Antiplane scattering of SH waves by a circular cavity in an exponentially graded half space

In this study, an analytical solution of antiplane scattering of plane SH waves by a circular cavity in an exponentially graded material is obtained via the complex variable method and image technique, and dynamic response of the interface and the cavity is investigated. The medium is a bimaterial with a semi-infinite homogeneous part and an exponentially graded half space containing a circular cavity. The study provides a treatment to the orthogonality of boundary conditions along the half surface and the cavity periphery. Based on Helmholtz decomposition, the stress and displacement components are expressed by complex variables. The scattered waves by the interface surface are regarded as transmitting from the origin of the cavity and its image. These waves can be also satisfy the far-field radiation conditions. The boundary value problem results in a set of infinite algebraic equations which can be solved straightforwardly. Finally, parametric study shows that the inhomogeneous parameter, the dimensionless frequency of the incident waves and the distance-radius ratio of the cavity have significant effect on dynamic response of the medium.