出平面线源载荷对浅埋弹性圆柱散射与地震动
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摘要
为研究半空间内圆柱与裂纹同时存在时复合缺陷的动力学响应,采用复变函数、多极坐标方法,求解了与时间谐和的出平面线源荷载对含有弹性圆柱的半空间散射问题,给出了弹性圆柱周边的动应力集中与地表位移的数值结果.采用"分区"的方法,分别构造出含有弹性圆柱半空间内的散射波和弹性圆柱体内驻波的表达式,应用位移与应力边界条件求解出表达式中的未知数,确定散射波和驻波;从而给出含有弹性圆柱半空间的位移场与应力场.通过数值算例,讨论了各种参数对弹性圆柱周边的动应力集中系数与地表位移的影响规律.结果表明,线源荷载埋深大于60时,对地表位移就没有影响了.
In order to investigate the dynamic response of a composite flaw with both crack and a column in a half space,complex function and multi-polar coordinate methods were employed to study the scattering problem in elastic half space containing an elastic column being subjected to an out-of-plane time harmonic line source load.Numerical results for dynamic stress concentration and ground motion around the elastic column were given.The scattering waves caused by the elastic column in half space and its standing wave were constructed based on the "sub-area" method.The unknowns were evaluated according to boundary conditions of both displacement and stress,the scattering waves and the standing waves were then determined;as a result the displacement field and the stress field were established.Finally,numerical examples were given.The influences of different parameters on dynamic stress concentration factors and ground motion were discussed.It was found that when the depth of the line source load is greater than 60,the line source load will have little effect on the surface displacement.
In order to investigate the dynamic response of a composite flaw with both crack and a column in a half space,complex function and multi-polar coordinate methods were employed to study the scattering problem in elastic half space containing an elastic column being subjected to an out-of-plane time harmonic line source load.Numerical results for dynamic stress concentration and ground motion around the elastic column were given.The scattering waves caused by the elastic column in half space and its standing wave were constructed based on the "sub-area" method.The unknowns were evaluated according to boundary conditions of both displacement and stress,the scattering waves and the standing waves were then determined;as a result the displacement field and the stress field were established.Finally,numerical examples were given.The influences of different parameters on dynamic stress concentration factors and ground motion were discussed.It was found that when the depth of the line source load is greater than 60,the line source load will have little effect on the surface displacement.
引文
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[5]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 acircular cavity in half space[J].Earthquake Engineeringand Engineering Vibration,2002,22(2):9-16.
[6]YANG Zailin,LIU Dankui.Scattering far field solution ofSH-wave by movable rigid cylindrical interface[J].ActaMechanica Solida Sinica,2002,15(3):214-220.
[7]LIU Diankui,SHI Shouxia.The scattering of plane SH-wave by circular interface cavity with lining[J].Acta Me-chanica Sinica,2002,34(5):796-802.
[8]刘殿魁,林宏.浅埋的圆形孔洞对SH波散射与地震动[J].爆炸与冲击,2003,23(1):6-12.LIU Diankui,LIN Hong.Scattering of SH-waves by ashallow buried cylindrical cavity and the ground motion[J].Explosion and Shock Waves,2003,23(1):6-12.
[9]梁昆淼.数学物理方法[M].3版.北京:高等教育出版社,1998:374.
[2]PAO Y H.Elastic wave in solids[J].ASME Trans J Ap-pl Mech,1983,50(4):1152-1164.
[3]黎在良,刘殿魁.固体中的波[M].北京:科学出版社,1995.
[4]刘殿魁,刘宏伟.SH波散射与界面圆孔附近的动应力集中[J].力学学报,1998,30(5):597-604.LIU Diankui,LIU Hongwei.Scattering and dynamicstress concentration of SH-wave by interface circular hole[J].ACTA Mechanica Sinica,1998,30(5):597-604.
[5]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 acircular cavity in half space[J].Earthquake Engineeringand Engineering Vibration,2002,22(2):9-16.
[6]YANG Zailin,LIU Dankui.Scattering far field solution ofSH-wave by movable rigid cylindrical interface[J].ActaMechanica Solida Sinica,2002,15(3):214-220.
[7]LIU Diankui,SHI Shouxia.The scattering of plane SH-wave by circular interface cavity with lining[J].Acta Me-chanica Sinica,2002,34(5):796-802.
[8]刘殿魁,林宏.浅埋的圆形孔洞对SH波散射与地震动[J].爆炸与冲击,2003,23(1):6-12.LIU Diankui,LIN Hong.Scattering of SH-waves by ashallow buried cylindrical cavity and the ground motion[J].Explosion and Shock Waves,2003,23(1):6-12.
[9]梁昆淼.数学物理方法[M].3版.北京:高等教育出版社,1998:374.
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