地震作用下刚体滑动位移的计算与比较——基于Coulomb摩擦模型
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摘要
首先对滑动干摩擦模型的研究现状进行了系统的论述。推导了基于Coulomb摩擦模型时刚体在简谐地面运动时滑动位移的解析方程;讨论了滑动状态与粘结状态过渡时刻的求解精度对刚体与地面相对位移的影响;对基于摩擦力-位移模型和基于Coulomb摩擦模型下刚体在简谐地面运动作用下滑动位移的差异进行了对比。然后采用Newmark线性加速度法推导了基于Coulomb摩擦模型刚体在任一地震加速度作用下滑动位移的数值求解方法;对比了基于摩擦力-位移模型和基于Coulomb摩擦模型下刚体在任一地面运动作用下滑动位移的差异。
Firstly,the current studying state of dry friction model was sumarrized.Based on Coulomb friction model,Sliding displacement of a rigid block under harmonic base excitation was deduced.The influence of solving accuracy of transition time from stick to slip on relative displacement between a rigid block and base was discussed.Difference of relative displacement based on Coulomb friction model and that based on the friction force-displacement one was compared.Then,based on Coulomb friction model,sliding displacement of a rigid block under any base excitation was deduced with Newmark linear acceleration method.Under El-centro earthquake,difference of relative displacement based on Coulomb friction model and that based on the friction force-displacement one was compared.
Firstly,the current studying state of dry friction model was sumarrized.Based on Coulomb friction model,Sliding displacement of a rigid block under harmonic base excitation was deduced.The influence of solving accuracy of transition time from stick to slip on relative displacement between a rigid block and base was discussed.Difference of relative displacement based on Coulomb friction model and that based on the friction force-displacement one was compared.Then,based on Coulomb friction model,sliding displacement of a rigid block under any base excitation was deduced with Newmark linear acceleration method.Under El-centro earthquake,difference of relative displacement based on Coulomb friction model and that based on the friction force-displacement one was compared.
引文
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[2]Wojewoda J,StefaDski A,Wiercigroch M,et al.Hystereticeffects of dry friction:modelling and experimental studies[J].Phil.Trans.R.Soc,2008,366:747-765.
[3]Mostaghel N,Davis T.Representations of Coulomb Frictionfor Dynamic Analysis[J].Earthquake Engineering andStructural Dynamics,1997,26:P541-548.
[4]Tariku F A,Rogers R J.Improved Dynamic Friction Modelsfor Simulation of One-Dimensional and Two-DimensionalStick-Slip Motion[J].Journal of Tribology,2001,123:661-669.
[5]Stein G J,Zahoransky R,Mucka P.On dry friction modellingand simulation in kinematically excited oscillatory systems[J].Journal of Sound and Vibration,2008,311:74-96.
[6]Do N B,Ferri A A.Efficient simulation of a Dynamic Systemwith LuGre Fricion[J].Journal of Computational andNonlinear Dynamics,2007,2:281-289.
[7]Dimova S,Meskouris K,Kratzig W.B.Numerical techniquefor dynamic analysis of structures with friction devices[J].Earthquake Engineering andStructural Dynamics,1995,24,881-898.
[8]ER G K,Iu V P.Stochastic Response of Base-excitedCoulomb Oscillator[J].Journal of Sound and vibration,2000,233(1):81-92.
[9]Levitan E S.Forced Oscillation of a Spring-Mass Systemhaving Combined Coulomb and Viscous Damping[J].theJournal of the Acoustical Society of America,1960,32(10):1265-1269.
[10]Konstantinidis D,Makris N.Experimental and AnalyticalStudies on the Seismic Response of Freestanding andAnchored Laboratory Equipment[R].PEER2005/07,2005.
[11]Vafai A,Hamidi M,Ahmadi G.Numerical Modelding ofMDOF Structures with Sliding Supports Using Rigid-PlasticLink[J].Earthquake Engineering and Structural Dynamics,2001,30:27-42.
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