Half-Space Green’s Functions for Transversely Isotropic Piezoelectric Solids

Abstract

We obtain explicit closed-form solutions for the half-space Green’s functions for a transversely isotropic piezoelectric solid. The boundary of the half-space is taken to be a plane normal to the unique material axis. The Green’s functions are obtained using a formulation where general solutions in transversely isotropic piezoelectricity are expressed in terms of two potential functions; one satisfying a weighted triharmonic equation and the other satisfying a weighted harmonic equation. By assuming a series solution for the potentials we derive explicit expressions for the Green’s functions.