一个行人行走激励下的悬索桥动力模型
A Suspension Footbridge Model under Crowd-Induced Excitation
DOI: 10.12677/HJCE.2019.81010, PDF,    国家自然科学基金支持
作者: 张 涛, 镇 斌, 欧阳利军, 李婷婷：上海理工大学，上海
关键词: 悬索桥；双线摆；Mathieu方程；Hill方程；稳定性；Suspension Footbridge； Bifilar Pendulum； Mathieu Equation； Hill Equation； Stability
摘要: 提出了一个“双线摆模型”用于描述行人激励下悬索桥的动力行为。该模型中用两根弦和一块刚体分别代表悬索和桥面板。桥上行人行走时产生的竖向和侧向激励都用振幅为常数的简谐函数表示。在这一简化条件下根据Lagrange方法发现行人激励下悬索的动力学控制方程是一个Hill方程。利用扰动法对Hill方程进行了求解和稳定性分析，并通过数值计算证明了解析结果的正确性。利用该解析结论可以解释著名的伦敦千禧桥为何会在行人激励下出现0.48和0.96 Hz的侧向振动并伴有锁频现象。本文研究表明在人与悬索桥相互作用研究中不应该忽略悬索桥的悬挂结构特征。
Abstract: In this paper “the plane bifilar pendulum model” is proposed to study vibration of a suspension footbridge under crowd excitation. We use a plane bifilar pendulum to describe a suspension bridge by considering its structural features, which consists of two strings and a central rigid body representing the cables and deck of the footbridge, respectively. In addition, the vertical and lateral forces exerted by crowd on the deck both are considered to be harmonic with constant amplitudes. According to Lagrange method, we found that the dynamic behavior of the suspension footbridge under crowd-induced excitation can be described by a Hill equation. The solution and its stability of the plane pendulum model are theoretically analyzed based on the perturbation method, the correctness of which is verified by numerical simulations. By applying the analytical results to the London Millennium Bridge, we can easily explain the occurrence of excessive lateral vibration with 0.48 and 0.96 Hz and the “lock-in” phenomenon. Our research suggests that structural features of a suspension footbridge should not be ignored in the investigation of the pedestrian-footbridge interaction.
文章引用：张涛, 镇斌, 欧阳利军, 李婷婷. 一个行人行走激励下的悬索桥动力模型[J]. 土木工程, 2019, 8(1): 70-78. https://doi.org/10.12677/HJCE.2019.81010

参考文献

[1] Bachmann, H. and Ammann, W. (1987) Structural Engineering Documents 3e, Vibrations in Structures: Induced by Man and Machines. International Association for Bridge and Structural Engineering (IABSE), Zurich, Switzer-land.
[2] Fujino, Y., Pacheco, B.M., Nakamura, S. and Warnitchai, P. (1993) Synchornization of Human Walking Observed during Lateral Vibration of a Congested Pedestrian Bridge. Earthquake Engineering Structural Dynamics, 22, 741-758. [Google Scholar] [CrossRef] 
[3] Dallard, P., Fitzpatrick, A.J., Flint, A., Le Bourva, S., Low, A., Ridsdill Smith, R.M. and Willford, M. (2001) The London Millennium Footbridge. Structural Engineer, 79, 17-33.
[4] Dallard, P., Fitzpatrick, A.J., Flint, A., Low, A., Ridsdill Smith, R.M., Willford, M. and Roche, M. (2001) London Millennium Bridge: Pedestrian-Induced Lateral Vibration. Journal of Bridge Engineering, 6, 412-417. [Google Scholar] [CrossRef] 
[5] Roberts, T.M. (2005) Lateral Pedestrian Excitation of Footbridges. Journal of Bridge Engineering, 10, 107-112. [Google Scholar] [CrossRef] 
[6] Newland, D.E. (2004) Pedestrian Excitation of Bridges. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 218, 477-492. [Google Scholar] [CrossRef] 
[7] Piccardo, G. and Tubino, F. (2008) Parametric Resonance of Flexible Footbridges under Crowd-Induced Lateral Excitation. Journal of Sound and Vibration, 311, 353-371. [Google Scholar] [CrossRef] 
[8] MCRobie, A., Morgenthal, G., Lasenby, J. and Ringer, M. (2003) Section Model Tests on Human Structure Lock In. Proceedings of the Institution of Civil Engineering-Bridge Engineering, 156, 71-79. [Google Scholar] [CrossRef] 
[9] Zhou, D. and Ji, T.J. (2008) Dynamic Characteristics of a Gener-alized Suspension System. International Journal of Mechanical Sciences, 50, 30-42. [Google Scholar] [CrossRef] 
[10] Grundamann, H., Kreuzinger, H. and Schneider M. (1993) Dynamic Calculation of Footbridges. Bauingenieur-Germany, 68, 215-225.

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