Analysis of acoustic waves in multilayers using compound matrices

Abstract

A modification of the matrix formalism for studying acoustic wave propagation in anisotropic piezoelectric multilayers is developed. The modification is based upon the use of the compound matrices, well known from the theory of the matrices. Using the modified method, analytical expressions for the relationship between the real and imaginary parts of the determinant of the boundary conditions are derived. One of the advantages of the method is demonstrated for thick plates and thick film structures. On considering the dispersion curves for thick multilayers, the slow dispersion regions inherent for anisotropic materials are discovered. The regions are related with the cutoff velocities of the bulk waves in the film materials.