Influence of Point Source on Love-Type Waves in Anisotropic Layer Overlying Viscoelastic FGM Half-Space: Green’s Function Approach

Abstract

This article is framed to examine the influence of heterogeneities, viscosity, initial stress, rigidity and density ratios, and thickness on traversal characteristics of Love-type surface wave in a heterogeneous anisotropic medium over heterogeneous Voigt-type viscoelastic functionally graded material (FGM) orthotropic half-space influenced by a point source. The rigidity and density of the anisotropic layer are considered to vary hyperbolically with depth, whereas the density, elastic parameter, initial stress, and viscoelastic coefficient for the semi-infinite stratum are assumed to vary quadratically with depth. The complex velocity of the Love-type wave has been achieved by the method of Green’s function and Fourier transformation under effective boundary conditions. After complex expansion of the velocity equation, we get the dispersion and absorption relations from the real and imaginary parts, respectively. In some special cases, we have derived the classical relation of Love wave for the case when both the anisotropic layer and viscoelastic half-space are isotropic and homogeneous, which validates the assumed problem. Numerical solutions have been carried out and depicted graphically to elucidate the effect of these parameters on the traversal characteristics of a Love-type wave. The appearance of heterogeneities, initial stress, and viscoelasticity in the velocity equation reflects that these parameters significantly affect the attenuation and dispersion characteristics of Love-type waves.