On the Equivalence of Dispersion Relations Resulting from Rayleigh-Lamb Frequency Equation and the Operator Plate Model

Abstract

The Rayleigh-Lamb frequency equations for the free vibrations of an infinite isotropic elastic plate are expanded into the infinite power series and reduced to the polynomial frequency and velocity dispersion relations. The latter are compared to those of the operator plate model developed in [Losin, N. A., 1997, “Asymptotics of Flexural Waves in Isotropic Elastic Plates,” ASME J. Appl. Mech., 64, No. 2, pp. 336–342; Losin, N. A., 1998, “Asymptotics of Extensional Waves in Isotropic Elastic Plates,” ASME J. Appl. Mech., 65, No. 4, pp. 1042–1047] for both symmetric and antisymmetric vibrations. As a result of comparative analysis, the equivalence of the corresponding dispersion polynomials is established. The frequency spectra, generated by Rayleigh-Lamb equations, are illustrated graphically and briefly discussed with reference to those published in [Potter, D. S., and Leedham, C. D., 1967, “Normalized Numerical Solution for Rayleigh’s Frequency Equation,” J. Acoust. Soc. Am., 41, No. 1, pp. 148–153].