Surface/interfacial anti-plane waves in solids with surface energy

•We discuss a new model of surface/interfacial elasticity.•We obtained a new type of dispersive surface anti-plane waves.•The propagation properties are determined by material parameters of the interface.•An anomalous dispersion is possible for stiff surface/interface.

In this paper we discuss new type of surface anti-plane waves localized near the surface an elastic half-space and in the vicinity of plane interface between two half-spaces, when considering surface strain and kinetic energies. We also consider the case of non-perfect interface, i.e. when a jump of displacement or of its gradient, with the aim of modelling lacking of adhesion between solids. The phase velocity profiles and dispersion relations of surface waves are presented and several different material parameters are considered. Among the results, we observe an anomalous dispersion when the surface/interface is stiffer than the bulk material. These results can be exploited for the nondestructive characterization and the analysis of thin inter-phases between two solids, and can find several engineering applications.