SCATTERING OF ELASTIC WAVES BY TRANSVERSELY ISOTROPIC SPHERE

The scattering by a transversely isotropic sphere in a three-dimensional, homoge-neous, isotropic and infinite elastic medium is considered. The problem is a scalar one andis phrased as a scattering problem for an incident SH elastic waves propagating in the direc-tion parallel to the axis of material symmetry. The elastodynamic equations inside the sphereare transformed to spherical coordinates and the displacement field is expanded in associatedLegendre functions in the polar coordinate and powers in the radial coordinate. This leadsto recursion relations for the expansion coefficients inside the sphere. Using the boundaryconditions on the surface of the sphere results in a system of equations for all the expansioncoefficients for the fields outside and inside the sphere. As a result, the transition (T) matrixelements are calculated and given explicitly for low frequencies.