“…Equations of motion and Gauss' law are given by (1) (2) where σ ij is the stress tensor, u i is the displacement vector, ρ is the mass density, D i is the electric displacement vector, and a comma denotes partial differentiation with respect to the coordinates x i (i =1, 2,3)or the time t. We have employed Cartesian tensor notation and the summation convention for repeated tensor indices. Constitutive relations can be written as (3) (4) where ε ij is the strain tensor, E i is the electric field intensity vector, and s ijkl , d kij and ε ik are the elastic compliance, direct piezoelectric coefficient and permittivity at constant stress, which satisfy the following symmetry relations:…”