Scattering of Anti-Plane SH-Wave by the Semi-Cylindrical Gap with Multiple Shallow-Buried Inclusions in Elastic Semi-Space

Abstract

Semi-cylindrical gap and Multiple circular inclusions exists widely in natural media, composite materials and modern municipal construction. The scattering field produced by semi-cylindrical gap and multiple circular inclusions determines the dynamic stress concentration factor around the gap and circular inclusions, and therefore determines whether the material is damaged or not. These problems are complicated. It is hard to obtain analytic solutions except for several simple conditions. In this paper, the solution of displacement field for elastic semi-space with semi-cylindrical gap and multiple cylindrical inclusions by anti-plane SH-wave is constructed. In complex plane, considering the symmetry of SH-wave scattering , the displacement field aroused by the anti-plane SH-wave and the scattering displacement field impacted by the gap and the cylindrical inclusions comprised of Fourier-Bessel series with undetermined coefficients which satisfies the stress-free condition on the ground surface are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the displacement and stress condition around the edge of the gap and cylindrical inclusions. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. The total wave displacement field is the superposition of the displacement field aroused by the anti-plane SH-wave and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical inclusions.