Reflection and transmission of elastic waves by the spatially periodic interface between two solids (theory of the integral-equation method)
In this paper, the author develops the linear theory of reflection and transmission of time-harmonic, elastic waves by the spatially periodic interface between two perfectly elastic media -- the interface being cylindrical in one direction and periodic in another direction. A given phase progression of the incident wave in the direction of periodicity induces a modal structure in the elastodynamic field and leads to the introduction of the so-called spectral orders. In accordance with this structure, the incident field is represented by the superposition of an infinite set of spectral orders, composed of P-waves and SV-waves. Then, outside the corrugations of the interface, the scattered field, can be represented by a superposition of the same kind, but of an outgoing nature. The main tools in the analysis are the elastodynamic Green-type integral relations which follow from the two dimensional elastodynamic reciprocity theorem wherein a suitable Green state is used. The author shows that, by adapting the Green state to the periodicity of the configuration, the scattering problem needs solution in a single cell only. To obtain results for specific configuration, a numerical implementation of the method is required involving the evaluation of the Green tensors, the numerical solutions of the coupled integral equations and the subsequent computation of the amplitude factors of the scattered field.
represented by superposition of infinite set of spectral orders
elastodynamic Green-type integral relations
scattering problem needs solution in single cell only
scientific article; zbMATH DE number 3776988
scientific article