二维地基波阻板隔振的复变函数解
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摘要
对二维弹性地基波阻板隔振体系进行了理论解析分析。借助弹性力学复变理论,建立了二维弹性地基中矩形波阻板对波场散射问题的控制方程;据波阻板与半空间交界面处的连续性条件,考虑平面SH波入射,运用波动函数展开法得到了二维地基波阻板隔振性能的解析解答;利用振幅衰减系数(有屏障时的振幅与无屏障时的振幅之比)的变化,分析了波阻板剪切模量、波阻板埋深、弹性波入射角度对隔振效果的影响。结果表明,随着波阻板剪切模量的增加隔振性能提升明显;对地表位移的隔振效果随着波阻板埋深的增加逐渐减小;弹性波的入射角度对隔振效果随着入射角度的减小而提高。
Theoretical analysis of a two-dimensional elastic foundation wave impeding block(WIB) seismic isolation system was conducted. First, based on the theory of elastic mechanics, the governing equation of the rectangular wave impeding block in the two-dimensional elastic foundation was established. Then, based on the incident of plane SH wave and the continuity condition between wave impeding block and half-space interface, the analytic solution of vibration isolation performance for the two-dimensional foundation wave impeding block was obtained by the wave function expansion method. In the end, according to the variation of amplitude attenuation coefficient, the influence of the shear modulus of wave impeding block, the depth of wave impeding block and the incident angle of elastic wave on the vibration isolation effect was analyzed. The results show that, the vibration isolation performance is improved obviously with the increase of shear modulus of wave impeding block; the vibration isolation effect for surface displacement increases gradually with the depth of wave impeding block; the smaller the incidence angle of elastic wave is, the more obvious the vibration isolation effect is.
Theoretical analysis of a two-dimensional elastic foundation wave impeding block(WIB) seismic isolation system was conducted. First, based on the theory of elastic mechanics, the governing equation of the rectangular wave impeding block in the two-dimensional elastic foundation was established. Then, based on the incident of plane SH wave and the continuity condition between wave impeding block and half-space interface, the analytic solution of vibration isolation performance for the two-dimensional foundation wave impeding block was obtained by the wave function expansion method. In the end, according to the variation of amplitude attenuation coefficient, the influence of the shear modulus of wave impeding block, the depth of wave impeding block and the incident angle of elastic wave on the vibration isolation effect was analyzed. The results show that, the vibration isolation performance is improved obviously with the increase of shear modulus of wave impeding block; the vibration isolation effect for surface displacement increases gradually with the depth of wave impeding block; the smaller the incidence angle of elastic wave is, the more obvious the vibration isolation effect is.
引文
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[3] 徐平.蜂窝状空腔屏障隔振效果分析[J].振动与冲击,2014,33(14):1-5.XU Ping.Analysis of vibration isolation effect of honeycomb-cell Barriers[J].Journal of Vibration and Shock,2014,33(14):1-5.
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[12] 高广运,陈功奇,张博.列车荷载下竖向非均匀地基波阻板主动隔振分析[J].振动与冲击,2013,32(22):57-62.GAO Guangyun,CHEN Gongqi,ZHANG bo.Active vibration isolation using WIB in non-uniform ground under Train Loadings[J].Journal of Vibration and Shock,2013,32(22):57-62.
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[15] 高贝贝.二维地基中储液多孔波阻板的隔振性能研究[D].兰州:兰州理工大学,2016.
[16] 周凤玺,马强,赖远明.含液饱和多孔波阻板的地基振动控制研究[J].振动与冲击,2016,35(1):96-105.ZHOU Fengxi,MA Qiang,LAI Yuanming.Ground vibration control with fluid saturated porous wave impeding blocks[J].Journal of Vibration and Shock,2016,35(1):96-105.
[17] 马强,周凤玺,刘杰.梯度波阻板的地基振动控制研究[J].力学学报,2017,49(6):1360-1369.MA Qiang,ZHOU Fengxi,LIU Jie.Analysis of ground vibration control by graded wave impeding block[J].Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1360-1369.
