Propagation of Rayleigh-Type Waves on an Elastic Half-Space Covered by a Thin Multi-Layered Coating

The current manuscript models the propagation of surface waves on a mechanically loaded, thin, multi-layered coating half-space using the renowned asymptotic approximation method. Perfect interfacial conditions are imposed between the composite medium’s multiple layers, in addition to boundedness conditions along the depth of the underlying half-space. Approximate equations of plane motion and the secular equation for the propagation of Rayleigh-type waves on the governing multi-layered coating substrate have been derived, utilizing the effective boundary data on the multi-interface of the medium under the long-wave approximation limit. The acquisition of an approximate elliptic-hyperbolic equation of motion, featuring a pseudo-differential operator and characterized by impulsive point loading, led to the observation of oscillatory wave behaviors in both the longitudinal displacement and potential functions with respect to the scaled spatial-temporal variable χ. Finally, some numerical illustrations, considering prototypical high-contrast coatings and stiff substrates, exhibit slow oscillations of the progressing and receding fronts. Conversely, an opposite trend is noted when a soft underlying substrate is placed beneath a stiff multi-layered coating.