Matrix methods applied to acoustic waves in multilayers

Abstract

Matrix methods for analyzing the electroacoustic characteristics of anisotropic piezoelectric multilayers are described. The conceptual usefulness of the methods is demonstrated by examples that show the simplification of formal statements of propagation, transduction, and boundary-value problems in complicated acoustic layered geometries such as those in SAW (surface acoustic wave) devices, in multicomponent laminates, and in bulk-wave composite transducers. The formulation reduces the electroacoustic equations to a set of first-order matrix differential equations, one for each layer, in the variables which must be continuous across interfaces. The solution to these equations is a transfer matrix that maps the variables from one layer face to the other. Interface boundary conditions for a planar multilayer are automatically satisfied by multiplying the individual transfer matrices in the appropriate order, thus reducing the problem to the imposition of boundary conditions appropriate to the remaining two surfaces. The computational advantages of the matrix method lie in the fact that the problem rank is independent of the number of layers, and in the availability of PC software, which makes interactive numerical experimentation with complex layered structures practical.<>