出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射
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摘要
采用复变函数法和Green函数法,求解出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射。首先,给出在含有半圆形凸起的圆柱形弹性夹杂的弹性半空间中,水平表面上任意一点承受时间谐和的出平面线源荷载作用时的位移函数,取该位移函数作为Green函数;然后,采用分区的思想,分别构造出夹杂内的驻波和夹杂外的散射波,满足"公共边界"处位移和应力的连续性条件,建立起求解该问题的无穷代数方程组;最后,给出了动应力集中系数和水平地面位移幅值的数值结果,并进行了讨论。
The scattering of out-plane line source load by a cylindrical elastic inclusion with a semi-cylindrical hill in half space is studied based on complex variable and Green’s function. Firstly, the Green’s function is set as the displacement field function when the elastic half space with a semi-cylindrical hill bears out-plane harmonic line source load on horizontal surface. Secondly, a standing wave in the inclusion and a scattering wave outside it are formulated separately. Finally, a series of infinite algebraic equations are derived by considering the continuous condition of the displacement and stress at the common boundary. In the examples, numerical results for dynamic stress concentration factor and ground motion amplitude of horizontal surface are presented and discussed.
The scattering of out-plane line source load by a cylindrical elastic inclusion with a semi-cylindrical hill in half space is studied based on complex variable and Green’s function. Firstly, the Green’s function is set as the displacement field function when the elastic half space with a semi-cylindrical hill bears out-plane harmonic line source load on horizontal surface. Secondly, a standing wave in the inclusion and a scattering wave outside it are formulated separately. Finally, a series of infinite algebraic equations are derived by considering the continuous condition of the displacement and stress at the common boundary. In the examples, numerical results for dynamic stress concentration factor and ground motion amplitude of horizontal surface are presented and discussed.
引文
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[4]Yuan Xiaoming,Men Fulu.Scattering of plane SH-waves by a semi-cylindrical hill[J].Earthquake Engineering and Structure Dynamics,1992,21(12):1091―1098.
[5]崔志刚,邹永超,刘殿魁.SH波对圆弧形凸起地形的散射[J].地震工程与工程振动,1998,18(4):8―14.Cui Zhigang,Zou Yongchao,Liu Diankui.Scattering of plane SH-wave by a cylindrical hill of circular-arc cross section[J].Earthquake Engineering and Engineering Vibration,1998,18(4):8―14.(in Chinese)
[6]Lee V W,Manoogian M E.Surface motion above an arbitrary shape underground cavity for incident SH wave[J].European Earthquake Engineering,1995,8(1):3―11.
[7]Lee V W,Chen S,Hsu I R.Antiplane diffraction from canyon above subsurface unlined tunnel[J].The American Society of Civil Engineers Journal of Engineering Mechanics Div,1999,125(2):668―674.
[8]林宏,史文谱,刘殿魁.SH波入射时浅埋结构的动力分析[J].哈尔滨工程大学学报,2001,22(3):83―87.Lin Hong,Shi Wenpu,Liu Diankui.Dynamic analysis of shallow filled structure with incident SH-wave[J].Journal of Harbin Engineering University,2001,22(3):83―87.(in Chinese)
[9]刘殿魁,王国庆.浅埋圆形孔洞附近的半圆形凸起对SH波的散射[J].力学学报,2006,38(2):209―218.Liu Diankui,Wang Guoqing.Antiplane SH-deformation of a semi-cylindrical hill above a subsurface cavity[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(2):209―218.(in chinese)
[10]黎在良,刘殿魁.固体中的波[M].北京:科学出版社,1995.Li Zailiang,Liu Diankui.Waves in solid[M].Beijing:Science Press,1995.(in Chinese)
[2]Liu Diankui,Han Feng.Scattering of plane SH-waves by cylindrical canyon of arbitrary shape in anisotropic media[J].Acta Mechanics Sinica,1990,6(3):256―260.
[3]Liu Diankui,Han Feng.Scattering of plane SH-waves by a cylindrical canyon of arbitrary shape[J].International Journal of Soil Dynamic and Earthquake Engineering,1991,10(5):249―255.
[4]Yuan Xiaoming,Men Fulu.Scattering of plane SH-waves by a semi-cylindrical hill[J].Earthquake Engineering and Structure Dynamics,1992,21(12):1091―1098.
[5]崔志刚,邹永超,刘殿魁.SH波对圆弧形凸起地形的散射[J].地震工程与工程振动,1998,18(4):8―14.Cui Zhigang,Zou Yongchao,Liu Diankui.Scattering of plane SH-wave by a cylindrical hill of circular-arc cross section[J].Earthquake Engineering and Engineering Vibration,1998,18(4):8―14.(in Chinese)
[6]Lee V W,Manoogian M E.Surface motion above an arbitrary shape underground cavity for incident SH wave[J].European Earthquake Engineering,1995,8(1):3―11.
[7]Lee V W,Chen S,Hsu I R.Antiplane diffraction from canyon above subsurface unlined tunnel[J].The American Society of Civil Engineers Journal of Engineering Mechanics Div,1999,125(2):668―674.
[8]林宏,史文谱,刘殿魁.SH波入射时浅埋结构的动力分析[J].哈尔滨工程大学学报,2001,22(3):83―87.Lin Hong,Shi Wenpu,Liu Diankui.Dynamic analysis of shallow filled structure with incident SH-wave[J].Journal of Harbin Engineering University,2001,22(3):83―87.(in Chinese)
[9]刘殿魁,王国庆.浅埋圆形孔洞附近的半圆形凸起对SH波的散射[J].力学学报,2006,38(2):209―218.Liu Diankui,Wang Guoqing.Antiplane SH-deformation of a semi-cylindrical hill above a subsurface cavity[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(2):209―218.(in chinese)
[10]黎在良,刘殿魁.固体中的波[M].北京:科学出版社,1995.Li Zailiang,Liu Diankui.Waves in solid[M].Beijing:Science Press,1995.(in Chinese)
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