Approximate analysis of surface wave-structure interaction

Surface wave-structure interaction is studied starting from a specialised approximate formulation involving a hyperbolic equation for the Rayleigh wave along with pseudostatic elliptic equations over the interior of an elastic half-space. The validity of the proposed approach for modelling a point contact is analysed. Explicit dispersion relations are derived for smooth contact stresses arising from averaging the effect of a regular array of spring-mass oscillators and also of elastic rods attached to the surface. Comparison with the exact solution of the associated plane time-harmonic problem in elasticity for the array of rods demonstrates a high efficiency of the developed methodology.