Scattering of a Rayleigh Wave by the Edge of a Thin Surface Layer

Abstract

This investigation treats the problem of the scattering of a Rayleigh wave by the edge of a thin layer which covers half the surface of an elastic half-space. The interaction between the layer and the half-space is described approximately by means of a model in which the effect of the layer is represented by a pair of boundary conditions at the surface of the half-space. Two parameters- one representing mass and the other, stiffness- are found to characterize the layer. The incident Rayleigh wave impinges normally upon the plated region from the unplated side. In the case where the mass of the layer vanishes, the problem is solved exactly using Fourier transforms and the Wiener-Hop£ technique, and numerical results are obtained for the amplitudes of the reflected and transmitted surface waves. In the more general case of a layer possessing both mass and stiffness, a perturbation procedure leads to a sequence of problems, each of which may be solved using Fourier transforms. The zeroth- and first-order problems are solved and the resulting approximate reflection and transmission coefficients are evaluated numerically for various ratios of layer mass to stiffness.