Analysis of Dispersion and Damping Characteristics of Love Wave Propagation in Orthotropic Visco-Elastic FGM Layer with Corrugated Boundaries

Abstract

A mathematical model was designed to analyze the propagation characteristics of Love waves traversing through an orthotropic visco-elastic FGM layer under initial stress lying over a half-space with void pores. The uppermost surface layer and common interface between the layer and half-space are considered irregular in nature. Using Biot’s theory, the governing equations of motion were obtained, and further displacement components for the layer and half-space were derived with the aid of the variable separable method. After applying the suitable boundary conditions, the complex form of the velocity equation was derived. In order to study the propagation and damping characteristics of Love waves in the present model, the velocity equation was expanded into its real and imaginary parts. From the imaginary part, damped velocity characteristics were analyzed, whereas from the real part, the phase velocity characteristics are discussed in detail. A comparative study was conducted in which the curves were plotted for two cases: one when both boundaries are corrugated and another when boundaries are planar. The study reveals the fact that Love waves propagate faster in a stratified medium with corrugated boundaries than a medium with planar boundaries. The presence of corrugated surfaces minimizes the damping characteristics of Love waves. Curves were plotted to analyze the impact of initial stress, heterogeneity, and visco-elasticity on the amplitude and frequency content of Love waves. Moreover, in order to strengthen the validity and applicability of the considered model, error analysis was carried out graphically.