Two-dimensional equations for piezoelectric thin-film acoustic wave resonators

We derived a system of two-dimensional equations for thickness-extensional vibrations of a four-layered plate consisting of a piezoelectric thin film on an elastic substrate with driving and ground electrodes. It takes into consideration the couplings of the thickness-extensional mode to with the others including extensional, flexural, fundamental and second-order thickness-shear modes. Mindlin's approach of using a power series expansion of the displacement field in the plate thickness coordinate was employed. The propagation of straight-crested waves in the plate were studied. It is shown that the equations obtained are very accurate for long waves in the plate. Hence they can be used for theoretical and numerical modeling of thin-film piezoelectric acoustic wave resonators operating with long thickness-extensional modes.