基于虚拟激励法的车桥系统车速影响分析
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摘要
本文基于虚拟激励法提出列车-桥梁耦合系统的非平稳随机振动分析的新方法,并借此重点分析车速对系统随机振动的影响。列车每节车辆考虑27个自由度,桥梁模型采用空间Euler梁单元,轨道不平顺假设为多点异相位平稳随机激励。根据时变系统的虚拟激励法,推导得到方向、高低和水平三类轨道不平顺作用下车桥系统响应的时变功率谱及标准差,并采用精细积分法进行迭代计算,最后以高斯型随机变量的三倍标准差为误差范围给出系统响应最大值估计。在数值算例中,用时间历程法验证本文方法的正确性和有效性,并重点讨论列车速度的影响。
The non-stationary random vibration analysis on train-bridge coupled systems is performed with the pseudo-excitation method(PEM),and the influence of train speeds on system random responses are mainly discussed.Each vehicle of the train is described by 27 degrees of freedom,and the bridge deck is modeled as a three-dimensional Euler beam.The lateral,rotational and vertical irregularities of the track are assumed to be multi-point different-phase stationary random excitations.By PEM for the time-variant system,these track irregularities are transformed into a series of deterministic pseudo harmonic excitations.The corresponding pseudo responses are solved by using the precise integration method(PIM) iteratively.Then the time-dependent PSD and standard deviation of interested quantities can be obtained easily.Finally,an estimation method of the maximum value for such system responses is suggested by taking the 3 times standard deviation of the Gaussian random variable as the error range.In the numerical example,the effectiveness and accuracy of the proposed method are justified numerically by the time history method,and the influence of the train speed on system random responses is mainly discussed.
The non-stationary random vibration analysis on train-bridge coupled systems is performed with the pseudo-excitation method(PEM),and the influence of train speeds on system random responses are mainly discussed.Each vehicle of the train is described by 27 degrees of freedom,and the bridge deck is modeled as a three-dimensional Euler beam.The lateral,rotational and vertical irregularities of the track are assumed to be multi-point different-phase stationary random excitations.By PEM for the time-variant system,these track irregularities are transformed into a series of deterministic pseudo harmonic excitations.The corresponding pseudo responses are solved by using the precise integration method(PIM) iteratively.Then the time-dependent PSD and standard deviation of interested quantities can be obtained easily.Finally,an estimation method of the maximum value for such system responses is suggested by taking the 3 times standard deviation of the Gaussian random variable as the error range.In the numerical example,the effectiveness and accuracy of the proposed method are justified numerically by the time history method,and the influence of the train speed on system random responses is mainly discussed.
引文
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[2]Law S S,Zhu X Q.Bridge Dynamic Responses Due to RoadSurface Roughness and Braking of Vehicle[J].Journal ofSound and Vibration,2005,282(3-5):805-830.
[3]夏禾.车辆与结构动力相互作用[M].北京:科学出版社,2005:93-105,140-198.
[4]Song M K,Noh H C,Choi C K.A New Three-dimensionalFinite Element Analysis Model of High Speed-train-bridgeInteraction[J].Engineering Structures,2003,25(13):1611-1626.
[5]张昕,蒋通.考虑轨道不平顺的车-桥动力分析[J].力学季刊,2003,24(1):15-22.ZHANG Xin,JIANG Tong.Dynamic Analysis of Train-bridge System Considering Rail Irregularity[J].ChineseQuarterly of Mechanics,2003,24(1):15-22.
[6]Lee C H,Kawatani M,Kim C W,et al.Dynamic Response of aMonorail Steel Bridge under a Moving train[J].Journal of Soundand Vibration,2006,294(3):562-579.
[7]Fryba L.Non-stationary Response of a Beam to MovingRandom Force[J].Journal of Sound and Vibration,1976,46(3):328-338.
[8]吕峰.车辆与结构相互作用随机动力分析[D].大连:大连理工大学,2008:67-82.
[9]Zibdeh H S.Dynamic Response of a Rotating Beam Subjec-ted to a Random Moving Load[J].Journal of Sound and Vi-bration,1999,223(5):741-758.
[10]Au F T K,Wang J J,Cheung Y K.Impact Study of Cable-stayed Railway Bridge with Random Rail Irregularities[J].En-gineering Structures,2002,24(5):529-541.
[11]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.
[12]Lin J H,Zhang Y H.Seismic Random Vibration of Long-span Structures,Chapter 30 of Vibration and Shock Hand-book[M].Boca Raton,Florida:CRC Press,2005,30:1-41.
[13]钟万勰.应用力学对偶体系[M].北京:科学出版社,2002:5-10.
[14]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(5):22-28.ZHANG Zhi-chao,LIN Jia-hao.Precise Integration ofBridge Responses Due to a Moving Mass[J].Journal ofDalian University of Technology,2006,46(5):22-28.
[15]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 Zhi-chao,ZHANG Ya-hui,LIN Jia-hao.PEM-PIM Scheme for Non-stationary Random Vibration Analy-sis of Vehicle-bridge Systems[J].Engineering Mechanics,2008,25(11):197-204.
[16]韩艳.地震作用下高速铁路桥梁的动力响应及行车安全性研究[D].北京:北京交通大学,2006:137.
[17]铁路第三勘察设计院.京沪高速铁路设计暂行规定[Z].北京:中国铁道出版社,2003.
[18]张亚辉,李丽媛,陈艳,等.大跨度结构地震行波效应研究[J].大连理工大学学报,2005,45(4):480-486.ZHANG Ya-hui,LI Li-yuan,CHEN Yan,et al.Wave Pas-sage Effect on Random Seismic Response of Long-spanStructures[J].Journal of Dalian University of Technolo-gy,2005,45(4):480-486.
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