Green's functions for a two–phase infinite piezoelectric plane

Abstract

First, on the basis of the governing equations of piezoelectric materials, a displacement function is introduced and the general solutions are derived. Second, by employing the generalized Almansi's theorem, these solutions are further simplified, i.e. all physical quantities are expressed in three displacement functions ψi (i = 1,2,3), which satisfy, respectively, three similar harmonic second–order partial differential equations. Then the Green's functions for point forces and point charge acting in the interior of a two–phase infinite piezoelectric plane are given using the method of mirror image source. The paper is concluded by a discussion of some special cases, in which the point force and charge solutions for an infinite uniform piezoelectric plane and for a half–plane with free or fixed straight boundary are given.