Scattering of Rayleigh waves by an arbitrarily oriented sub‐surface crack

Abstract

The diffraction of acoustic waves by a crack in an unbounded elastic medium has been extensively discussed in the literature. For practical purposes the problem in a semi‐infinite solid is a more realistic one. A rigorous theory of the diffraction of time‐harmonic elastic waves by an arbitrarily oriented, cylindrical, stress‐free crack of finite width embedded in a semi‐infinite elastic medium has been developed. The incident wave is taken to be either a P wave, an SV wave, or a Rayleigh wave. The resulting boundary‐value problems for the unknown jump in the particle displacement across the crack are solved by employing the integral‐equation method in combination with the Galerkin method. Numerical results are presented in the form of normalized power scattering characteristics, dynamic stress intensity factors, and Rayleigh‐wave transmission and reflection coefficients, for a range of geometricai parameters. The most striking feature in the scattering characteristics are the sharp peaks that occur for sc...