橡胶支座与柱串联体系的动力特性分析
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摘要
针对工程界比较关注的橡胶隔震支座与柱串联的隔震体系,研究了串联隔震体系横向振动的固有频率,探讨了轴向压力和不同隔震支座等效弯曲刚度对串联隔震系统固有频率的影响。考虑横截面转动和剪切变形以及轴向压力的影响,建立了串联隔震系统横向自由振动的数学模型;采用微分求积单元法(DQEM)对所得控制方程和边界条件进行离散处理,避免了繁琐的偏微分方程求解;数值求解固支—自由边界条件下串联隔震体系的横向固有频率,并得到该系统横向固有频率参数随压力变化的曲线。数值结果表明:轴向力的增加将显著降低串联隔震系统的低阶固有频率;在总高度一定的情况下,隔震支座尺寸的增大对串联隔震体系的力学特性也有显著的影响。
Aiming at a system of rubber bearings serially connected with columns,its natural frequencies were investigated,and the effects of axial load and different rubber bearings were discussed.Taking the effects of cross-section rotatry,shear distortion and compression axial force into account,the mathematical model for free vibration of the system was established.The differential quadrature method was employed for discretizing the governing equations and the boundary conditions.The natural frequencies of the system with clamped-free boundary conditions were solved numerically,and the curves of natural frequencies versus compression axial force were presented.It was shown that increase in axial force reduces the lower order natural frequencies significantly,and in cases of the unchanged total height,decrease in the equivalent bending stiffness of rubber bearings reduces the natural frequencies to a certain level.
Aiming at a system of rubber bearings serially connected with columns,its natural frequencies were investigated,and the effects of axial load and different rubber bearings were discussed.Taking the effects of cross-section rotatry,shear distortion and compression axial force into account,the mathematical model for free vibration of the system was established.The differential quadrature method was employed for discretizing the governing equations and the boundary conditions.The natural frequencies of the system with clamped-free boundary conditions were solved numerically,and the curves of natural frequencies versus compression axial force were presented.It was shown that increase in axial force reduces the lower order natural frequencies significantly,and in cases of the unchanged total height,decrease in the equivalent bending stiffness of rubber bearings reduces the natural frequencies to a certain level.
引文
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[13]周锡元,韩淼,曾徳民,等.叠层钢板橡胶垫的稳定性分析与强度验算[J].建筑科学,1997(6):13-19.ZHOU Xi-yuan,HAN Miao,ZENG De-min,et al.Stability analysis and strength checing of laminated rubber bearing[J].Building Science,1997(6):13-19.
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[16]刘金堂,杨晓东,闻邦椿.基于微分求积法的轴向运动板横向振动分析[J].振动与冲击,2009,28(3):178-181.LIU Ji-tang,YANG Xiao-dong,WEN Bang-chun.Transverse vibration of an axially moving plate based on differential quadrature method[J].Journal of Vibration and Shock,2009,28(3):178-181.
[17]李晶晶,胡育佳,程昌钧,等.粘弹性Timoshenko梁非线性动力学行为的微分求积分析[J].振动与冲击,2010,29(4):143-145.LI Jing-jing,HU Yu-jia,CHENG Chang-jun,et al.Differental Quadrature method for nonlinear dynamical Behavior of a viscoelastic timoshenko beam[J].Journal of Vibration and Shock,2010,29(4):143-145.
[2]Gent A N.Elastic stability of rubber compression springs[J].Journal of Engineering Mechanics,1964,6(4):318-326.
[3]Koh C G,Kelly J M.A simple mechanical model for electrometric bearings used in base isolation[J].Journal of Engineering Mechanics,1988,30(12):933-943.
[4]Ryan K L,Kelly J M,Chopra A K.Nonlinear model for lead-rubber bearings including axial-load effects[J].Journal of Engineering Mechanics,2005,131(12):1270-1278.
[5]Kelly J M.Tension buckling in multilayer elastomeric bearings[J].Journal of Engineering Mechanics,2003,129(12):1363-1368.
[6]Kelly J M.Earthquake resistant design with rubber[M].London:Spriger,2nd Ed.,1997.
[7]周锡元,韩淼,曾德民,等.橡胶支座与R/C柱串联隔震系统水平刚度系数[J].振动工程学报,1999,12(2):157-165.ZHOU Xi-yuan,HAN Miao,ZENG De-min,et al.Horizontal rigidity cofficient of the serial system of rubber bearing with column[J].Journal of Bibration Engineering,1999,12(2):157-165.
[8]周锡元,韩淼,曾德民,等.组合橡胶支座及橡胶支座与住串联系统的水平刚度计算方法[J].地震工程与工程振动,1999,19(4):67-75.ZHOU Xi-yuan,HAN Miao,ZENG De-min,et al.Calculatin method of lateral stiffness of combined rubber bearing and serial system of bearing with columns[J].Earthquake Engineering and Engineering Vibration,1999,19(4):67-75.
[9]马长飞,谭平,张亚辉,等.考虑P-△效应的柱顶隔震结构的动力响应分析[J].土木工程学报,2010,43:230-234.MA Chang-fei,TAN Ping,ZHANG Ya-hui,et al.Dynamic responses Anslysis of structures with isolators on the top of the columns considering P-△effects[J].China Civil Engineering Journal,2010,43:230-234.
[10]Wang X,Bert C W.A new approach in applying differential quadrature to static and free vibration analyses of beams and plates[J].J.Sound and Vibration,1993,162(3):566-572.
[11]Wang X W,Liu F,Wang X F,Gan L F.New approaches in application of differential quadra-ture method to fourth-order differential equations[J].Commun.Numer.Meth.Engng,2005,21:61-71.
[12]Liu G R,Wu T Y.Vibration analysis of beams using the generalized differential quadrature rule and domain decomposition[J].Journal of Sound and Vibration,2001,246(3):461-481.
[13]周锡元,韩淼,曾徳民,等.叠层钢板橡胶垫的稳定性分析与强度验算[J].建筑科学,1997(6):13-19.ZHOU Xi-yuan,HAN Miao,ZENG De-min,et al.Stability analysis and strength checing of laminated rubber bearing[J].Building Science,1997(6):13-19.
[14]唐家祥,刘再华.建筑结构基础隔震[M].武汉:华中理工大学出版社,1993.
[15]Imbimbo M,Kelly J M.Stability of isolators at large horizontal displacements[J].Earthquake Spectra,1997,13(3):415-430.
[16]刘金堂,杨晓东,闻邦椿.基于微分求积法的轴向运动板横向振动分析[J].振动与冲击,2009,28(3):178-181.LIU Ji-tang,YANG Xiao-dong,WEN Bang-chun.Transverse vibration of an axially moving plate based on differential quadrature method[J].Journal of Vibration and Shock,2009,28(3):178-181.
[17]李晶晶,胡育佳,程昌钧,等.粘弹性Timoshenko梁非线性动力学行为的微分求积分析[J].振动与冲击,2010,29(4):143-145.LI Jing-jing,HU Yu-jia,CHENG Chang-jun,et al.Differental Quadrature method for nonlinear dynamical Behavior of a viscoelastic timoshenko beam[J].Journal of Vibration and Shock,2010,29(4):143-145.
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