Rayleigh-type waves on a coated elastic half-space with a clamped surface

Elastodynamics of a half-space coated by a thin soft layer with a clamped upper face is considered. The focus is on the analysis of localized waves that do not exist on a clamped homogeneous half-space. Non-traditional effective boundary conditions along the substrate surface incorporating the effect of the coating are derived using a long-wave high-frequency procedure. The derived conditions are implemented within the framework of the earlier developed specialized formulation for surface waves, resulting in a perturbation of the shortened equation of surface motion in the form of an integral or pseudo-differential operator. Non-uniform asymptotic formula for the speeds of the sought for Rayleigh-type waves, failing near zero frequency and the thickness resonances of a layer with both clamped faces, follow from the aforementioned perturbed equation. Asymptotic results are compared with the numerical solutions of the full dispersion relation for a clamped coated half-space. A similarity with Love-type waves proves to be useful for interpreting numerical data. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'.