Thermal effects on the frequency response of piezoelectric crystals

In this paper we describe a solution strategy to determine the natural frequencies of piezoelectric crystals subject to moderate changes in temperature and a variety of boundary constraints. The finite element equations governing piezoelectricity are derived based upon a Galerkin formulation of the problem. Suitable assumptions are made to linearize the steady-state (static) problem leading to an iteration scheme that can be used to refine the solution and include non-linear geometric effects caused by deformation. The eigenvalue problem is cast in this perturbed state to allow more accurate prediction of resonant frequencies