Scattering of SH-waves by oblique semi-elliptical notches in half space

Abstract

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.