Reduced model for the surface dynamics of a generally anisotropic elastic half-space

Abstract

Near-surface resonance phenomena often arise in semi-infinite solids. For instance, when a moving load with a speed v close to the surface wave speed v R is applied to the surface of an elastic half-space, it will give rise to a large-amplitude disturbance inversely proportional to v − v R . The latter can be determined by a multiple-scale approach using an extra slow time variable. It has also been shown for isotropic elastic half-spaces that the reduced governing equation thus derived is capable of describing the surface wave contribution even for arbitrary dynamic loading. In this paper, we first derive the analogous evolution equation for a generally anisotropic elastic half-space, and then assess its applicability in the study of travelling waves in a half-space that is coated with a continuous array of spring-like vertical resonators or bonded to an elastic layer of different properties. Our results are validated by comparison with previously known results, and illustrative calculations are carried out for a fibre-reinforced half-space and a coated half-space that is subjected to a finite deformation.

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

“…The current work is based on the long-wave asymptotic formulation presented in [7], which has been applied to problems on a moving load for elastic half-space [17,10,8,26], see also [18] for a more systematic exposition of the methodology of hyperbolic-elliptic models for surface waves. Recent advances of the approach include in particular extensions incorporating the effects of anisotropy [13] and pre-stress [21], composite models for elastic layers [9], as well as development of seismic meta-surfaces [29] and the second-order refined model [30].…”

Explicit model for bending edge wave on an elastic orthotropic plate supported by the Winkler–Fuss foundation

“…Future plans may involve accounting for more sophisticated foundations, see e.g. [20], treating a plate of arbitrary anisotropy, which will require Stroh formalism in parallel with recent results for the Rayleigh waves [31]. Finally, we mention exciting applications related to elastic plates with resonators, see e.g.…”

Rayleigh waves in micro-structured elastic systems: Non-reciprocity and energy symmetry breaking

“…Asymptotic approaches have also played an important role in modelling surface waves for coated elastic materials, which are of high practical importance in the design of composites for engineering applications. Some examples, where the analytical treatment of such problems can be found, include the work of Kaplunov et al (2019), who considered interfacial resonances between an elastic half-space coated by a thin elastic layer with a clamped surface, and Fu et al (2020), where surface resonances for anisotropic half-spaces with stratified and elastic coatings have been studied.…”