Guided elastic waves in orthotropic surface layers

Abstract

Propagation of guided waves along the interface of an elastic surface layer of uniform thickness overlying an elastic homogeneous half-space is examined. The structure is made of materials with arbitrary strain energy functions. To gain understanding of the propagation characteristics and their dependence on the elastic constants and mass densities, the mathematically tractable case of material orthotropy is considered. For propagation along a material axis of symmetry, the dispersion equation is obtained in explicit form when the axes of symmetry of the two materials coincide and one of them is normal to the plane separating the surface layer from the underlying half-space. Analysis of the dispersion equation reveals the propagation characteristics of interfacial waves and their dependence on the material parameters. Propagation occurs either in single or multiple modes, depending on the material parameters of both the surface layer and the underlying half-space. The low-frequency phase speed is obtained from the dispersion equation in terms of wavelength and layer thickness, elastic constants and mass densities. The influence of the two materials on phase speed as it deviates from its value in an orthotropic half-space is, thus, given explicitly. Parameter conditions are defined under which guided waves are not allowed to propagate in certain frequency regimes. Numerical results complement the analysis.