结构地震作用的基底激励模型及其适用性
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摘要
基于Rayleigh阻尼假设的一致激励和多点激励情形,对基底大质量法(LMM)和支座强迫位移法(DM)进行了算例分析,并与传统理论方法进行了比较,探讨了两种方法的计算精度、误差来源、适用条件及其原因。基于严格的理论推导分别提出了相应的修正措施并验证了有效性。结果表明:无阻尼或刚度比例阻尼情况下基底激励模型与传统理论方法符合精度高,完全等效;Rayleigh阻尼情形下,基底激励模型会带来不可忽略的误差,其大小与阻尼系数α密切相关,α越大误差越大,甚至可能导致错误的结果,此时,LMM不适用于多点激励分析,DM不适用于一致激励分析;基于LMM的多点激励分析应对输入的地震动加速度进行修正;基于DM的一致激励分析应对所输入的位移进行修正;LMM和DM适用性的不同缘于Rayleigh阻尼假设、一致激励和多点激励理论方法本身的差别;经过改进的LMM和DM误差很小且表现稳定,与传统理论方法有着高精度的一致。
Based on finite element models respectively subjected to uniform and non-uniform seismic excitations with Rayleigh damping assumption,numerical simulations are performed using base excitation models,which include the Large Mass Method(LMM) and Displacement Method(DM).The calculation precisions,error origins and applicability of the two methods are discussed.The improved measures are presented and validated through numerical simulations.It indicates that the results of base excitation models exactly accord with those of traditional analytical methodologies when no damping or only stiffness-proportional damping is considered.Rayleigh damping assumption leads to significant errors,which depend on the mass correlative damping coefficient α.The LMM isn′t applicable to non-uniform excitation analysis,especially when the damping coefficient α is a big value.Otherwise the DM isn′t applicable to uniform excitation analysis.The acceleration time histories should be modified in non-uniform excitation analysis when the LMM is adopted,and likewise the displacement time histories should be modified in uniform excitation analysis when the DM is used.The different applicability of LMM and DM derives from the Rayleigh damping assumption and the differences between the analytical methodologies of uniform excitation and non-uniform excitation.The improved LMM and DM can yield results that are identical to those of theoretical methods.
Based on finite element models respectively subjected to uniform and non-uniform seismic excitations with Rayleigh damping assumption,numerical simulations are performed using base excitation models,which include the Large Mass Method(LMM) and Displacement Method(DM).The calculation precisions,error origins and applicability of the two methods are discussed.The improved measures are presented and validated through numerical simulations.It indicates that the results of base excitation models exactly accord with those of traditional analytical methodologies when no damping or only stiffness-proportional damping is considered.Rayleigh damping assumption leads to significant errors,which depend on the mass correlative damping coefficient α.The LMM isn′t applicable to non-uniform excitation analysis,especially when the damping coefficient α is a big value.Otherwise the DM isn′t applicable to uniform excitation analysis.The acceleration time histories should be modified in non-uniform excitation analysis when the LMM is adopted,and likewise the displacement time histories should be modified in uniform excitation analysis when the DM is used.The different applicability of LMM and DM derives from the Rayleigh damping assumption and the differences between the analytical methodologies of uniform excitation and non-uniform excitation.The improved LMM and DM can yield results that are identical to those of theoretical methods.
引文
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[12]Yuji Tian,Qingshan Yang.On time-step in structuralseismic response analysis under ground displacement/acceleration[J].Earthquake Engineering andEngineering Vibration,2009,8(3):341-347.
[2]Leger P,Ide I M,Paultre P.Multiple support seismicanalysis of large structures[J].Computers&Structures,1990,36:1153-1158.
[3]Wilson E L.Three dimensional static and dynamicanalysis of structures:A physical approach withemphasis on earthquake engineering[M].Berkley,CA:Computers and Structures,Inc,2002.
[4]田玉基,杨庆山.地震地面运动作用下结构反应的分析模型[J].工程力学,2005,22(6):170-174.
[5]于海丰,张耀春.地震动输入方法研究[J].工程力学,2009,26(增刊1):1-6.
[6]黄小国,胡大琳,张后举.行波效应对大跨度连续刚构桥地震反应的影响[J].长安大学学报,2008,28(1):72-76.
[7]谢开仲,秦荣,林海瑛.大跨度CFST拱桥地震反应分析方法研究[J].武汉理工大学学报,2005,29(5):700-703.
[8]王田友,丁洁民,楼梦麟.地铁运行所致建筑物振动的传播规律的影响[J].土木工程学报,2009,42(5):33-39.
[9]杨庆山,刘文华,田玉基.国家体育场在多点激励作用下的地震反应分析[J].土木工程学报,2008,41(2):35-41.
[10]苏成,陈海斌.大跨度桥梁的地震反应[J].华南理工大学学报:自然科学版,2008,36(11):101-107.
[11]柳国环,李宏男,林海.结构地震响应计算模型的比较与分析[J].工程力学,2009,26(2):10-15.
[12]Yuji Tian,Qingshan Yang.On time-step in structuralseismic response analysis under ground displacement/acceleration[J].Earthquake Engineering andEngineering Vibration,2009,8(3):341-347.
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