Rayleigh waves in linear isotropic elastic media
The problem of the generation of Rayleigh wave on the smooth surface of a three-dimensional linear isotropic media is discussed. Since the Rayleigh waves have characteristic exponential decay with depth, displacements are expanded in terms of a local coordinate system with origin at the surface of the medium and \(x_ 3>0\) representing the medium near this point. It is found that depending on the components of the load on the boundary of the media, either all kinds of waves (volume and surface) or only surface waves can be generated. Surface waves are not generated by volume (dilatational and shear) waves and can be produced only by special load imposed on the boundary of the elastic media. The boundary operator T which represents the boundary conditions on the surface of the medium, is elliptic in the hyperbolic (real phases) and mixed (one phase real and other imaginary) regions, and is real (both phases imaginary) with a single zero on the hypersurface T*(R\(\times \partial K)\), where \(\partial K\) is the surface of the medium. It is the last case which generates pure surface waves on the boundary.
three-dimensional linear isotropic media
scientific article; zbMATH DE number 3999396