多点激励下绝对位移直接求解算法的误差频域分析
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摘要
多点激励地震响应分析时,相对运动法将结构内部节点绝对位移分解成拟静位移和动态位移两部分分别进行求解,而绝对位移直接求解法直接对内部节点绝对位移进行求解,在两种求解算法中,阻尼分别假定与内部结点相对速度、绝对速度成比例。两种算法的阻尼假定不同可能会引起计算结果误差,在瑞利阻尼、单元阻尼模型下,采用随机振动方法对两种算法计算结果误差在频域内进行了理论分析,指出了瑞利阻尼模型下两种算法得出的动态内力功率谱误差由质量阻尼产生,主要受结构阻尼比大小、激励频率与结构基频率比值影响,但刚度阻尼不产生误差。单元阻尼模型下,由于单元阻尼力由单元两节点之间的速度差产生,无论采用绝对位移还是相对位移,单元两节点间的速度差是相等的,故单元阻尼模型下,两种算法计算结果不存在误差。
Under multi-support earthquake excitations,nodal displacements were decomposed into pseudo-static and dynamic parts,respectively with the relative motion method,while the nodal displacements were solved directly with the absolute displacement solving method.The damping was proportional to the relative velocity in relative motion method,but the damping was proportional to the absolute velocity in the method of directly solving absolute displacement.The different damping assumptions may cause calculation errors on structural responses.The theoretical analysis based on random vibration showed that the structural response power spectral density errors obtained with the two solving methods are caused by mass damping,and affected by damping ratio and the ratio between excitation frequency and fundamental frequency of the structures with Rayleigh damping.The damping forces are determined by the nodal velocity difference with element damping model,and the nodal velocity difference are equal in the two solving method,so the calculation errors don't exist using element damping model.
Under multi-support earthquake excitations,nodal displacements were decomposed into pseudo-static and dynamic parts,respectively with the relative motion method,while the nodal displacements were solved directly with the absolute displacement solving method.The damping was proportional to the relative velocity in relative motion method,but the damping was proportional to the absolute velocity in the method of directly solving absolute displacement.The different damping assumptions may cause calculation errors on structural responses.The theoretical analysis based on random vibration showed that the structural response power spectral density errors obtained with the two solving methods are caused by mass damping,and affected by damping ratio and the ratio between excitation frequency and fundamental frequency of the structures with Rayleigh damping.The damping forces are determined by the nodal velocity difference with element damping model,and the nodal velocity difference are equal in the two solving method,so the calculation errors don't exist using element damping model.
引文
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[2]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004.
[3]刘文华.大跨复杂结构在多点地震动激励作用下的非线性反应分析[D].北京:北京交通大学,2008.
[4]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,2009,25(4):25-32.
[5]刘枫,肖从真,徐自国,等.首都机场3号航站楼多维多点输入时程地震反应分析[J].建筑结构学报,2006,27(5):56-63.
[6]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.
[7]谢开仲,秦荣,韦立林,等.大跨度CFST拱桥行波效应的地震反应分析[J].桂林工学院学报,2005,25(4):455-459.
[8]江洋,石永久,王元清.实用多点输入虚拟激励法在通用有限元软件中的实现[J].地震工程与工程振动,2010,30(1):46-52.
[9]李永华,李思明.绝对位移直接求解的虚拟激励法[J].振动与冲击,2009,28(10):185-190.
[10]周乾,闫维明,周宏宇.中国古建筑木结构随机地震响应分析[J].武汉理工大学学报,2010,32(9):115-18.
[11]JTG7-2010.空间网格结构技术规程[S].北京:中国建筑工业出版社,2010.
[12]Wilson E L.Static and dynamic analysis of structures:aphysical approach with emphasis on earthquake engineering[M].Berkley,California:Computers and Structures,Inc,2004.
[13]Tsai H C.Modal superposition method for dynamic analysis ofstructures excited by prescribed support displacements[J].Computers and Structures,1998,66(5):675-683.
[14]俞载道,曹国敖.随机振动理论及其应用[M].上海:同济大学出版社,1988.
[15]Ates S,Dumanoglu A A,Bayraktar A.Stochastic response ofseismically isolated highway bridges with friction pendulumsystems to spatially varying earthquake ground motion[J].Engineering Structures,2005,27(13):1843-1858.
[16]Dumanogluid A A,Soyluk K.A stochastic analysis of longspan structures subjected to spatially varying ground motionsincluding the site-response effect[J].EngineeringStructures,2003,25(10):1301–1310.
[17]薛素铎,王雪生,曹资.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,2003,36(5):5-10.
[18]倪振华.振动力学[M].西安:西安交通大学出版社,1998.
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