Title :
Matrix methods applied to acoustic waves in multilayers
Author_Institution :
Dept. of Electr. Eng., McGill Univ., Montreal, Que., Canada
Abstract :
Matrix methods for analyzing the electroacoustic characteristics of anisotropic piezoelectric multilayers are described. The conceptual usefulness of the methods is demonstrated in a tutorial fashion by examples showing how formal statements of propagation, transduction, and boundary-value problems in complicated acoustic layered geometries such as those which occur in surface acoustic wave (SAW) devices, in multicomponent laminates, and in bulk-wave composite transducers are simplified. The formulation given reduces the electroacoustic equations to a set of first-order matrix differential equations, one for each layer, in the variables that 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 just having to impose boundary conditions appropriate to the remaining two surfaces. The computational advantages of the matrix method result from the fact that the problem rank is independent of the number of layers, and from the availability of personal computer software that makes interactive numerical experimentation with complex layered structures practical.<>
Keywords :
acoustoelectric effects; boundary-value problems; matrix algebra; numerical methods; partial differential equations; piezoelectric thin films; piezoelectric transducers; surface acoustic wave devices; surface acoustic waves; ultrasonic propagation; ultrasonic transducers; SAW devices; acoustic layered geometries; acoustic wave propagation; anisotropic piezoelectric multilayers; boundary-value problems; bulk-wave composite transducers; electroacoustic characteristics; electroacoustic equations; first-order matrix differential equations; interactive numerical experimentation; matrix method; multicomponent laminates; personal computer software; planar multilayer; surface acoustic wave devices; transduction; transfer matrix; Acoustic devices; Acoustic propagation; Acoustic waves; Anisotropic magnetoresistance; Boundary conditions; Differential equations; Geometry; Nonhomogeneous media; Surface acoustic waves; Transmission line matrix methods;
Journal_Title :
Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on