Two-dimensional time-harmonic elastodynamic Green's functions for anisotropic media

Abstract

An exact matrix formulation for 2D time-harmonic elastodynamic Green's functions for anisotropic media is presented. In this formulation, a Fourier transform with respect to spatial coordinates is employed. The displacement and stress in the Fourier transform domain is obtained by using the method of modal expansion. A technique is suggested to evaluate the 2D inverse integral in the polar coordinate system to obtain the solution for the displacement and stress. In this technique, the inverse integration is carried out in a very efficient way along the wave number axis over a semi-infinite region by changing integral paths. Therefore a numerical integration is needed only for the polar angle over a finite region. Numerical examples are presented to demonstrate the present method, and wave fields for the displacement are investigated for isotropic and anisotropic media.