界面点源和半圆柱在直角域中的反平面散射

为得到直角域中垂直边界上的半圆柱对点源载荷的反平面弹性动力学解析解,按照镜像方法和波函数展开法,研究了点源对半圆柱的稳态散射以及其与边界的相互作用,得到直角域中的位移场和应力场.首先,延拓直角域为半空间,延拓半圆柱为圆柱,得到等价问题;其次,构造位移波的波函数级数表达式;最后,对圆柱边界做Fourier展开,定解波函数系数.数值计算了圆柱边沿的动应力,结果表明,半圆柱的散射总是明显地分为投射侧和隐蔽侧,相对低频总是能引起更大的动应力,介质参数对径向动应力和周向动应力的分布,有着截然不同的影响.理论分析得到的稳态解丰富了SH波散射的理论,为双相介质界面圆柱的SH波散射的Green函数方法奠定了基础,数值算例为相应的工程问题提供了参考.

Anti-plane scattering of interfacial point source load and semi-circular cylinder in an elastic quarter space

To obtain anti-plane elastodynamic analytic solution of a semi-circular cylinder, subject to anti-plane point source loading in a vertical bound of an elastic quarter space, image method and wave function expansion method are employed to study steady state scattering of the semi-circular cylinder and interaction of bounds, then displacement and stress are determined in this quarter space. More specifically, firstly, the quarter space is extended as a half space, and the semi-circular cylinder is also extended as a circular cylinder. Then, displacement wave is constructed as series form of wave function and circular cylindrical bound is expanded as Fourier series to determine coefficients of wave function finally. Dynamic stress distributed around circular cylinder is calculated to show that scattering of the semi-circular cylinder is apparently to distinguish front and back, and relative low frequency of loading usually causes more dynamic stress around the semi-circular cylinder, and material parameters also have two widely divergent influences on the radial and circumferential dynamic stress distribution. This steady state solution is presented to enrich SH wave scattering theory and to formulate Green function method for SH wave scattering of bi-material interfacial circular cylinder with theoretical analysis. Numerical calculating examples demonstrate the related engineering problem for underground engineers, earthquake engineers, geotechnical engineers and civil engineers as well.