弹性直角域中半圆形凹陷的SH波散射的稳态解

Steady State Solution of SH Wave Scattering of a Semi-Circular Cylindrical Canyon in an Elastic Quarter Space

按照波函数展开法和镜像方法,分析了直角域中半圆形凹陷对平面SH波的弹性动力学反平面稳态响应,得到了弹性波的位移场和应力场的具体形式.根据Hankel函数在宗量零点的渐近性讨论了波函数级数的收敛性;根据Hankel函数在宗量无穷远点的渐近性和Graf加法公式构造了圆柱散射波的远场位移模式.数值算例分别计算了代表计算误差的凹陷边沿的径向动应力集中因子、周向动应力集中因子和平面波应力场的动应力集中因子以及凹陷散射波的远场位移模式.结果表明,直角域中凹陷与竖直边界的距离很大程度地影响着SH波散射的稳态解.

Steady state response of elastodynamics anti-plane for a semi-circular cylindrical canyon in a quarter space subjected by plane SH wave is analyzed to obtain specific forms of displacement and stress fields by adopting the wave function expansion method and the image method. The convergence of wave function series is discussed through asymptotic behavior of Hankel function at zero. The far field displacement mode of cylindrical scattering wave is for- mulated through asymptotic behavior of Hankel function at infinity and Graf addition formula. Numerical examples are calculated to present radial dynamic stress concentrations factor around the canyon which denotes computational error, circumferential dynamic stress concentrations factor, dynamic stress concentrations factor of plane SH wave around the canyon, and far field displacement mode of the canyon scattering wave. Results indicate that the distance between canyon and vertical bound of quarter space has a great effect on steady state solution of SH wave scattering.