Impact of losses on Love wave propagation in multilayered composite structures loaded with a Newtonian liquid

Abstract

In this study, we analyze theoretically and numerically the properties of Love surface waves propagating in lossy multilayered composite waveguides, loaded on the upper surface with a Newtonian liquid. The propagation of Love surface waves was formulated in terms of a direct Sturm–Liouville problem. An analytical form of the complex dispersion equation of the Love surface wave was derived using the Thomson–Haskell transfer matrix method. By separating the complex dispersion equation into its real and imaginary parts, we obtained a set of two nonlinear algebraic equations, which were subsequently solved numerically. The effect of various physical parameters of the lossy viscoelastic waveguide on the velocity and attenuation of the Love surface wave was then analyzed numerically. It was found that because of the presence of losses in the analyzed waveguide, Love surface waves displayed a number of new original phenomena, such as resonant-like maxima in attenuation as a function of thicknesses $h_1$ of the first viscoelastic surface layer and thickness $h_2$ of the second elastic surface layer. These phenomena are completely absent in lossless waveguides.