Effective boundary condition method and Rayleigh waves in orthotropic half-spaces coated by a thin layer with sliding contact

This  paper is concerned with the propagation of Rayleigh waves in an orthotropic elastic half-space coated by a thin orthotropic elastic layer. The half-space and the layer are assumed to be compressible and incompressible and they are in sliding contact with each other. The main aim of the paper is to establish approximate secular equations of the wave for all (four) possibilities of a (compressible or incompressible) half-space covered with a (compressible or incompressible) thin layer, except the case of a compressible half-space coated by a compressible layer that has been considered [Int. J. Eng. Sci. 75 (2014), 154-164]. In order to do that,  the effective boundary condition method is employed and the approximate secular equations of  third-order in terms of the dimensionless thickness of the layer are derived.  It is shown  that these approximate secular equations have  high accuracy. Based on the obtained secular equations, the effect of incompressibility on the  Raleigh wave propagation is considered through some numerical examples. It is shown that the incompressibility  affects strongly  the Raleigh wave velocity and the effect becomes stronger when the coating is incompressible.