SCATTERING OF ELASTIC SH WAVES BY TRANSVERSELY ISOTROPIC SPHERE

摘要

The scattering by a transversely isotropic sphere in a three-dimensional, homogeneous, isotropic and infinite elastic medium is considered. The problem is a scalar one and is phrased as a scattering problem for an incident SH elastic waves propagating in the direction parallel to the axis of material symmetry. The elastodynamic equations inside the sphere are transformed to spherical coordinates and the displacement field is expanded in associated Legendre functions in the polar coordinate and powers in the radial coordinate. This leads to recursion relations for the expansion coefficients inside the sphere. Using the boundary conditions on the surface of the sphere results in a system of equations for all the expansion coefficients for the fields outside and inside the sphere. As a result, the transition (T) matrix elements are calculated and given explicitly for low frequencies.