An exact secular equations of Rayleigh waves in a compressible pre-stressed elastic half-spaces coated with an elastic layer

Abstract

   This paper is concerned with the propagation of Rayleigh waves in a compressible pre-tressed elastic half-space coated with a compressible pre-stressed elastic layer. The main purpose of the paper is to establish an approximate secular equation of the wave. First, the relations between the traction amplitude vector and the displacement amplitude one of Rayleigh waves at two sides of the interface between the layer and the half-space are created. From the continuity condition at the interface and these relations the displacement amplitude vector of Rayleigh waves at the interface is determined. Then, an exact secular equation of the wave has been derived by using these relations. From this equation, an secular equation of Rayleigh wave is obtained for a compressible prestressed elastic half-space and this equation coincides in the equation of M. A. Dowaikh and R. W. Ogden (M. A. Dowaikh and R. W. Ogden, 1991) and Vinh (Vinh, 2011). The explicit seculars derived in this paper are useful for scientists