[18] 张海,杨国岗,刘中宪.弹性半空间中含直边界半圆形衬砌隧道对SH波的散射解析解[J].应用力学学报,2017,34(2):243-249.ZHANG Hai,YANG Guogang,LIU Zhongxian.An analytical solution to scattering of plane SH waves by a semi-circle lined tunnel in elastic half-space boundary [J].Chinese Journal of Applied Mechanics,2017,34(2):243-249.
[19] 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 Zailin,XU Huanan,HEI Baoping.Interaction of elliptical inclusion and crack under incident SH-wave in a half-space[J].Journal of Vibration and Shock,2013,32(11):56-61.
[20] 赵凯,刘长武,张国良.用弹性力学的复变函数法求解矩形硐室周边应力[J].采矿与安全工程学报,2007,24(3):361-365.ZHAO Kai,LIU Changwu,ZHANG Guoliang.Solution for perimeter stresses of rocks around a rectangular chamber using the complex function of elastic mechanics[J].Journal of Mining & Safety Engineering,2007,24(3):361-365.
[21] 陈志刚,刘殿魁.椭圆孔对SH波散射的远场解[J].哈尔滨工程大学学报,2003,24(3):334-338.CHEN Zhigang,LIU Diankui.Far field solution of SH-wave scattering by elliptic cavity[J].Journal of Harbin Engineering University,2003,24(3):334-338.
[22] 王贻荪.地面波动分析若干问题[J].建筑结构学报,1982,3(2):56-67.WANG Yisun.Some problems in the ground vibrarion analysis[J].Journal of Building Structures,1982,3(2):56-67.
[2] 李志毅,高广运,邱畅,等.多排桩屏障远场被动隔振分析[J].岩石力学与工程学报,2005,24(27):3990-3995.LI Zhiyi,GAO Guangyun,QIU Chang.Analysis of multi-row of piles as barries for isolation vibration in far field[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(27):3990-3995.
[3] 徐平.蜂窝状空腔屏障隔振效果分析[J].振动与冲击,2014,33(14):1-5.XU Ping.Analysis of vibration isolation effect of honeycomb-cell Barriers[J].Journal of Vibration and Shock,2014,33(14):1-5.
[4] 徐平.多排弹性空心管桩屏障对平面SV波的隔离[J].岩土工程学报,2011,33(3):392-397.XU Ping.Rows of elastic hollow pipe piles as isolation barriers for plane SV waves[J].Chinese Journal of Geotechnical Engineering,2011,33(3):392-397.
[5] 徐平.空沟对SH波隔离效果的理论解答[J].地下空间与工程学报,2015,11(3):647-651.XU Ping.Theoretical analysis of isolation effects of an open trench on incident SH waves[J].Chinese Journal of Underground Space and Engineering,2015,11(3):647-651.
[6] SCHMID G,CHOUW N,LE R.Shielding of structures from soil vibrations [C]//.Proceedings of Soil Dyn.and Earth.Eng.USA.San Francisco:Computational Mechanics Publications,1992:651-662.
[7] PEPLOW A T,JONES C J C,PETYT M.Surface vibration propagation over a layered elastic half-space with an inclusion[J].Applied Acoustics,1999,56(4):283-296.
[8] TAKEMIYA H,FUJIWARA A.Wave propagation/impediment in a stratum and wave impeding block(WIB)measured for SSI response reduction[J].Soil Dynamics and Earthquake Engineering,1994,13(1):49-61.
[9] TAKEMIYA H.Field vibration mitigation by honeycomb WIB for pile foundations of a high-speed train viaduct[J].Soil Dynamics and Earthquake Engineering,2004,24(1):69-87.
[10] 高广运,李伟.二维地基波阻板隔振分析[J].地震工程与工程振动,2005,25(2):130-135.GAO Guangyun,LI Wei.2-D analysis of ground vibration isolation using wave impeding block[J].Earthquake Engineering and Engineering Vibration,2005,24(2):130-135.
