Elastic waves in the anisotropic layer-substrate structure. I. General theory

The elastic dynamics of a bicrystal structure consisting of a layer and a s ubstrate and characterized by an arbitrary anisotropy of the constituent cr ystallites has been considered. The wave fields are constructed as linear s uperpositions of six-dimensional vector functions possessing the properties of completeness and orthogonality. These functions are expressed in terms of two sets of eigenvectors and eigenvalues of the Stroh problem for both m edia of the structure. The general solutions of the plane-wave problems of two types are obtained-those of reflection and eigenwave states. The corres ponding real dispersion equation determining the phase velocities of eigenw aves is derived. The eigensolutions for the leaky modes are discussed. As a n example, two limiting cases are considered-those of a thin and a thick la yer (in comparison with the wavelength). In these cases, the eigensolution reduces to a weakly perturbed Rayleigh wave either in the substrate or at t he free surface of the layer. The conditions are indicated under which the perturbed solution in a thick layer is characterized by a weak leaky wave p ropagating into the substrate. The reflection resonance in the vicinity of the given leaky mode is also discussed.