Interaction of elastic waves with the unilateral interface between a layer and a half-space

In this paper, the interaction of an incident harmonic plane elastic wave with the unilateral interface between a layer and a half-space has been investigated. Based on the general traveling solutions of the linear governing equations for the layer and half-space, a method to solve this kind of the problems by means of functional equations has been proposed. Under the conditions of neglecting friction between the layer and half-space and the incident angle less than the critical value, the concrete solution for the problem has been given. The results show that the nonlinear distortions of the elastic wave ®eld in the layer and half-space have arisen, which depend only on two dimensionless parameters relative to the properties of media, wave number, applied pressure and thickness of the layer. Similar to the case for in®nite media, when thickness of the layer is ®nite, the leading edge of the separate zone at the interface is smooth, the distribution of the compressive stress is continuous, but not smooth at the trailing edge and result here in the jump of the compressive stress. The extent of the separate zone increase with the decrease of thickness of the layer. 7