The Full-Space Elastodynamic Green’s Functions for Time-Harmonic Radial and Axial Ring Sources in a Homogeneous Isotropic Medium

Abstract

The elastodynamic Green’s functions for time-harmonic radial and axial ring sources in a homogeneous, isotropic, linear elastic full-space medium are derived using the Fourier-Hankel transform. The Green’s functions are found to have the same logarithmic singularities as the Legendre functions of positive and negative half-degree of the second kind. As the frequency approaches zero, the Green’s functions approach the corresponding elastostatic Green’s functions. The far-field displacement and stress components are also derived.