An approximate secular equation of Rayleigh waves propagating in an orthotropic elastic half-space coated by a thin orthotropic elastic layer

The present paper is concerned with the propagation of Rayleigh waves in an orthotropic elastic half-space coated with a thin orthotropic elastic layer and 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 secular equation of third-order in terms of the dimensionless thickness of the layer has been derived. From this equation two different third-order approximate secular equations are obtained for the case when the half-space and the layer are both isotropic, one of which recovers the secular equation of second-order derived by Bovik [P. Bovik, A comparison between the Tiersten model and O(H) boundary conditions for elastic surface waves guided by thin layers, J. Appl. Mech. 63 (1996) 162–167]. An explicit second-order approximate formula for the Rayleigh wave velocity has been created based on the obtained approximate secular equation. Since explicit dispersion relations are employed as theoretical bases for extracting the mechanical properties of the thin films from experimental data, the obtained secular equation and formula for the velocity may be useful in practical applications.

► By using the effective boundary condition method an approximate secular equation of third-order has been derived.
► From it two different third-order approximate secular equations are obtained for the isotropic case.
► One of which recovers the secular equation of second-order derived by Bovik [P. Bovik, J. Appl. Mech. 63 (1996) 162–167].
► An explicit second-order approximate formula for the Rayleigh wave velocity has been created.
► The obtained secular equation and formula for the velocity may be useful in practical applications.