Elastodynamics of a coated half-space under a sliding contact

Abstract

The paper deals with elastic wave propagating in a layer on a half-space induced by a vertical force. The focus is on the effect of a sliding contact along the interface and its comparative study with a perfect one. The effective boundary conditions substituting the presence of the layer are derived. The leading order term in these conditions corresponds to vertical inertia of the layer, whereas next order correction involves the effect of plate waves in the coating. Analysis of the associated dispersion relation confirms the existence of a Rayleigh-type wave, along with extensional and shear plate waves. An asymptotic hyperbolic-elliptic formulation for surface wave field is also presented. This includes a hyperbolic equation singularly perturbed by a pseudo-differential operator playing a role of a boundary condition for the elliptic equation governing decay over the interior. The sign of the coefficient at the pseudo-differential operator is demonstrated to be always negative, corresponding to a local maximum of the phase speed at zero wave number, and consequently to a distinct receding type of the Rayleigh-type wave quasi-front induced by an impulse load.