Perturbation theory for linear electroelastic equations for small fields superposed on a bias

Abstract

A perturbation formulation of the equations of linear piezoelectricity for small fields superposed on a bias is obtained from a Green’s function representation. It is shown that the resulting equation for the first perturbation of the eigenvalue may be obtained without the use of a Green’s tensor or a complete set of orthogonal eigensolutions. Since the bias enters the constitutive equations, the boundary conditions contain perturbation terms as well as the differential equations. The linear electroelastic equations for small fields superposed on a bias differ from the equations of linear piezoelectricity because the effective material constants of linear electroelasticity have less symmetry than the constants of linear piezoelectricity. Consequently, a perturbation formulation of the linear electroelastic equations for small fields superposed on a bias is presented. It is shown that the effective constants of linear electroelasticity have just the symmetry required for the condition of the orthogonality of linear electroelastic vibrations to hold.