Legendre polynomial approach for modeling free-ultrasonic waves in multilayered plates

Abstract

Modeled on the Laguerre polynomial approach used for surface acoustic waves, a formulation is presented for the study of free-acoustic wave propagation in layered plates. It uses the Legendre polynomials. Each layer can be of arbitrary anisotropy and piezoelectricity with arbitrary crystal orientation with the only restriction that the parameters of the constituent materials are close to each other. Formulations are given for open-circuit and short-circuit surfaces. Phase velocity dispersion curves, attenuations, power distributions, and field profiles are easily obtained from an algorithm easily implemented on a computer using commercial software. Numerical results are given for AlAs/GaAs multilayered structures which illustrate the capabilities of the described method. Its major advantages are: (i) in a unified formulation, all types of modes, surface modes, interface modes, and plate modes are naturally encompassed. (ii) Large values of the frequency-thickness product as compared to the values allowed by the usual methods may be dealt with. (iii) For propagation loss calculation, the usual multivariable search is avoided since the proposed method naturally works in the complex plane.