改进的Kelvin碰撞分析模型
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摘要
在强烈地震作用下紧密相邻的结构将会发生碰撞从而导致结构部件或者整体结构的严重破坏。由于结构碰撞是一复杂的非线性问题,为了研究碰撞作用下结构的响应,使用合理的碰撞分析模型是十分有必要的。该文首先对文献中已有的碰撞分析方法或模型进行了介绍,讨论了它们之间的不足。然后针对Kelvin模型的不足提出了改进,并对改进的Kelvin模型中的阻尼常数确定进行了理论推导。最后通过数值试验证明改进的Kelvin模型及其参数确定的理论假设和推导是正确合理的,能够在实际的工程结构碰撞分析中获得可靠的结果。
The earthquake-induced pounding between closely spaced structures can lead to structural damage.Because a structural pounding is a complicated nonlinear problem,in order to investigate the response of structures involving the pounding,it is important to select a reasonable impact analytical model in the pounding analysis.In this paper,the review for impact analytical models and methods for structural poundings is firstly performed.And then,an improvement on the Kelvin model is proposed to remedy the drawbacks of the Kelvin model;the determination of the relevant parameter in this modified Kelvin model is theoretically derived.Finally,through a numerical experiment,the correctness of the modified Kelvin model is verified,and reliable results can be obtained by using the modified Kelvin model in the analysis of structural poundings.
The earthquake-induced pounding between closely spaced structures can lead to structural damage.Because a structural pounding is a complicated nonlinear problem,in order to investigate the response of structures involving the pounding,it is important to select a reasonable impact analytical model in the pounding analysis.In this paper,the review for impact analytical models and methods for structural poundings is firstly performed.And then,an improvement on the Kelvin model is proposed to remedy the drawbacks of the Kelvin model;the determination of the relevant parameter in this modified Kelvin model is theoretically derived.Finally,through a numerical experiment,the correctness of the modified Kelvin model is verified,and reliable results can be obtained by using the modified Kelvin model in the analysis of structural poundings.
引文
[1]Anagnostopoulos S A.Pounding of buildings in series during earthquakes[J].Earthquake Engineering and Structural Dynamics,1988,16(3):443―456.
[2]Davis R O.Pounding of buildings modelled by an impact oscillator[J].Earthquake Engineering&Structural Dynamics,1992,21(3):253―274.
[3]Papadrakakis M,Mouzakis H P,Alevridis A S.Three dimensional non-linear analysis of building pounding during earthquakes[C].Proceedings of the19961st International Conference on Earthquake Resistant Engineering Structures,ERES96,Thessaloniki,Greece,Computational Mechanics Publ,Southampton,Engl,1996.
[4]Kasai Kazuhiko,Maison Bruce F.Building pounding damage during the1989Loma Prieta earthquake[J].Engineering Structures,1997,19(3):195―207.
[5]李忠献,岳福清.城市桥梁地震碰撞反应研究与发展[J].地震工程与工程振动,2005,25(4):91―98.Li Zhongxian,Yue Fuqing.State of arts of study on the seismic pounding of urban bridges[J].Earthquake Engineering and Engineering Vibration,2005,25(4):91―98.(in Chinese)
[6]Goldsmith W.Impact:The theory and physical behaviour of colliding solids[M].London,England:Edward Arnold,1960.
[7]Jankowski R.Non-linear viscoelastic modelling of earthquake-induced structural pounding[J].Earthquake Engineering and Structural Dynamics,2005,34(6):595―611.
[8]Jankowski R.Analytical expression between the impact damping ratio and the coefficient of restitution in the non-linear viscoelastic model of structural pounding[J].Earthquake Engineering and Structural Dynamics,2006,35(4):517―524.
[9]Lankarani H M,Nikravesh P E.Contact force model with hysteresis damping for impact analysis of multibody systems[J].Journal of Mechanisms,Transmissions,and Automation in Design,1990,112(3):369―376.
[10]Muthukumar S,DesRoches R.A Hertz contact model with non-linear damping for pounding simulation[J].Earthquake Engineering and Structural Dynamics,2006,35(7):811―828.
[11]Malhotra Praveen K.Dynamics of seismic pounding at expansion joints of concrete bridges[J].Journal of Engineering Mechanics,1998,124(7):794―802.
[2]Davis R O.Pounding of buildings modelled by an impact oscillator[J].Earthquake Engineering&Structural Dynamics,1992,21(3):253―274.
[3]Papadrakakis M,Mouzakis H P,Alevridis A S.Three dimensional non-linear analysis of building pounding during earthquakes[C].Proceedings of the19961st International Conference on Earthquake Resistant Engineering Structures,ERES96,Thessaloniki,Greece,Computational Mechanics Publ,Southampton,Engl,1996.
[4]Kasai Kazuhiko,Maison Bruce F.Building pounding damage during the1989Loma Prieta earthquake[J].Engineering Structures,1997,19(3):195―207.
[5]李忠献,岳福清.城市桥梁地震碰撞反应研究与发展[J].地震工程与工程振动,2005,25(4):91―98.Li Zhongxian,Yue Fuqing.State of arts of study on the seismic pounding of urban bridges[J].Earthquake Engineering and Engineering Vibration,2005,25(4):91―98.(in Chinese)
[6]Goldsmith W.Impact:The theory and physical behaviour of colliding solids[M].London,England:Edward Arnold,1960.
[7]Jankowski R.Non-linear viscoelastic modelling of earthquake-induced structural pounding[J].Earthquake Engineering and Structural Dynamics,2005,34(6):595―611.
[8]Jankowski R.Analytical expression between the impact damping ratio and the coefficient of restitution in the non-linear viscoelastic model of structural pounding[J].Earthquake Engineering and Structural Dynamics,2006,35(4):517―524.
[9]Lankarani H M,Nikravesh P E.Contact force model with hysteresis damping for impact analysis of multibody systems[J].Journal of Mechanisms,Transmissions,and Automation in Design,1990,112(3):369―376.
[10]Muthukumar S,DesRoches R.A Hertz contact model with non-linear damping for pounding simulation[J].Earthquake Engineering and Structural Dynamics,2006,35(7):811―828.
[11]Malhotra Praveen K.Dynamics of seismic pounding at expansion joints of concrete bridges[J].Journal of Engineering Mechanics,1998,124(7):794―802.
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