摘要
利用Green函数法、镜像法与多级坐标法,对半空间中半圆凹陷和圆形衬砌对SH波的散射进行分析,得到其稳态响应。利用镜像法得到了满足水平边界应力自由、垂直边界位移与应力连续的波函数解析表达式。根据垂直边界连续性条件,利用"裂纹切割法"和"契合法"建立起求解问题的第一类Fredholm型积分方程,得到了圆形衬砌周边的动应力集中系数与裂纹尖端动应力强度因子的解析表达式。数值算例分析了入射波数、衬砌深度、半圆凹陷大小、裂纹长度等对动应力集中系数、裂纹尖端动应力强度因子与地表位移的影响,并与已有文献进行比较。
The scattering problem of SH-wave by a circular lining and a semi-circular canyon in the bi-material half space was analyzed by the Green function method, the mirror method and the multi-level coordinate method to obtain the steady state response. The analytical expression of the wave function which satisfies the stress free on the horizontal boundaries, displacement and stress continuity on the vertical boundaries was obtained by the image method. According to the continuity condition on the vertical boundary, the first kind of Fredholm integral equation was set up to obtain analytical expression of dynamic stress concentration factor around the edge of circular lining and dynamic stress intensity factor at crack tip by “ the conjunction method” and “ the crack-division method” ？ The influence of the incident wave number, the ground depth of circular lining and the size of semi-circular canyon and the length of crack on the dynamic stress concentration factor, the dynamic stress intensity factor and the displacement along horizontal surface was analyzed and compared with the existed literature through a numerical example.
出处
《振动与冲击》
EI
CSCD
北大核心
2017年第20期137-145,共9页
Journal of Vibration and Shock
基金
黑龙江省自然科学基金资助项目(A201404)
