Rectangular piezoelectric plate loaded on each face: a three-dimensional approach

Abstract

This paper deals with the vibration mode determination of a rectangular plate loaded on each face. The resonant frequencies, the mechanical displacement and the electrical impedance of the plate are calculated using a three-dimensional approach based on the plane wave propagation along each coordinate axis. Then, the constitutive piezoelectric equations reduce and by introducing the relevant boundary conditions — that is, the stresses and particle displacements are continuous — a 7 × 7 linear matrix system is obtained. Solving this system yields the particle displacements in terms of the load impedances located on the sample faces. The electrical impedance of the sample can also be easily computed. It is shown that due to lateral coupling, there is no nodal plane inside the sample and the material losses used are less than those introduced with the one-dimensional approach.