Rayleigh waves in an isotropic elastic half-space coated by a thin isotropic elastic layer with smooth contact

•The propagation of Rayleigh waves in an elastic half-space coated by a thin elastic layer is considered.•The half-space and the layer are both isotropic and the contact between them is smooth.•By using the effective boundary condition method an approximate secular equation of fourth-order has been derived.•From it, an explicit third-order approximate formula for the Rayleigh wave velocity has been established.•The approximate secular equation and the formula for the velocity will be useful in practical applications.

In the present paper, we are interested in the propagation of Rayleigh waves in an isotropic elastic half-space coated with a thin isotropic elastic layer. The contact between the layer and the half space is assumed to be smooth. The main purpose of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method, an approximate, yet highly accurate secular equation of fourth-order in terms of the dimensionless thickness of the layer is derived. From the secular equation obtained, an approximate formula of third-order for the velocity of Rayleigh waves is established. The approximate secular equation and the formula for the velocity obtained in this paper are potentially useful in many practical applications.