Low frequency scattering of elastic waves by a cavity using a matched asymptotic expansion method

Abstract

This work deals with low-frequency asymptotic solutions using the method of matched asymptotic expansions. It is based on two papers by Buchwald [3] and Buchwald and Tran Cong [4] who studied the diffraction of elastic waves by a small circular cavity and a small elliptic cavity, respectively, in an otherwise unbounded domain. Here we clarify and systematize some aspects of their work and extend it to the diffraction of elastic waves by a small cylindrical cavity with a hypotrochoidal boundary. Results for the case of an incident P-wave are compared, in the special case of an elliptic boundary, with the results from the numerical solution of the boundary integral equation method.