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

Abstract

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)’.

Moving Load on an Elastic Half-Space Coated With a Thin Vertically Inhomogeneous Layer

“…Further possible developments include addressing transient problems [17], generalizations to coatings with more sophisticated mechanical properties, taking into account the effects of viscosity, curvature, long-wave high-frequency waves [20], as well as a more general treatment of a vertically inhomogeneous half-space, see e.g. [3].…”

Analysis of the Rayleigh wave field due to a tangential load applied on the surface of a coated elastic half-space

“…On inserting the transformed potentials into displacement and boundary equations (12) and (13) we obtain…”

“…A surface wave of arbitrary pro-…le in anisotropic half-space was constructed by means of the Stroh formalism in [11]. We also mention [12] which considered surface waves in a coated half-space with a clamped surface because of the applicability of the hyperbolic-elliptic model for surface wave in high frequency domain. Analysis of the Rayleigh …eld in a three dimensional elastic half space subject to in-plane surface loading was given in [13].…”

Near-Resonant Regimes of a Moving Load on a Pre-Stressed Incompressible Elastic Half-Space

“…The advantage of this approach is related to the representation of the surface wave field in terms of a single harmonic function, providing reduction of the vector problem of elastodynamics to a scalar formulation. Recent developments in this area include the incorporation of effects of anisotropy (Fu et al, 2020), a refined second-order model (Wootton et al, 2020), explicit formulations for seismic meta-surfaces in the form of an array of resonators attached to the surface (Ege et al, 2018;Wootton et al, 2019) and formulations for surface wave on a coated halfspace with non-classical boundary conditions (Kaplunov et al, 2019).…”