复阻尼模型结构地震时程响应研究
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摘要
阻尼是结构动力分析的重要参数,对动力响应计算的结果有明显影响。目前,结构动力响应分析中的阻尼模型大都采用的是传统的Rayleigh阻尼模型,这种模型是为计算解耦而构造出的,其物理意义不是很明确。该文根据复阻尼系统理论,利用Newmark-β积分法,编制了Rayleigh阻尼和复阻尼模型的三维有限元程序。以三维钢框架结构为研究对象,计算了两种阻尼模型的结构地震时程响应和复阻尼模型的损耗因子,并讨论了不同加速度峰值和时间积分步长对复阻尼结构响应和损耗因子的影响。研究表明:在加速度峰值为2m/s2的El-Centro波作用下,两种阻尼模型的响应相差50%―100%,后者的结构动力响应远大于前者,损耗因子随应力或位移的增大而增大;复阻尼模型结构动力响应和损耗因子的稳定性和精度,与时间积分步长密切相关,不合适的时间积分步长将导致结果发散。
Damping is an important parameter in governing structural dynamic responses.Traditionally,the Rayleigh damping model,constructed for the convenience of computational decoupling,is used in structure dynamic analysis,but it has no clear physical meaning.Based on complex damping theory,the 3D FEM dynamic program is developed using newmark-β integration method,which can be used for solving Rayleigh damping model and complex damping model.The seismic time-history response and loss factor of a steel frame structure are obtained.Furtherly,this paper discusses the effects of peak acceleration and time integration size on time-history response and loss factor.With complex damping model,the structural response is 50%-100% larger than that with Rayleigh damping model under El-Centro earthquake excitation.It is also found 1) the loss factor increases with the stress or displacement development,2) using complex damping model,the precision of structure dynamic response is affected by time integration size,inappropriate time integration size may result in the divergence of results.
Damping is an important parameter in governing structural dynamic responses.Traditionally,the Rayleigh damping model,constructed for the convenience of computational decoupling,is used in structure dynamic analysis,but it has no clear physical meaning.Based on complex damping theory,the 3D FEM dynamic program is developed using newmark-β integration method,which can be used for solving Rayleigh damping model and complex damping model.The seismic time-history response and loss factor of a steel frame structure are obtained.Furtherly,this paper discusses the effects of peak acceleration and time integration size on time-history response and loss factor.With complex damping model,the structural response is 50%-100% larger than that with Rayleigh damping model under El-Centro earthquake excitation.It is also found 1) the loss factor increases with the stress or displacement development,2) using complex damping model,the precision of structure dynamic response is affected by time integration size,inappropriate time integration size may result in the divergence of results.
引文
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[7]朱敏,朱镜清.复阻尼地震反应谱计算的再研究[J].地震工程与工程振动,2001,21(2):36―40.Zhu Min,Zhu Jingqing.Futher studies on calcu-lation of complex damping seismic response spectra[J].Earthq-uake Engineering and Engineering Vibration,2001,21(2):36―40.(in Chinese)
[8]李鹏,王元丰.粘性阻尼与复阻尼对钢筋混凝土框架结构地震响应影响的分析[J].地震工程与工程振动,2007,27(3):54―57.Li Peng,Wang Yuanfeng.Analysis of seismic response of RC frames with viscous damping or complex damping[J].Earthquake Engineering and Engineering Vibration,2007,27(3):54―57.(in Chinese)
[9]Chen Yung-Hsiang,Tsaur Deng-How.Generalized com-plex damping and spectral integration[J].Journal of Engineering Mechanics,1991,117(5):986―1004.
[10]胡海岩.结构阻尼模型及系统时域响应[J].振动工程学报,1992,5(1):8―16.Hu Haiyan.Structural damping model and system dynamic response at time domain[J].Journal of Vibration Engineering,1992,5(1):8―16.(in Chinese)
[11]Lazan B J.Damping of material and members in struct-ural mechanics[M].London:Pergamon Press,1968.
[12]朱敏,朱镜清.逐步积分法求解复阻尼结构运动方程的稳定性问题[J].地震工程与工程振动,2001,21(4):59―69.Zhu Min,Zhu Jingqing.Studies on stability of step-by-step methods under complex damping conditions[J].Earthquake Engineering and Engineering Vibration,2001,21(4):59―69.(in Chinese)
[2]Weged R L,Walther.International dissipation in solids for small[J].Physics,1935,6:141―157.
[3]Soroka W W.Note on the relation between viscous and structural damping coeffieients[J].J.Aerom.Sci.,1949,16:409―410.
[4]Myklestad N O.The concept of complex damping[J].Journal of Applied Mechanics,1952,19(3):20―30.
[5]Gounaris G D,Anifantis N K.Structural damping deter-mination by finite element approach[J].Computers and Structures,1999,73:445―452.
[6]朱镜清,朱敏.复阻尼地震反应谱的计算方法及其它[J].地震工程与工程振动,2000,20(2):19―23.Zhu Jingqing,Zhu Min.Calculation of complex damping response spectra from earthquake records[J].Earthquake Engineering and Engineering Vibration,2000,20(2):19―23.(in Chinese)
[7]朱敏,朱镜清.复阻尼地震反应谱计算的再研究[J].地震工程与工程振动,2001,21(2):36―40.Zhu Min,Zhu Jingqing.Futher studies on calcu-lation of complex damping seismic response spectra[J].Earthq-uake Engineering and Engineering Vibration,2001,21(2):36―40.(in Chinese)
[8]李鹏,王元丰.粘性阻尼与复阻尼对钢筋混凝土框架结构地震响应影响的分析[J].地震工程与工程振动,2007,27(3):54―57.Li Peng,Wang Yuanfeng.Analysis of seismic response of RC frames with viscous damping or complex damping[J].Earthquake Engineering and Engineering Vibration,2007,27(3):54―57.(in Chinese)
[9]Chen Yung-Hsiang,Tsaur Deng-How.Generalized com-plex damping and spectral integration[J].Journal of Engineering Mechanics,1991,117(5):986―1004.
[10]胡海岩.结构阻尼模型及系统时域响应[J].振动工程学报,1992,5(1):8―16.Hu Haiyan.Structural damping model and system dynamic response at time domain[J].Journal of Vibration Engineering,1992,5(1):8―16.(in Chinese)
[11]Lazan B J.Damping of material and members in struct-ural mechanics[M].London:Pergamon Press,1968.
[12]朱敏,朱镜清.逐步积分法求解复阻尼结构运动方程的稳定性问题[J].地震工程与工程振动,2001,21(4):59―69.Zhu Min,Zhu Jingqing.Studies on stability of step-by-step methods under complex damping conditions[J].Earthquake Engineering and Engineering Vibration,2001,21(4):59―69.(in Chinese)
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