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。
Abstract
The scattering problem of SH-wave by a circular lining and a semi-circular canyon in the bi-material half space is analyzed by the Green function method, mirror method and multi - level coordinate method to obtain the steady state response. The analytical expression of wave function which satisfies the stress free on the horizontal boundaries, displacement and stress continuity on the vertical boundaries is obtained by the image method. According to the continuity condition on the vertical boundary, the first kind of Fredholm integral equation is 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 is analyzed and compared with the existed literature through a numerical example.
关键词
半空间 /
圆形衬砌 /
半圆凹陷 /
Green函数 /
动应力集中系数（DSCF） /
动应力强度因子
{{custom_keyword}} /
Key words
half space /
circular lining /
semi-circular canyon /
Green function /
dynamic stress concentration factor (DSCF) /
dynamic stress intensity factor(DSIF)
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] QI Hui, YANG Jie, SHI Yong. Scattering of SH-wave by Cylindrical Inclusion near Interface in Bi-material Half-space [J].Journal of Mechanics, 2011, 27(1): 37-45.
[2] QI Hui, YANG Jie. Dynamic Analysis for Circular Inclusion of Arbitrary Positions near Interfacial Crack Impacted by SH-wave in Half-space[J]. European Journal of Mechanics /A Solids, 2012, 36: 18-24.
[3] 齐辉, 张根昌, 郭晶. SH波入射半空间双相介质界面附近圆形衬砌的动力分析[J]. 固体力学学报, 2013, 34(4): 426―432.
Qi Hui, Zhang Genchang, Guo Jing. Dynamic analysis of the scattering of SH waves by circular inclusion near bimaterial interface in half-space[J]. Journal of Solid Mechanics, 2013, 34(4): 426―432. (in Chinese)
[4] 齐辉, 赵嘉喜, 刘殿魁, 王慧文. SH 波对脱胶圆夹杂及其边缘直裂纹的散射[J]. 哈尔滨工程大学学报, 2007, 28(12): 1321―1325.
Qi Hui, Zhao Jiaxi, Liu Diankui, Wang Huiwen. SH waves by cylindrical inclusion and the edge of the horizontal cracks scattering [J]. Journal of Harbin Engineering University, 2007, 28(12): 1321―1325. (in Chinese)
[5] 韩峰，王光政，陈翰. SH波对多个凸起与凹陷相连地形的散射问题研究[J]. 应用数学和力学， 2013, 34(4): 355-363.
HAN Feng, WANG Guang-zheng, CHEN Han. Research on Scattering of SH Waves on Multiple Hills and Canyons[J]. Applied Mathematics and Mechanics, 2013, 34(4): 355-363(in Chinese).
[6] 许贻燕，韩峰. 平面SH波在相邻多个半圆形凹陷地形上的散射[J]. 地震工程与工程振动， 1992, 12(2): 12-18.
Xu Yiyan, HAN Feng. Scattering of SH Waves by multiple semi-cylindrical canyons[J]. Journal of Earthquake Engineering and Engineering Viberation, 1992, 12(2): 12-18. (in Chinese).
[7] 梁建文,丁美,杜金金. 柱面SH波在地下圆形衬砌洞室周围散射解析解[J]. 地震工程与工程振动,2013,33(1):1-7.
LIANG Jian-wen, DING Mei, DU Jin-jin. Diffraction of Cylindrical SH Waves Around Circular Lined Cavity: Analytical Solution[J].Journal of Earthquake Engineering and Engineering Vibration,2013,33(1):1-7(in Chinese).
[8]孙苗苗. 任意排列的空心管桩屏障对SH 波的多重散[J].
岩土力学, 2014, 35(4): 943－950.
SUN Miao-miao. Multiple scattering of SH waves by rows of arbitrarily arranged tubular piles[J]. Rock andSoil Mechanics, 2014, 35(4): 943－950.
[9] 刘殿魁, 许贻燕. 各项异性介质中SH波与多个半圆形凹陷地形的相互作用[J]. 力学学报, 1993, 25(1): 93―102.
Liu Diankui, Xu Yiyan. Interaction of multiple semi-cylindrical canyons by plane SH-waves in anisotropic media[J]. Chinese Journal of Theoretical and Applied Mechanics, 1993, 25(1): 93―102. (in Chinese)
[10] 林宏,刘殿魁. 半无限空间中圆形孔洞周围 SH 波的散射[J]. 地震工程与工程振动,2002, 22(2): 9-16.
Lin Hong,Liu Diankui. Scattering of SH-wave around a circular cavity in half space [J]. Journal of Earthquake Engineering and Engineering Viberation,2002, 22(2): 9-16. (in Chinese)
[11] 南景富，齐辉，折勇. 垂直半空间界面裂纹及附近圆孔对SH波的散射[J]. 工程力学, 2009, 26(5): 245―256.
NAN Jing-fu1 , QI Hui,SHE Yong1.Scattering of SH-WAVE by interface crack and neighbouring circular cavity in bi-materal vertical half-space[J]. Engineering mechanics, 2009, 26(5): 245―256. (in Chinese).
[12] 杨在林，许华南，黑宝平. 半空间椭圆夹杂与裂纹对 SH波的散射[J]. 振动与冲击，2013, 32(11): 56-61.
YANG Zai-lin, XU Hua-nan, HEI Bao-ping. Interaction of Elliptical and Crack Under Incident SH-Wave in a Half-space[J]. Journal of Vibration and Shock, 2013, 32(11): 56-61(in Chinese).
[13] NAZARET D,LEE V W,LIANG J W. Antiplane deformations around arbitrary-shaped canyons on a wedge-shape half space: moment method solutions [J]. Journal of Earthquake Engineering and Engineering Vibration,2003,2(2):281-287.
[14] Liu Diankui,HAN Feng Scattering of plane SH-Waves by cylindrical canyons of arbitrary shapes[J].IntH Soil Dyn and EarEng 1991,10(5):249-255
[15] 赵博,石永久,江洋，王元清，陈志华. 一种空间相关多点地震动合成的实用模拟方法[J]. 天津大学学报,2015,48(8):717-722.
Zhao Bo, Shi Yongjiu, Jiang Yang, Chen Zhihua. A Practical Simulation Method of Spatially Correlated Earthquake Ground Motions[J]. Journal of Tianjin University, 2015,48(8):717-722.(in Chinese).
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(1874 KB)