[11] 高广运,张博,李伟.层状和竖向非均匀地基中水平-摇摆耦合激振波阻板三维隔振分析[J].岩土力学,2012,33(2):349-353.GAO Guangyun,ZHANG bo,LI Wei.3D analysis of vibration isolation using wave impeding block in layered and vertical heterogeneous foundation under horizontal-rocking coupled excitation[J].Rock and Soil Mechanics,2012,33(2):349-353.
[12] 高广运,陈功奇,张博.列车荷载下竖向非均匀地基波阻板主动隔振分析[J].振动与冲击,2013,32(22):57-62.GAO Guangyun,CHEN Gongqi,ZHANG bo.Active vibration isolation using WIB in non-uniform ground under Train Loadings[J].Journal of Vibration and Shock,2013,32(22):57-62.
[13] 高广运,王非,陈功奇.轨道交通荷载下饱和地基中波阻板主动隔振研究[J].振动工程学报,2014,27(3):433-440.GAO Guangyun,WANG Fei,CHEN Gongqi.Active vibration isolation of the saturated ground with wave impedence block inside and under the load of the travelling train[J].Journal of Vibration Engineering,2014,27(3):433-440.
[14] 李宁,高广运,郑建国.水平激振下波阻板主动隔振试验与数值计算[J].地下空间与工程学报,20l0,6(1):90-95.LI Ning,GAO Guangyun,ZHENG Jiangguo.Field experimental and numerical study on active vibration isolation by WIB under horizontal loading[J].Chinese Journal of Underground Space and Engineering,2010,6(1):90-95.
[15] 高贝贝.二维地基中储液多孔波阻板的隔振性能研究[D].兰州:兰州理工大学,2016.
[16] 周凤玺,马强,赖远明.含液饱和多孔波阻板的地基振动控制研究[J].振动与冲击,2016,35(1):96-105.ZHOU Fengxi,MA Qiang,LAI Yuanming.Ground vibration control with fluid saturated porous wave impeding blocks[J].Journal of Vibration and Shock,2016,35(1):96-105.
[17] 马强,周凤玺,刘杰.梯度波阻板的地基振动控制研究[J].力学学报,2017,49(6):1360-1369.MA Qiang,ZHOU Fengxi,LIU Jie.Analysis of ground vibration control by graded wave impeding block[J].Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1360-1369.
[18] 张海,杨国岗,刘中宪.弹性半空间中含直边界半圆形衬砌隧道对SH波的散射解析解[J].应用力学学报,2017,34(2):243-249.ZHANG Hai,YANG Guogang,LIU Zhongxian.An analytical solution to scattering of plane SH waves by a semi-circle lined tunnel in elastic half-space boundary [J].Chinese Journal of Applied Mechanics,2017,34(2):243-249.
[19] 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 Zailin,XU Huanan,HEI Baoping.Interaction of elliptical inclusion and crack under incident SH-wave in a half-space[J].Journal of Vibration and Shock,2013,32(11):56-61.
[20] 赵凯,刘长武,张国良.用弹性力学的复变函数法求解矩形硐室周边应力[J].采矿与安全工程学报,2007,24(3):361-365.ZHAO Kai,LIU Changwu,ZHANG Guoliang.Solution for perimeter stresses of rocks around a rectangular chamber using the complex function of elastic mechanics[J].Journal of Mining & Safety Engineering,2007,24(3):361-365.
[21] 陈志刚,刘殿魁.椭圆孔对SH波散射的远场解[J].哈尔滨工程大学学报,2003,24(3):334-338.CHEN Zhigang,LIU Diankui.Far field solution of SH-wave scattering by elliptic cavity[J].Journal of Harbin Engineering University,2003,24(3):334-338.
[22] 王贻荪.地面波动分析若干问题[J].建筑结构学报,1982,3(2):56-67.WANG Yisun.Some problems in the ground vibrarion analysis[J].Journal of Building Structures,1982,3(2):56-67.