SH波对直角平面区域内圆形衬砌的散射与地震动
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摘要
研究了以任意方向入射的平面SH波对直角平面区域内圆形衬砌的散射与地震动问题.利用复变函数法、多极坐标移动技术及镜像法,将直角平面区域内的波场延拓于半无限空间,根据边界条件将该问题的解答可归结为对一组无穷代数方程组的求解问题,通过算例考虑衬砌的动应力集中和地表位移.结果表明,衬砌的动应力集中和地表位移幅值取决于入射波频率、角度、衬砌的位置和厚度比.
The scattering of SH-wave with arbitrary incident angle by a circular lining in a right-angle plane is studied together with its influence on the seismic ground motion.The problem in a right-angle plane is transformed into the scattering of SH-wave in half-space by using the complex function method,the multi-polar coordinate transformation and the image method.According to the boundary conditions,the solution of the problem can be reduced to a series of algebraic equations.The numerical examples show that the concentration of the dynamic stress and the ground motion are related with the different wave numbers,the angle,the geometrical location and the thickness of the circular cavity.
The scattering of SH-wave with arbitrary incident angle by a circular lining in a right-angle plane is studied together with its influence on the seismic ground motion.The problem in a right-angle plane is transformed into the scattering of SH-wave in half-space by using the complex function method,the multi-polar coordinate transformation and the image method.According to the boundary conditions,the solution of the problem can be reduced to a series of algebraic equations.The numerical examples show that the concentration of the dynamic stress and the ground motion are related with the different wave numbers,the angle,the geometrical location and the thickness of the circular cavity.
引文
1 Pao Y-H.Applied mechanics in science and engineering.Applied Mechanics Review,1998,51(2):141-153
2 Liu DK,Gai BZ,Tao GY.Applications of the method ofcomplex function to dynamic stress concentration.WaveMotion,1982(4):293-304.
3折勇,齐辉,杨在林.SH波对直角平面区域内圆形孔洞的散射与地震动.应用力学学报,2008,25(3):392-397(Shi Yong,QiHui,Yang Zailin.Scattering of SH-wave by circular cavityin right-angle plane and seismic ground motion.ChineseJournal of Applied Mechanics,2008,25(3):392-397(inChinese))
4林宏,刘殿魁.半无限空间中圆形衬砌周围SH波的散射.地震工程与工程振动,2002,22(2):9-16(Lin Hong,Liu Diankui.Scatte ring of SH-wave around a circular cavity in haflfspace.Journal of Earthquake Engineering and Engineer-ing Vibration,2002,22(2):9-16(in Chinese))
5史文谱,刘殿魁,宋永涛.直角平面区域内固定圆形刚性夹杂问题的Green函数解.固体力学学报,2006,27(2):207-212(Shi Wenpu,Liu Diankui,Song Yongtao.The anti planegreen function solution of the problem of a fixed rigid cir-cular inclusion in right-angle plane.Acta Mechanica SolidaSinica,2006,27(2):207-212(in Chinese))
6 Shi WP,Liu DK,Song YT,et al.Scattering of circular cav-ity in right-angle plane space to steady SH-wave.AppliedMathematics and Mechanics,2006,27(12):1619-1626
7史文谱,褚京莲,李禄昌等.直角平面角点衬砌对稳态平面SH波的散射.力学与实践,2006,28(5):34-38(Shi Wenpu,ChuJinglian,Li Luchang,et al.Scattering of steady incidentsh-wave by circular arc lining at the corner point of rectan-gular plane.Mechanics in Engineering,2006,28(5):34-38(in Chinese))
8赵嘉喜,齐辉.界面脱胶圆夹杂对SH波散射的远场解析解.力学与实践,2009,31(1):47-51(Zhao Jiaxi,Qi Hui.Far fieldsolution of sh-wave scattered by an interface cylindrical in-clusion with disconnected curve.Mechanics in Engineer-ing,2009,31(1):47-51(in Chinese))
9姜艳,黄荣富,刘殿魁等.SH波在浅埋多个衬砌处的散射与地震动.地震工程与工程振动,2004,24(1):7-14(Jiang Yan,Huang Rongfu,Liu Diankui,et al.Scattering of SH-waveby shallow fill multiple circular cavities and the ground mo-tion.Journal of Earthquake Engineering and EngineeringVibration,2004,24(1):7-14(in Chinese))
2 Liu DK,Gai BZ,Tao GY.Applications of the method ofcomplex function to dynamic stress concentration.WaveMotion,1982(4):293-304.
3折勇,齐辉,杨在林.SH波对直角平面区域内圆形孔洞的散射与地震动.应用力学学报,2008,25(3):392-397(Shi Yong,QiHui,Yang Zailin.Scattering of SH-wave by circular cavityin right-angle plane and seismic ground motion.ChineseJournal of Applied Mechanics,2008,25(3):392-397(inChinese))
4林宏,刘殿魁.半无限空间中圆形衬砌周围SH波的散射.地震工程与工程振动,2002,22(2):9-16(Lin Hong,Liu Diankui.Scatte ring of SH-wave around a circular cavity in haflfspace.Journal of Earthquake Engineering and Engineer-ing Vibration,2002,22(2):9-16(in Chinese))
5史文谱,刘殿魁,宋永涛.直角平面区域内固定圆形刚性夹杂问题的Green函数解.固体力学学报,2006,27(2):207-212(Shi Wenpu,Liu Diankui,Song Yongtao.The anti planegreen function solution of the problem of a fixed rigid cir-cular inclusion in right-angle plane.Acta Mechanica SolidaSinica,2006,27(2):207-212(in Chinese))
6 Shi WP,Liu DK,Song YT,et al.Scattering of circular cav-ity in right-angle plane space to steady SH-wave.AppliedMathematics and Mechanics,2006,27(12):1619-1626
7史文谱,褚京莲,李禄昌等.直角平面角点衬砌对稳态平面SH波的散射.力学与实践,2006,28(5):34-38(Shi Wenpu,ChuJinglian,Li Luchang,et al.Scattering of steady incidentsh-wave by circular arc lining at the corner point of rectan-gular plane.Mechanics in Engineering,2006,28(5):34-38(in Chinese))
8赵嘉喜,齐辉.界面脱胶圆夹杂对SH波散射的远场解析解.力学与实践,2009,31(1):47-51(Zhao Jiaxi,Qi Hui.Far fieldsolution of sh-wave scattered by an interface cylindrical in-clusion with disconnected curve.Mechanics in Engineer-ing,2009,31(1):47-51(in Chinese))
9姜艳,黄荣富,刘殿魁等.SH波在浅埋多个衬砌处的散射与地震动.地震工程与工程振动,2004,24(1):7-14(Jiang Yan,Huang Rongfu,Liu Diankui,et al.Scattering of SH-waveby shallow fill multiple circular cavities and the ground mo-tion.Journal of Earthquake Engineering and EngineeringVibration,2004,24(1):7-14(in Chinese))
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