On the Propagation of Surface Waves

Abstract

Rayleigh waves in classical, isotropic elasticity /1/ may be regarded as a superposition of two nondispersive inhomogeneous plane waves with the same direction of propagation along the stress-free surface and direction of attenuation orthogonal to the surface, equal phase speeds but with different values of the attenuation coefficients. The displacement field decays to zero uniformly with increasing distance from the stress-free surface. These characteristic features of Rayleigh waves do not remain valid when thermoelastic interactions /2–6/, viscoelastic properties /7–8/, constrained materials /9/, etc., are considered. Then the surface waves may be interpreted as a superposition of dispersive inhomogeneous plane waves. The superposed waves have different directions of propagation and attenuation and different phase speeds and attenuation coefficient values. Their directions of propagation are not parallel to the stress-free surface. For each of them the plane of constant phase and the plane of constant amplitude are not orthogonal. The displacement /or displacement-temperature/ field decays again to zero with increasing distance from the surface but not uniformly. These results were obtained for the thermoelastic Rayleigh waves in /10/. Appropriate criteria for behaviour at infinity were also discussed there in order to preserve some of the most characteristic features of the Rayleigh waves known from classical elasticity.