Fundamental solutions for variable density two-dimensional elastodynamic problems

Abstract

Fundamental solutions in the form of free-space Green's functions are developed for a class of two-dimensional, variable density elastodynamic problems. These fundamental solutions are evaluated by means of a coordinate transformation based on conformal mapping in conjunction with wave decomposition, which allows for both vertical and lateral heterogeneities, and can be used within the context of a boundary integral equation formulation analogous to that originally proposed by Cruse and Rizzo (J Math Anal Appl 22 (1968) 244). Finally, a numerical example serves to illustrate the methodology developed herein.