THE PROPAGATION OF RAYLEIGH WAVES IN A HETEREGENOUS MEDIUM

This study investigates linear Rayleigh wave propagation in a layered half-space composed of different homogeneous materials, with irregular boundary surfaces. The analysis of such irregularities poses mathematical challenges and often requires representing boundary variations with specific functions. Assuming that the surface is free of traction and that displacement and stress remain continuous across the interfaces, the surfaces are modeled as functions of the propagation direction without specifying their form. The problem is formulated using elasticity theory, and asymptotic perturbation methods are applied to derive governing equations. The dispersion relation is expressed in terms of phase velocity, wavenumber, and propagation direction, with later analysis assuming periodic boundary irregularities and actual material properties.