Anti-plane SH-Deformation Of A Arc-Cylindrical Hill Above A Subsurface Cavity In Half-Space

In this paper, the scattering of SH-wave by a arc-shaped cylindrical hill above a subsurface cavity in half-space is studied based on 'conjunction', by using complex function and multi-polar coordinate method. To solve the problem, we divide the domain of solution into two parts, the first one is a circle domain, which includes the boundary of the hill, and all of the rest is considered as the second one. A solution is constructed in the circle domain, which satisfies the requirements that stress is zero at the hill edge and it could be arbitrary at the other part. The second domain contain a arc-shaped cylindrical canyon and a subsurface cavity, in which we can construct the scattered wave function, which satisfies the requirements of stress free on he horizontal surface. Then, by using moving coordinate method, the two solutions are conjoined on the junction interface and which should satisfy the boundary condition at the subsurface cavity edge. The problem to be solved can be reduced to a series of infinite linear algebraic equations. Finally the computational results of surface displacement and the discussion are provided.