Nonlinear Mode Coupling Between Rayleigh and Love Waves on an Isotropic Layered Half-Space

Abstract

In this paper we use a multiscale perturbation method to study the nonlinear mode coupling between (initially) monochromatic Rayleigh and Love waves on a half-space of homogeneous isotropic elastic solid with a thin superficial layer of another such solid. This coupling between a Rayleigh-wave mode and a Love-wave mode is possible only at those frequencies, called critical frequencies [1], for which the phase speeds of the two modes in question coincide for the given (favourable) combination of material constants and layer thickness. For this problem the solvability conditions at the third stage of the perturbation analysis take the form of a pair of coupled nonlinear ordinary differential equations governing the slow variations in the complex amplitudes of the two modes with propagation distance. Exact solution of these coupled amplitude equations (CAEs), in terms of Jacobian elliptic functions, shows that there is, in general, a continuous exchange of energy back and forth between the two interacting modes.