Exact secular equations of Rayleigh waves in an orthotropic elastic half-space overlaid by an orthotropic elastic layer

•The propagation of Rayleigh waves in an orthotropic half-space coated by an orthotropic layer is investigated.•The half-space and the layer may be compressible or incompressible and they are in welded contact.•For the compressible/compressible case, the exact secular equation is derived by using the effective boundary condition method.•For three remaining cases, the exact secular equations are obtained by the incompressible limit technique. In this paper, the propagation of Rayleigh waves in an orthotropic elastic half-space overlaid by an orthotropic elastic layer of arbitrary uniform thickness is investigated. The layer and the half-space may be compressible or incompressible and they are in welded contact with each other. The main aim of the paper is to derive explicit exact secular equations of the wave for four possible combinations of a (compressible/incompressible) half-space coated by a (compressible/incompressible) layer. For the compressible/compressible case, the explicit secular equation is derived by using the effective boundary condition method. For three remaining cases, the explicit secular equations are derived from the secular equation for the compressible/compressible case by using the incompressible limit technique along with the expressions of the reduced elastic compliances in terms of the elastic stiffnesses. Based on the obtained secular equations, the effect of incompressibility on the Raleigh wave propagation is considered numerically. It is shown that the incompressibility strongly affects the Raleigh wave velocity and it makes the Raleigh wave velocity increasing.