2000 IEEE/EIA International Frequency Control Symposium and Exhibition THREE-DIMENSIONAL ANALYSIS OF FORCED PIEZOELECTRIC VIBRATIONS OF RECTANGULAR AT -CUT QUARTZ PLATES AND X-CUT LiTaOJ PLATES

spurious resonances whose frequencies are close to that of the main resonance. The three-dimensional (3D) finite element method (FEM) is one of the most powerful techniques used in solving piezoelectric problems, but it is difficult to apply the 3-D FEM to the analysis of spurious vibrations directly because the short wavelengths of spurious modes result in a very large matrix equation. This paper describes a new method for analyzing the forced vibrations of rectangular piezoelectric plates. It is an extension of a method used to analyze 3-D vibrations of elastic plates [2] and it enables the electric response of piezoelectric plates to be calculated with a small matrix system. We treat a plate excited by a driving voltage V. The displacements and electric potential of the plate are represented by a sum of two parts: a 2-D forced solution satisfying the driving requirement (V # 0) and a 3D free solution in the short-circuit case (V = 0). The latter is further expanded in a series of guided waves. The guided waves and also the 2-D solution must obey a set of differential equations and must satisfy boundary