Far Field Solution of SH-Wave Scattered by a Circular Cavity and a Mode III Crack in Half Space

Based on Green’s function, complex function and multi-polar coordinate system, the far field solution of SH wave scattered by an elastic half space with a circular cavity and a crack at an arbitrary position and orientation is investigated. First, a suitable Green’s function is constructed, which is the fundamental solution of the displacement field for a half space with a circular cavity subjected to an out-plane time-harmonic line force at an arbitrary position in half space. Second, by means of crack-division technique, a crack with any location and orientation can be constructed in the region of the half space. The displacement field and stress field are established in the situation of coexistence of circular cavity and crack. At last expressions of far field, such as displacement mode of scattering wave are deduced. Some examples and numerical results are illustrated. The influences of the combination of different media parameters on solutions of far field are discussed.