An approximate secular equation of Rayleigh-like waves in coated elastic half-space containing voids

Abstract

Propagation of Rayleigh-like surface waves is studied in an isotropic elastic solid half-space coated with a thin isotropic elastic solid layer. The half-space and the thin coated layer are in welded contact with each other and contain a uniform distribution of small void pores. Effective boundary condition method is employed to derive an approximate secular equation of second-, third-, and fourth-orders in terms of dimensionless wavenumber. The corresponding secular equations are solved numerically to obtain the speed of propagating Rayleigh-like waves for a particular model. The computed results are presented graphically and compared with those obtained from exact secular equation. The fourth-order approximate secular equation is found to have high accuracy as it provides solutions that are in close vicinity of those obtained from the exact secular equation in the considered model. The presence of voids in the model is found to influence the speed of Rayleigh-like waves theoretically and verified numerically. By ignoring the presence of voids in the model, the secular equation is found to be in complete agreement to the earlier known results in the literature for the corresponding model.