水平地震下列车过桥的非平稳随机响应及其极值估计
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摘要
推广虚拟激励法来研究水平地震作用时三维车桥耦合时变系统的非平稳随机振动以及最大值估计方法。水平地震动假设为均匀调制非平稳随机过程;轨道不平顺假设为多点异相位均匀调制非平稳随机激励。借助时变系统的虚拟激励法将水平地震和轨道不平顺随机激励分别转化为一系列确定性简谐激励,为了能更真实地模拟车轮作用力在时间域和空间域的连续变化,采用精细积分格式进行数值积分,得到了系统随机响应的时变功率谱密度函数和标准差。最后基于首次穿越破坏准则给出了系统非平稳随机响应的最大值估计方法。在数值算例中,通过多样本时间历程法的统计平均验证了该文随机振动分析方法的正确性和最大值估计方法的有效性;并讨论了场地土条件对系统随机响应的影响。
Non-stationary random vibration and peak value estimation of 3-D train-bridge systems subjected to the action of lateral horizontal earthquake are investigated based on the pseudo-excitation method(PEM).The lateral horizontal earthquake is assumed to be a uniformly modulated non-stationary random process,while the excitations of track irregularity are assumed to be multi-phase uniformly modulated non-stationary random excitations.The pseudo-excitation method is extended and applied to transform the random excitations due to horizontal earthquake and track irregularities into a series of deterministic pseudo harmonic excitations respectively.And then the corresponding pseudo responses are solved by using the precise integration method(PIM) iteratively.By this means,various non-stationary random responses including the time-dependent PSD and RMS of interested quantities can be obtained easily.Furthermore,a new estimation method of peak value for such non-stationary random responses is suggested based on first-passage failure criteria.The effectiveness and accuracy of the proposed method are justified numerically by the time history method,and the influence of site type on random responses of the system is discussed.
Non-stationary random vibration and peak value estimation of 3-D train-bridge systems subjected to the action of lateral horizontal earthquake are investigated based on the pseudo-excitation method(PEM).The lateral horizontal earthquake is assumed to be a uniformly modulated non-stationary random process,while the excitations of track irregularity are assumed to be multi-phase uniformly modulated non-stationary random excitations.The pseudo-excitation method is extended and applied to transform the random excitations due to horizontal earthquake and track irregularities into a series of deterministic pseudo harmonic excitations respectively.And then the corresponding pseudo responses are solved by using the precise integration method(PIM) iteratively.By this means,various non-stationary random responses including the time-dependent PSD and RMS of interested quantities can be obtained easily.Furthermore,a new estimation method of peak value for such non-stationary random responses is suggested based on first-passage failure criteria.The effectiveness and accuracy of the proposed method are justified numerically by the time history method,and the influence of site type on random responses of the system is discussed.
引文
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[15]曹资,薛素铎.空间结构抗震理论与设计[M].北京:科学出版社,2005:113―139.Cao Zi,Xue Suduo.Seismic analysis and design of spatial structures[M].Beijing:Science Press,2005:113―139.(in Chinese)
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[17]Davenport A G.Note on the distribution of the largest value of a random function with application to gust loading[J].Proceedings of the Institution of Civil Engineers,1964,28:187―196.
[18]江近仁,洪峰.功率谱与反应谱的转换和人造地震波[J].地震工程与工程振动,1984,4(3):1―10.Jiang Jinren,Hong Feng.Conversion between power spectrum and response spectrum and artificial earthquakes[J].Earthquake Engineering and Engineering Vibration,1984,4(3):1―10.(in Chinese)
[19]李桂青,李秋胜.工程结构时变可靠度理论及其应用[M].北京:科学出版社,2001:152―190.Li Guiqing,Li Qiusheng.Time dependent structural reliability:Theory and application[M].Beijing:Science Press,2001:152―190.(in Chinese)
[2]Fryba L.Vibration of solids and structures under moving loads[M].London:Thomas Telford,1999.
