WAVE-PROPAGATION IN INHOMOGENEOUS VISCOELASTIC SOLIDS

A viscoelastic solid is considered whose material properties are inhomogeneous in a localized region and homogeneous elsewhere. The exact differential equation is derived for the perturbation of the displacement field due to inhomogeneities. Upon recourse to Kirchhoff-type integral formulae, the perturbation is found to be the volume integral of a Green function times an appropriate body force. Detailed results are determined in the approximation that the diameter of the inhomogeneity region is much smaller than the distance to the observation point. Finally, specific expressions are given for the transverse-like and the longitudinal-like parts of the perturbed field, thus characterizing mode conversion.