Integral equation formulation of piezo-electric diffraction problems

Abstract

In this paper the integral equation formulation of scattering or diffraction problems associated with wave motions in a piezo-electric solid is investigated. Starting from the basic equations a power balance and a reciprocity relation are derived. In the power balance the mechanical and the electric power flow density occur. The reciprocity relation serves as a starting point for the integral equation formulation of diffraction problems. In the reciprocity relation, two possible but different field situations occur. In one of them the field quantities are chosen to be the actual ones, in the other the field quantities are chosen to be the auxiliary ones that are generated by either an electric point charge or a mechanical point force. In this way, Helmholtz type of integral representations for the electric potential and the mechanical displacement are obtained.