网络时滞动力学观点下人行桥过度侧向振动新机制

Lateral vibration of footbridges induced by pedestrians has become a topic of great interest in many fields including bridge engineering, physics, biomechanics etc. in the last decade. How large numbers of persons on a footbridge synchronize their footsteps to cause excessive lateral vibration of the footbridge is the top issue for this problem. In this project, we attempt to regard every single person on a footbridge as one node in a network consisted of all pedestrians on the footbridge. The dynamics of every node is determined by considering both the interaction between a person and the footbridge and that between persons. Then the study on mechanism that pedestrians tending to walk in synchronization result in excessive lateral vibration of the footbridge can be carried out by researching various kinds of complex synchronization phenomena in the network. The work will be completed is as follows: (1) Study mechanism of the interaction between pedestrians and a footbridge (2) Study mechanism of the interaction between pedestrians when a big crowd cross a footbridge (3) Experiment to guarantee the reliability of the study on mechanism of both the interaction between pedestrians and a footbridge and that between pedestrians (4) Study mechanism that a big crowd tend to walk in synchronization under the viewpoints of dynamics of networks with time delay. The study is aimed at finding out the affecting factors of walk synchronization of a big crowd crossing a footbridge, and determining the correspondence between the critical conditions of lateral instability of the footbridge and walk synchronization of pedestrians. The results of this project can provide a basis for revision of the design code of footbridges of our country and offer thinking of study and consult for vibration reduction that might appear.

行人行走导致的人行桥侧向振动问题是当前桥梁工程、物理、生物力学等众多领域关心的学术热点。桥上大量行人如何同步行走最终引发桥的过度侧向振动是这些研究领域最为关心的问题。本项目计划将桥上单个行人视为网络中的节点，节点动力学行为综合考虑人-桥和人-人之间的相互作用，从而将人行桥上大量行人同步行走导致人行桥过度侧向振动机理的研究转化为时滞网络中各种复杂同步现象的研究，具体研究计划如下：(1)行人激励下人-桥相互作用机理的研究 (2)人行桥上大量行人行走时人-人相互作用机理的研究 (3)进行必要的实验确保人-桥和人-人相互作用机理研究的可靠性 (4)网络时滞动力学观点下网络同步现象的研究。研究目的是弄清楚大量行人同步行走的影响因素，确定人行桥侧向失稳的临界条件与桥上行人同步行走之间的对应关系，为我国人行桥设计规范的修订提供依据，为后期可能出现的动力减振提供相应的思路和参考。

本项目针对行人引发的人行桥过度侧向振动问题，从时滞非线性动力学的角度进行了机理研究，内容包括四个方面：一、从理论上讨论了桥上行人行走时产生的侧向激励力；二、结合人行桥结构特征以及行人行走的动力学特征提出了新的人桥相互作用模型；三、讨论了行人与人行桥作用过程中的延时效应的影响；四、从行人和人行桥运动的相位关系角度讨论了人行桥过大侧向振动出现的机理。本项目对上述内容的研究结论对应如下：一、可以用支点上下简谐运动的倒摆来模拟人的行走，并解析地分析行人激励力的产生和变化规律。这部分研究可以避免直接确定行人产生的侧向力带来的困难。二、以前的研究中很少完整描述人行桥侧向振幅如何从小到大增加，此外也很少考虑桥梁结构形式对侧向振幅的影响。本项目中将悬索桥和斜拉桥均视为两自由度系统，将桥上行人产生的侧向力用具有随机相位的简谐函数描述。行人身体摆动相位的随机性和桥的侧向振动幅值有密切的关系，桥的侧向振幅小时桥上行人身体可以自由摆动，相位较为散乱，随机性强；桥的侧向振幅大时桥上行人身体随桥一起摆动，行人身体摆动相位的随机性减弱，因此相位随机性的强弱可以反映桥侧向振幅大小对行人的影响。本项目由此提出了新的人桥相互作用动力模型。三、人桥相互作用的延时效应对人行桥的侧向振动性质和侧向振幅都有较大影响，调整相互作用的延时大小可能是人行桥侧向减振的一个新的思路。四、人行桥过大侧向振动出现的原因是桥上行人身体摆动和桥的侧向振动之间的相位同步。本项目从分析行人身体摆动和桥侧向运动之间的相位关系入手研究桥的过大侧向振幅的出现，得到了有别于传统动力学分析结论之外的新结论。本项目研究有助于进一步理解人桥相互作用的力学机理，推导总结了可以直接用于工程实践的半经验公式，可以为人行桥的设计和动力学计算提供参考。