Linear dispersive shear waves in two-layer elastic medium

Abstract

In linear isotropic elasticity, cases exist where pure shear waves are possible even in bounded media; these have a nondispersive mode with propagation speed equal to that in an infinite medium. For these cases, consideration of a two-layer medium shows the existence of dispersion which vanishes only with equality of the propagation speeds. The present study uses the method of asymptotic expansions; a uniformly valid approximation is obtained to describe the speed and dispersive nature of these waves. The elegance of this approach is brought out by derivation of the basic result of this study viz., Jeffrey equation to describe the farfield structure of these waves.