多点激励拟静力分量分离的响应矩阵法
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摘要
针对大质量法(LMM)无法直接求得多点激励下结构拟静力响应和动力响应的困境,以多点激励下结构的受力本质为切入点,提出一种在通用有限元程序中分离结构拟静力响应和动力响应的通用方法——响应矩阵法;详细推导响应矩阵的构造过程;并以两个自由度的质量-弹簧模型为例,利用响应矩阵将LMM求得的总响应分解为拟静力响应和动力响应,分别与相对运动法(RMM)直接求得的拟静力响应和动力响应进行对比。结果表明:响应矩阵法具有较高的分离精度,它建立起了线性系统支撑位移与体系内部拟静力项之间的线性传递关系,完善了结构的多点激励分析理论。
This paper,aiming at the problem which relative static response and dynamic response couldn't be directly obtained by the Large Mass Method( LMM) under multi-support excitation,a common method( response matrix method) to separate relative static response and dynamic response in the general finite element program was proposed and deduced in detail. A 2-DOF Mass-spring model was taken as an example,and the total response from LMM was separated relative static response and dynamic response by response matrix method,compared with the corresponding response by Relative Motion Method( RMM) respectively. The result shows that the response matrix method have extremely high separation precision,establish a linear transfer relation from support displacement to relative static response,and improve on the analysis theory of structure under multi-support excitation.
This paper,aiming at the problem which relative static response and dynamic response couldn't be directly obtained by the Large Mass Method( LMM) under multi-support excitation,a common method( response matrix method) to separate relative static response and dynamic response in the general finite element program was proposed and deduced in detail. A 2-DOF Mass-spring model was taken as an example,and the total response from LMM was separated relative static response and dynamic response by response matrix method,compared with the corresponding response by Relative Motion Method( RMM) respectively. The result shows that the response matrix method have extremely high separation precision,establish a linear transfer relation from support displacement to relative static response,and improve on the analysis theory of structure under multi-support excitation.
引文
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[2]Dendrou B,Werner S,Toridis T.Three-dimensional response of a concrete bridge system to traveling seismic waves[J].Computers and Structures,1985,20(1/2/3):593-603
[3]刘洪兵,范立础.大跨桥梁考虑地形及多点激励的地震响应分析[J].同济大学学报:自然科学版,2003,31(6):641-646(Liu Hongbin,Fan Lichu.Seismic analysis of long span bridges considering topographic effects and multi-supported excitations[J].Journal of Tongji University:Natural Science Edition,2003,31(6):641-646(in Chinese))
[4]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(Yang Qingshan,Liu Wenhua,Tian Yuji.Response analysis of national stadium under specially variable earthquake ground motions[J].China Civil Engineering Journal,2008,41(2):35-41(in Chinese))
[5]周国良,鲍叶欣,李小军,等.结构动力分析中多点激励问题的研究综述[J].世界地震工程,2009(4):25-32(Zhou Guoliang,Bao Yexin,Li Xiaojun,et al.Review on dynamic analyses of structures under multi-support excitation[J].World Earthquake Engineering,2009(4):25-32(in Chinese))
[6]Leger P,Ide I M,Paultre P.Multiple support seismic analysis of large structures[J].Computers and Structures,1990,36(6):1153-1158
[7]于海丰,张耀春.地震动输入方法研究[J].工程力学,2009,26(增1):1-6,19(Yu Haifeng,Zhang Yaochun.Discussion on earthquake input method[J].Engineering Mechanics,2009,26(S1):1-6,19(in Chinese))
[8]Clough R W,Penzien J.Dynamics of structures[M].second edition.McGraw-Hill,1993
[9]胡聿贤.地震工程学[M].第2版.北京:地震出版社,2006
[10]周国良,李小军,刘必灯,等.大刚度法在结构动力分析中的应用、误差分析与改进[J].工程力学,2011,28(8):30-36(Zhou Guoliang,Li Xiaojun,Liu Bideng,et al.Error analysis and improvements of large spring/stiffness method for structural dynamic response analysis[J].Engineering Mechanics,2011,28(8):30-36(in Chinese))
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