Nonlocal elastic analysis of Rayleigh wave propagation in three-layered heterogeneous media

Abstract

The present study investigates the propagation characteristics of Rayleigh waves in a three-layered nonlocal medium consisting of a nonlocal fiber-reinforced layer over a nonlocal sandy intermediate layer, underlain by a nonlocal transversely isotropic half-space. The theoretical model is derived using Eringen’s concept of nonlocal elasticity and the governing equations are solved using harmonic wave analysis and the method of separation of variables. The dispersion relation is obtained by applying appropriate boundary conditions and is solved numerically using Mathematica. The effects of nonlocal parameters, layer thickness, sandy parameter, fiber orientation and wavenumber on phase velocity are examined in detail. The results reveal that nonlocality leads to a reduction in phase velocity, with the dominant influence arising from the upper fiber-reinforced layer. Displacement analysis shows that wave motion is localized near the surface, gradually attenuating with depth and partially transmitting into the intermediate layer. Overall, the study highlights the combined influence of nonlocality, anisotropy, and layer configuration on Rayleigh wave propagation in layered media, which is useful in geophysical exploration and advanced material design. The proposed model is applicable in seismic wave analysis, subsurface characterization, and geotechnical engineering, particularly for layered Earth structures involving sandy deposits and anisotropic formations.