SH波对直角平面区域内圆形孔洞的散射与地震动
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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孔洞的散射与地震动问题。首先,利用复变函数法、多极坐标移动技术及叠加原理,构造了一个可以预先满足直角平面区域自由表面上应力自由边界条件的圆孔对SH波散射的波函数;其次,利用镜像法,将直角平面区域内的波场镜像于半无限空间,并得到了满足边界条件的总波场;最后,作为对抗暴抗震问题的研究,通过算例考虑了圆孔的动应力集中和地表的动位移.结果表明,圆孔的动应力集中和地表的位移幅值取决于入射波频率、角度和圆孔的位置。
Scattering of SH-wave with arbitrary incident angle by a circular cavity in right-angle plane is studied together with its influence on seismic ground motion. A scattering wave function, satisfying zero-stress condition on uncontrolled surfaces in right-angle plane, is constructed with the complex function method, the multi-polar coordinate transformation and the overlapping principle of SH-wave. Then the image method is used, and the problem in right-angle plane is transformed into the scattering of SH-wave in half-space, and the total wave field satisfying boundary condition can be obtained. The numerical examples reveal that the concentration of dynamic stress and ground motion depended on the different wave number, angles and geometrical locations of the circular cavity.
Scattering of SH-wave with arbitrary incident angle by a circular cavity in right-angle plane is studied together with its influence on seismic ground motion. A scattering wave function, satisfying zero-stress condition on uncontrolled surfaces in right-angle plane, is constructed with the complex function method, the multi-polar coordinate transformation and the overlapping principle of SH-wave. Then the image method is used, and the problem in right-angle plane is transformed into the scattering of SH-wave in half-space, and the total wave field satisfying boundary condition can be obtained. The numerical examples reveal that the concentration of dynamic stress and ground motion depended on the different wave number, angles and geometrical locations of the circular cavity.
引文
[1]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.
[2]姜艳,黄荣富,刘殿魁,等.SH波在浅埋多个圆孔处的散射与地震动[J].地震工程与工程振动,2004,24(1):7-14.
[3]田家勇,张国宏,王恩福.煤田采空区对地面地震动的影响[J].中国安全科学学报,2006,16(2):5-11.
[4]陈志刚,杨在林,刘殿魁.SH波冲击下浅埋任意形孔洞的动力分析[J].地震工程与工程振动,2004,24(4):32-36.
[5]陈志刚,刘殿魁.SH波在浅埋椭圆孔上的散射对地震动的影响[J].哈尔滨工程大学学报,2006,27(1):5-9.
[6]袁晓铭,地表下圆形夹杂区出平面散射对地面运动的影响[J].地球物理学报,1996,39(3):373-381.
[7]杨宇.含圆弧形沉积的楔形地形对平面SH波和P波的散射[D].天津:天津大学,2005.
[8]Achenbach J D.Wave Propagation in Elastic Solids[M].North Holland,Amesterdam,1973,164-198.
[9]Liu D K,Gai B Z,Tao G Y.Applications of the Method ofComplex Function to Dynamic Stress Concentration[J].Wavemotion,1982,(4):293-304.
[10]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[J].固体力学学报,2006,27(2):207-212.
[11]Shi Wenpu,Liu Diankui,Song Yongtao,et al.Scattering ofcircular cavity in right-angle plane space to steady SH-wave[J].Applied Mathematics and Mechanics,2006,27(12):1619-1626.
[12]Nazaret D,Lee V W,Liang J W.Antip lane deformations a-round arbitrary shaped canyons on a wedge-shape half space:moment method solution[J].Earthquake Engineering and En-gineering Vibration,2003,2(2):281-287.
[2]姜艳,黄荣富,刘殿魁,等.SH波在浅埋多个圆孔处的散射与地震动[J].地震工程与工程振动,2004,24(1):7-14.
[3]田家勇,张国宏,王恩福.煤田采空区对地面地震动的影响[J].中国安全科学学报,2006,16(2):5-11.
[4]陈志刚,杨在林,刘殿魁.SH波冲击下浅埋任意形孔洞的动力分析[J].地震工程与工程振动,2004,24(4):32-36.
[5]陈志刚,刘殿魁.SH波在浅埋椭圆孔上的散射对地震动的影响[J].哈尔滨工程大学学报,2006,27(1):5-9.
[6]袁晓铭,地表下圆形夹杂区出平面散射对地面运动的影响[J].地球物理学报,1996,39(3):373-381.
[7]杨宇.含圆弧形沉积的楔形地形对平面SH波和P波的散射[D].天津:天津大学,2005.
[8]Achenbach J D.Wave Propagation in Elastic Solids[M].North Holland,Amesterdam,1973,164-198.
[9]Liu D K,Gai B Z,Tao G Y.Applications of the Method ofComplex Function to Dynamic Stress Concentration[J].Wavemotion,1982,(4):293-304.
[10]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[J].固体力学学报,2006,27(2):207-212.
[11]Shi Wenpu,Liu Diankui,Song Yongtao,et al.Scattering ofcircular cavity in right-angle plane space to steady SH-wave[J].Applied Mathematics and Mechanics,2006,27(12):1619-1626.
[12]Nazaret D,Lee V W,Liang J W.Antip lane deformations a-round arbitrary shaped canyons on a wedge-shape half space:moment method solution[J].Earthquake Engineering and En-gineering Vibration,2003,2(2):281-287.
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