SH wave in two-layered structure of functionally graded viscoelastic and monoclinic media under the influence of an interior point source

Abstract

This paper investigates the propagation characteristics of SH-type waves originating from a point source situated at the interface of a unique structure comprising a functionally graded viscoelastic (FGV) layer of finite depth overlying a functionally graded monoclinic (FGM) half-space. The upper viscoelastic layer exhibits a hyperbolic gradient property in its material constants, while an exponential gradient property characterizes the lower monoclinic half-space. Employing the Fourier transform and Green’s function method to account for surface and interfacial boundary conditions, a dispersion relation for the SH-type waves is derived. The obtained dispersion relation for the gradient layered structures reveals a complex interplay between wave phenomena and material properties. Numerical analysis is performed to illustrate the theoretical results for various gradient parameter values, demonstrating a significant influence on dispersion curves, phase velocity, group velocity, and wave number. This understanding holds paramount importance for seismic imaging, geological resource exploration, and the design of resilient infrastructure, thereby fostering innovation in geophysics and engineering. © The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025.