Scattering of plane compressional waves by a spherical inhomogeneity with a linear spring type interface

In this paper, we study the scattering of plane compressional waves by a spherical inhomogeneity with an imperfect interface. The interface is modeled by a linear spring assuming that the tangential and normal interfacial displacement jumps are proportional to the associated tractions. By using series expansion method an analytical solution is obtained for the displacement potentials of the reflected and refracted waves as well as the stress fields in the inhomogeneity and the matrix. Results of some special cases are then discussed.