An approximate secular equation of generalized Rayleigh waves in pre-stressed compressible elastic solids

The present paper is concerned with the propagation of Rayleigh waves in a pre-stressed elastic half-space coated with a thin pre-stressed elastic layer. The half-space and the layer are assumed to be compressible and in welded contact with each other. By using the effective boundary condition method, an explicit third-order approximate secular equation of the wave has been derived that is valid for any pre-strains and for a general strain-energy function. When the pre-strains are absent, the secular equation obtained coincides with the one for the isotropic case. Numerical investigation shows that the approximate secular equation obtained is a good approximation. Since explicit dispersion relations are employed as theoretical bases for extracting pre-stresses from experimental data, the secular equation obtained will be useful in practical applications.

► The propagation of Rayleigh waves in an elastic half-space coated by a thin elastic layer is investigated.
► Both the half-space and the layer are pre-stressed and compressible.
► By using the effective boundary condition method, an approximate secular equation of third-order has been derived.
► It recovers the approximate secular equation of third-order for the isotropic case.
► A numerical investigation shows that the approximate secular equation obtained is a good approximation.