Vibration Analysis of Bridges Excited by Uncertain Train Moving Loads
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摘要: 通过引入区间过程模型,提出了一种针对受列车移动载荷激励的桥梁的不确定振动分析方法,可以得到列车经过时桥梁振动挠度响应的上下边界曲线。将单节列车用两个等间隔轮载荷的子系统来模拟,一个包含前轮部分,另一个包含后轮部分。将桥梁简化为简支梁模型,用区间过程来描述列车对桥梁的不确定性移动载荷激励。基于区间过程模型和模态叠加理论,得到桥梁挠度响应的中值函数和半径函数,从而得到挠度响应的上下边界函数。通过数值算例说明本文方法的有效性。Abstract: By introducing the interval process model, this paper proposes an uncertain vibration analysis method for bridges subjected to train moving loads to obtain the upper and lower boundary curves of vibration deflection response of the bridges. Each train is modeled as two subsystems of wheel loads of constant intervals, one containing the front wheel section and the other consisting of the rear wheel section. The bridge is simplified to a simply supported beam model, and the interval process model is used to describe the uncertainty of the moving load flow excitation of the train applied to the bridge. By combining the interval process model and the modal superposition vibration analysis theory, the middle function and radius function of deflection response of the bridge can be obtained, based on which the upper and lower boundary functions of the deflection response can be obtained. Finally, the effectiveness of the proposed method is illustrated by investigating several numerical examples.
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Key words:
- train /
- bridge /
- interval process /
- uncertain vibration analysis /
- deflection
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图 1 受移动载荷流激励的弹性梁模型[16]
图 2 列车过桥模型[16]
图 3 列车载荷等效为两个等间距的子系统[16]
图 4 载荷间距与桥长关系的不同情形[16]
图 5 区间过程[15]
图 6 区间过程自协方差函数的求取[20]
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[1] Hino J, Yoshimura T, Konishi K, et al. A finite element method prediction of the vibration of a bridge subjected to a moving vehicle load[J]. Journal of Sound and Vibration, 1984, 96(1):45-53 http://www.sciencedirect.com/science/article/pii/0022460X84905935 [2] Michaltsos G T. Dynamic behaviour of a single-span beam subjected to loads moving with variable speeds[J]. Journal of Sound and Vibration, 2002, 258(2):359-372 doi: 10.1006/jsvi.2002.5141 [3] Lin Y H, Trethewey M W. Finite element analysis of elastic beams subjected to moving dynamic loads[J]. Journal of Sound and Vibration, 1990, 136(2):323-342 doi: 10.1016/0022-460X(90)90860-3 [4] Yang Y B, Yau J D, Hsu L C. Vibration of simple beams due to trains moving at high speeds[J]. Engineering Structures, 1997, 19(11):936-944 doi: 10.1016/S0141-0296(97)00001-1 [5] Frýba L. A rough assessment of railway bridges for high speed trains[J]. Engineering Structures, 2001, 23(5):548-556 doi: 10.1016/S0141-0296(00)00057-2 [6] 张晓丹.高速铁路车-轨-桥耦合作用下桥梁结构共振响应分析[D].武汉: 华中科技大学, 2012Zhang X D. Research on the resonant response about bridge structure under the dynamic interaction system of vehicle-ballastless track-bridge[D]. Wuhan: Huazhong University of Science and Technology, 2012(in Chinese) [7] Iwankiewicz R, Šniady P. Vibration of a beam under a random stream of moving forces[J]. Journal of Structural Mechanics, 1984, 12(1):13-26 doi: 10.1080/03601218408907460 [8] Kurihara M, Shimogo T. Vibration of an elastic beam subjected to discrete moving loads[J]. Journal of Mechanical Design, 1978, 100(3):514-519 http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMDEEC000100000003000514000001&idtype=cvips&gifs=Yes [9] Yu Z W, Mao J F, Guo F Q, et al. Non-stationary random vibration analysis of a 3D train-bridge system using the probability density evolution method[J]. Journal of Sound and Vibration, 2016, 366:173-189 doi: 10.1016/j.jsv.2015.12.002 [10] 杨建栋.移动随机荷载下含缺陷轨道结构振动分析[D].辽宁大连: 大连理工大学, 2016Yang J D. Vibration analysis of track structure containing imperfections under moving random loads[D]. Liaoning Dalian: Dalian University of Technology, 2016(in Chinese) [11] 李慧乐, 夏禾.基于车桥耦合随机振动分析的钢桥疲劳可靠度评估[J].工程力学, 2017, 34(2):69-77 http://cdmd.cnki.com.cn/Article/CDMD-10004-1016120633.htmLi H L, Xia H. Fatigue reliability evaluation of steel bridges based on coupling random vibration analysis of train and bridge[J]. Engineering Mechanics, 2017, 34(2):69-77(in Chinese) http://cdmd.cnki.com.cn/Article/CDMD-10004-1016120633.htm [12] Zhu Z H, Wang L D, Yu Z W, et al. Non-stationary random vibration analysis of railway bridges under moving heavy-haul trains[J]. International Journal of Structural Stability and Dynamics, 2018, 18(3):1850035 doi: 10.1142/S0219455418500359 [13] Zeng Z P, Liu F S, Lou P, et al. Formulation of three-dimensional equations of motion for train-slab track-bridge interaction system and its application to random vibration analysis[J]. Applied Mathematical Modelling, 2016, 40(11-12):5891-5929 doi: 10.1016/j.apm.2016.01.020 [14] Jiang C, Ni B Y, Han X, et al. Non-probabilistic convex model process:a new method of time-variant uncertainty analysis and its application to structural dynamic reliability problems[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 268:656-676 doi: 10.1016/j.cma.2013.10.016 [15] Jiang C, Ni B Y, Liu N Y, et al. Interval process model and non-random vibration analysis[J]. Journal of Sound and Vibration, 2016, 373:104-131 doi: 10.1016/j.jsv.2016.03.019 [16] 段民封.不确定移动载荷激励下弹性梁的非随机振动分析及应用[D].长沙: 湖南大学, 2018Duan M F. The Research on non-random vibration analysis of elastic beams subjected to uncertain moving loads and its application[D]. Changsha: Hunan University, 2018(in Chinese) [17] Paz M. Structural dynamics:theory and computation[M]. 3rd ed. New York:Van Nostrand Reinhold Company Inc, 1991 [18] Clough R W, Penzien J. Dynamics of structures[M]. New York:McGraw-Hill, 1975 [19] Jiang C, Han X, Lu G Y, et al. Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(33-36):2528-2546 doi: 10.1016/j.cma.2011.04.007 [20] Jiang C, Li J W, Ni B Y, et al. Some significant improvements for interval process model and non-random vibration analysis method[J]. Submitted, 2018 [21] Li J W, Ni B Y, Jiang C, et al. Dynamic response bound analysis for elastic beams under uncertain excitations[J]. Journal of Sound and Vibration, 2018, 422:471-489 doi: 10.1016/j.jsv.2018.02.025