成层场地地震反应分析中阻尼矩阵建模的讨论
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摘要
分别采用等效线性化频域法和有限元时域法对成层场地进行了地震反应分析,通过对比时域解和频率解,探讨了成层场地地震反应有限元时域分析中阻尼矩阵的建模方式对计算精度的影响。数值分析结果表明:整体Rayleigh比例阻尼矩阵不适合于各层土层阻尼不同的成层场地的阻尼矩阵建模,应该采用在单元级上建立Rayleigh比例阻尼矩阵,然后组成整体阻尼矩阵;确定单元Rayleigh阻尼矩阵的比例参数时,所有土层统一选取第二个频率ωn,对精确计算土层的加速度响应影响很大,对土层的位移响应影响有限;本文提出一种根据频域法计算得到的土层传递函数幅值谱进行分层选取ωn值确定单元Rayleigh阻尼矩阵比例系数的方法,该方法的时域解与频域解非常吻合。
The equivalent linearization frequency domain method and the finite element time domain method were used to analyze the seismic response of stratified ground. By comparing the results of two methods,the modeling of damping matrix in the finite element time history analysis of stratified ground was discussion. The results of the comparative analysis reveal that the whole Rayleigh damping was not appropriate for stratified ground consists of many soil layers with significantly different levels of damping. It was recommended that the element Rayleigh damping matrix was constructed firstly,and then assembled into the damping matrix for the complete ground. If the second frequency ωndetermining the coefficients of element Rayleigh damping selected the frequency of the same natural vibration mode,the calculation accuracy for the acceleration response of the soil layers was significantly affected,but displacement response limited. A modeling method to determine the coefficients of element Rayleigh damping was proposed that the ωnfor every soil layer was differently selected according the transfer function amplitude spectrum obtained in frequency domain method. The results of the method were perfectly consisted with the results of frequency method.
The equivalent linearization frequency domain method and the finite element time domain method were used to analyze the seismic response of stratified ground. By comparing the results of two methods,the modeling of damping matrix in the finite element time history analysis of stratified ground was discussion. The results of the comparative analysis reveal that the whole Rayleigh damping was not appropriate for stratified ground consists of many soil layers with significantly different levels of damping. It was recommended that the element Rayleigh damping matrix was constructed firstly,and then assembled into the damping matrix for the complete ground. If the second frequency ωndetermining the coefficients of element Rayleigh damping selected the frequency of the same natural vibration mode,the calculation accuracy for the acceleration response of the soil layers was significantly affected,but displacement response limited. A modeling method to determine the coefficients of element Rayleigh damping was proposed that the ωnfor every soil layer was differently selected according the transfer function amplitude spectrum obtained in frequency domain method. The results of the method were perfectly consisted with the results of frequency method.
引文
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[2]Anil K.Chopra.Dynamics of Structures:Theory and Applications to Earthquake Engineering:3rd edition[M].beijing:Tsinghua Press,2009.6:454-464.
[3]陈国兴.岩土地震工程学[M].北京:科学出版社,2007:255.CHEN Guoxing.Geotechnical Earthquake Engineering.Beijing:Science Press,2007:255.(in Chinese)
[4]谢定义.土动力学[M].北京:高等教育出版社,2011.5:409-412.XIE Dingyi.Soil Dynamics[M].Beijing:Higher Education Press,2011.5:409-412.(in Chinese)
[5]User's manual of SHAKE-2000:a computer program for the 1-D analysis of geotechnical earthquake engineering problems[Z].Geo Motions,2004.
[6]R.W.Clough,J.Penzien.Dynamics of Structures[M].New York:Mc-Graw Hill Inc.,1993.
[7]楼梦麟,邵新刚.土层地震反应显式计算中阻尼矩阵系数的选取[J].同济大学学报(自然科学版)2013,41(8):1126-1132.LOU Menglin,SHAO Xingang.Discussion on modeling issues of damping matrix in explicit calculations of soil layers seismic response[J].Journal of Tongji University,2013,41(8):1126-1132.(in Chinese)
[8]S.M,F M,Mh S,et al.Open system for earthquake engineering simulation:user command-language manual version 1.7.3[Z].Berkeley:Pacific earthquake Engineering Center.University of Califoenia,2006.
[9]Z Y,J L,A E.Open Sees soil models and solid-fluid fully coupled elements:user's manual,Version1[Z].San Diego:University of California,2008.
[10]Lysmer J,kuhlemeyer RL.Finite dynamic model for infinite media.J Engmech Div,ASCE 1969;95:859-77
[11]孙利民,张晨南,潘龙,等.桥梁桩土相互作用的集中质量模型及参数确定[J].同济大学学报,2002,30(4):409-415.SUN L M,ZHANG C N,PAN L,et al.Lumped-mass Model and Its Parameters for Dynamic Analysis of Bridge Pier-pile-soil system[J],Journal of Tongji University,2002,30(4):409-415.(in Chinese)
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