Exact analysis of the propagation of acoustic waves in multilayered anisotropic piezoelectric plates

Exact analysis of the propagation of acoustic waves in multilayered piezoelectric plates is performed using the transfer matrix method. A general technique for analyzing layered piezoelectric resonators under thickness and lateral field excitation is presented and applied to the study of zinc oxide on silicon thin-film resonators. Both 1-D and 2-D analysis with general material anisotropy is performed, and a simplified method for incorporating thin conducting electrodes on the plate´s free surface is presented. The general methodology described is summarized into efficient algorithms to aid in the implementation of the procedures, and some computational aspects are discussed. Fundamental resonant and antiresonant cutoff frequencies through both thickness and lateral field excitation are calculated for two and three layered plates. Along with these frequencies, thickness mode shapes for displacements, stress tractions, electric potential, and electric displacement are shown. Exact dispersion relations for propagating straight crested waves are also presented for these plates. Both real and imaginary branches of these dispersion relations are shown, and these calculations carried out for both open-circuit and short-circuit conditions. Two different crystal tensor rotations of the ZnO layers are considered, giving rise to different cases of electromechanical coupling