[3]Yau J D,Fryba L.Response of suspended beams due to moving loads and vertical seismic ground excitations[J].Engineering Structures,2007,29(12):3255―3262.
[4]夏禾.车辆与结构动力相互作用[M].北京:科学出版社,2002.Xia He.Dynamic interactions between vehicles and structures[M].Beijing:Science Press,2002.(in Chinese)
[5]Xia H,Han Y,Zhang N.Dynamic analysis of train-bridge system subjected to non-uniform seismic excitations[J].Earthquake Engineering and Structural Dynamic,2006,35(12):1563―1579.
[6]Miyamoto T,Ishida H,Matsuo M.Running safety of railway vehicle as earthquake occurs[J].Quarterly Report of RTRI,1997,38(3):117―122.
[7]Yang Y B,Wu Y S.Dynamic stability of trains moving over bridges shaken by earthquakes[J].Journal of Sound and Vibration,2002,258(1):65―94.
[8]徐昭鑫.随机振动[M].北京:高等教育出版社,1990:103―235.Xu Zhaoxin.Random vibration[M].Beijing:High Education Press,1990:103―235.(in Chinese)
[9]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004:42―184.Lin Jiahao,Zhang Yahui.Pseudo excitation method inrandom vibration[M].Beijing:Science Press,2004:42―184.(in Chinese)
[10]Lin J H,Zhang Y H.Seismic random vibration of long-span structures[M].Chapter30of Vibration and Shock Handbook,Boca Raton,Florida:CRC Press,2005,30:1―41.
[11]Zhong W X.Duality system in applied mechanics and optimal control[M].Boston:Kluwer Academic Pub,2004.
[12]张志超,林家浩.移动质量作用下桥梁响应的精细积分[J].大连理工大学学报,2006,46(s1):22―28.Zhang Zhichao,Lin Jiahao.Precise integration of bridge responses due to a moving mass[J].Journal of Dalian University of Technology,2006,46(s1):22―28.(in Chinese)
[13]张志超,张亚辉,林家浩.车桥耦合系统非平稳随机振动分析的虚拟激励-精细积分法[J].工程力学,2008,25(11):197―204.Zhang Zhichao,Zhang Yahui,Lin Jiahao.PEM-PIM scheme for non-stationary random vibration analysis of vehicle-bridge systems[J].Engineering Mechanics,2008,25(11):197―204.(in Chinese)
[14]吕蜂.车辆与结构相互作用随机动力分析[D].大连:大连理工大学,2008.Lu Feng.Stochastic analysis for dynamic interaction of vehicles and structures[D].Dalian:Dalian University of Technology,2008.(in Chinese)
[15]曹资,薛素铎.空间结构抗震理论与设计[M].北京:科学出版社,2005:113―139.Cao Zi,Xue Suduo.Seismic analysis and design of spatial structures[M].Beijing:Science Press,2005:113―139.(in Chinese)
[16]Lin J H,Zhang Y H,Li Q S.Seismic spatial effects for long-span bridges,using the pseudo excitation method[J].Engineering Structures,2004,26(9):1207―1216.
[17]Davenport A G.Note on the distribution of the largest value of a random function with application to gust loading[J].Proceedings of the Institution of Civil Engineers,1964,28:187―196.
[18]江近仁,洪峰.功率谱与反应谱的转换和人造地震波[J].地震工程与工程振动,1984,4(3):1―10.Jiang Jinren,Hong Feng.Conversion between power spectrum and response spectrum and artificial earthquakes[J].Earthquake Engineering and Engineering Vibration,1984,4(3):1―10.(in Chinese)
[19]李桂青,李秋胜.工程结构时变可靠度理论及其应用[M].北京:科学出版社,2001:152―190.Li Guiqing,Li Qiusheng.Time dependent structural reliability:Theory and application[M].Beijing:Science Press,2001:152―190.(in Chinese)
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