Anti-plane SH-Deformation Of A Semi-Cylindrical Hill Above A Subsurface Elastic Cylindrical Inclusion In Half-Space

In this paper, the scatting of SH-wave by a semi-cylindrical hill above a subsurface elastic cylindrical inclusion in half-space is studied based on "conjunction". The whole solution domain was divided into two parts, the first one is a circle domain, which includes the boundary of the semi-cylindrical hill, and all of the rest was considered to be the second one. The solution of displacement was constructed in the two parts respectively, and then the two solutions were conjoined on the junction interface. A steady wave function is constructed in the circle domain, which satisfies the condition that stress is zero at the hill edge and arbitrary at other part. In the second domain, including a semi-cylindrical canyon and a subsurface elastic cylindrical inclusion in half-space, a scattered wave function is constructed, which satisfies the condition that the stress is zero at the horizontal surface. Then by moving coordinate, the two solutions that satisfied the boundary condition at the subsurface elastic cylindrical edge are conjoined on the junction interface. Finally, the solution of the problem can be reduced to a series of algebraic equations that can be solved numerically by truncating the finite terms of infinite algebraic equations. The examples and computational results are given and discussed.