Attenuation of Guided Waves in Isotropic Viscoelastic Materials

Abstract

Wave propagation in an infinite isotropic elastic plate with tractionfree faces is governed by the Rayleigh-Lamb frequency equation. As is well-known, an analysis of the equivalent viscoelastic problem shows that the frequency equation for an isotropic viscoelastic plate may be obtained from the Rayleigh-Lamb equation by replacing the two independent elastic constants with complex functions of frequency. The propagation wavenumbers corresponding to modes that propagate unattenuated in an elastic plate are complex in a viscoelastic plate, the imaginary parts being attenuation constants. In this paper, an approximate method is developed for obtaining roots of the viscoelastic-frequency equation from known roots of the Rayleigh-Lamb equation with comparatively little additional calculation. The approximate method is applicable when the attenuation per wavelength is small. Calculations have been carried out for the lowest three longitudinal and flexural modes in plates with Poisson's ratios of 0.17 and 0.35, and curves are presented that show the contributions to the over-all attenuation owing to dissipation associated with dilatational and shear deformations separately. As an example, the variation of attenuation with frequency in a Voigt solid has been calculated and plotted for two ratios of dilatational to shear losses. The same procedure can be used to calculate the attenuation in an isotropic viscoelastic cylinder, using the Pochhammer-Chree equation, and numerical results are given for the longitudinal modes of a cylinder.