The scattering of steady-state SH waves in a half-space with oblique semi-elliptical notches is presented analytically. Mathieu function addition theorem and multi-elliptical coordinate systems are developed to solve the complex boundary value problem. The existence of local defects has a great influence on the scattering and diffraction of elastic waves. The wave function expansion method which can reveal the physical process of wave scattering and verify the accuracy of numerical methods is a common method to study the influence of defects. The numerical results of the solution are obtained by truncating the infinite equation. Although the truncation of the infinite equation is inevitable, the accuracy of the numerical results has been carefully checked. The proposed solution is verified by comparing the results obtained when the oblique semi-elliptical notch is degraded into a semi-elliptical notch or even a semi-circular notch with previous results. The numerical results for typical cases show the complex effects of the inclination of the notch, the axial ratio of the ellipse, and the incidence angle on the displacement amplitude and dynamic stress concentration near the notch.

分析性地提出了稳态SH波在半倾斜斜角半空间中的散射。开发了Mathieu函数加法定理和多椭圆坐标系来解决复杂的边值问题。局部缺陷的存在对弹性波的散射和衍射有很大的影响。可以揭示波散射的物理过程并验证数值方法的准确性的波函数展开法是研究缺陷影响的常用方法。该解决方案的数值结果是通过截断无穷大方程获得的。尽管无穷大的截断是不可避免的，但已经仔细检查了数值结果的准确性。通过将倾斜的半椭圆形槽口降级为半椭圆形甚至半圆形槽口时获得的结果与以前的结果进行比较，可以验证所提出的解决方案。典型情况下的数值结果表明，切口的倾斜度，椭圆的轴向比率和入射角对切口附近的位移幅度和动应力集中具有复杂的影响。