Scattering of SH-wave by multiple circular cavities in half space

Abstract

In this paper, an analytic method is developed to address steady SH-wave scattering and perform dynamic analysisof multiple circular cavities in half space. The scattered wave function used for scattering of SH-waves by multiple circularcavities, which automatically satisfies the stress-free condition at the horizontal surface, is constructed by applying thesymmetry of the SH-wave scattering and the method of multi-polar coordinates system. Applying this scattered wave functionand method of moving coordinates, the original problem can be transformed to the problem of SH-wave scattering by multiplecircular cavities in the full space. Finally, the solution of the problem can be reduced to a series of algebraic equations andsolved numerically by truncating the infinite algebraic equations to the finite ones. Numerical examples are provided for casewith two cavities to show the effect of wave number, and the distances between the centers of the cavities and from the centersto the ground surface on the dynamic stress concentration around the cavity impacted by incident steady SH-wave.