expression satisfies the conditions of being stress-free and electric insulation on the horizontal boundary of the orthogonal space where the circular cavity is located, and the condition of bearing a harmonic out-plane line source force on the vertical boundary. Next, on the basis of dividing the bi-material medium into two parts along the vertical boundary, the first kind of Fredholm integral equation with uncertain anti-plane forces is established by using the conjunction method and the crack-division technology. Then, the solution is obtained by solving an algebraic equation with finite terms, which is an effective truncation of the integral equation. Finally, the dynamic stress concentration factor around the edge of the circular cavity and the dynamic stress intensity factor at the crack tip are calculated numerically. On this basis, the effects of incident wave frequency, crack length, crack location and circular cavity position on the dynamic stress concentration factor and dynamic stress intensity factor are discussed.

中文翻译：

---

SH波作用下压电双材料半空间垂直界面裂纹及其附近圆形空腔的动力学分析

本问题旨在研究压电双材料半空间中两个对称可渗透界面裂缝附近的圆形空腔对 SH 波的散射行为。借助格林函数法和复函数法，得到问题的稳态响应。首先，格林函数的本质表达式是通过镜像方法构造的。该表达式满足圆腔所在正交空间水平边界上无应力和电绝缘的条件，以及垂直边界上承受谐波面外线源力的条件。接下来，在将双材料介质沿垂直边界分为两部分的基础上，利用结合法和裂纹分割技术，建立了具有不确定反平面力的第一类Fredholm积分方程。然后，通过求解具有有限项的代数方程得到解，这是积分方程的有效截断。最后，数值计算了圆腔边缘周围的动应力集中因子和裂纹尖端的动应力强度因子。在此基础上，讨论了入射波频率、裂纹长度、裂纹位置和圆腔位置对动应力集中因子和动应力强度因子的影响。这是积分方程的有效截断。最后，数值计算了圆腔边缘周围的动应力集中因子和裂纹尖端的动应力强度因子。在此基础上，讨论了入射波频率、裂纹长度、裂纹位置和圆腔位置对动应力集中因子和动应力强度因子的影响。这是积分方程的有效截断。最后，数值计算了圆腔边缘周围的动应力集中因子和裂纹尖端的动应力强度因子。在此基础上，讨论了入射波频率、裂纹长度、裂纹位置和圆腔位置对动应力集中因子和动应力强度因子的影响。