On The Scattering Of SH-Wave By Circular Lining Structure Near The Interface

An analytic method is developed for the problem of scattering of steady SH-wave and dynamic analysis of a shallow-embedded circular lining structure in the field of linearly elastic dynamic mechanics in this paper. The scattered wave function which satisfies the condition of stress free at the ground surface of half-space containing a shallow-embedded circular lining structure impacted by incident steady SH-wave is constructed based upon the symmetry of SH-wave scattering and the method of multipolar coordinates system. Using this wave function, the problem can be summarized to the scattering of SH-wave by a shallow-embedded circular lining structure in infinite space. And then, we take advantage of the boundary conditions around the lining structure to solve the problem, which are: the displacement and the stress are continuous around the external side of the lining structure; the stress is free around the internal side of the lining structure. Therefore, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations. Finally, given two kinds of incident wave and different dimensionless parameters, numerical examples are provided to show the influence of wave number, shear modulus, thickness and distance between the center of the cavity and ground surface upon the dynamic stress concentration by incident steady SH-wave.