人行桥人致横向振动的新型模型—IP-K模型  

A NOVEL MODEL FOR PEDESTRIAN-INDUCED LATERAL VIBRATION OF FOOTBRIDGES—THE IP-K MODEL

作　　者：贾布裕[1] 茅思奕 陈扬文 颜全胜[1] 余晓琳[1] JIA Bu-yu;MAO Si-yi;CHEN Yang-wen;YAN Quan-sheng;YU Xiao-lin(School of Civil Engineering and Transportation,South China University of Technology,Guangzhou,Guangdong 510640,China)

机构地区：[1]华南理工大学土木与交通学院,广东广州510640

出　　处：《工程力学》2022年第5期188-203,共16页Engineering Mechanics

基　　金：国家自然科学基金项目(51608207);广东省自然科学基金项目(2019A1515011941)。

摘　　要：目前关于人行桥人致横向振动机理仍不明确,在这个领域依旧存在争议和不足。有两种主要模型被用于解释人行桥人致大幅横向振动:同步锁定模型和倒摆模型。同步锁定模型认为桥上人群会受桥梁振动影响而逐渐调整步频和桥梁发生同步现象,导致桥梁发生大幅横向振动。而倒摆模型却认为人群调整步频产生的同步现象并不是桥梁大幅横向振动产生的前提条件,认为:即使行人不进行步频调整,其人-桥相互作用引起的自激力同样足够引起振动失稳。目前倒摆模型被认为更具普适性,但仍存在一个质疑:采用倒摆模型得到的行人正常步频下的速度同相自激力分量系数c;远小于实测值。产生这个问题的原因极有可能是倒摆模型忽视了实际中真实存在的同步效应。鉴于此,该研究提出了一种新型的人行桥人致横向振动模型:IP-K(inverted pendulumKuramoto)模型。其主要原理为:以倒摆模型为核心框架,同时,将Kuramoto生物同步模型引入倒摆模型,使其能考虑人群和桥梁振动之间的同步效应,以此使倒摆模型更合理、更接近实际。所提模型被应用于千禧桥北跨,验证了其有效性;同时,讨论了行人步频分布参数、行人数量、行人对桥梁振幅的敏感系数等一系列关键参数对c;的影响;并建立了一般线性非稳定/稳定的判定依据。该研究所提方法将为人行桥人致横向振动的机理的揭示提供有力的理论依据。The mechanism of pedestrian-induced lateral vibration of footbridges remains unclear and is accompanied by many controversies and deficiencies. Two main models are frequently used to explain the large lateral vibration of footbridges, that is, the synchronization locking model and the inverted pendulum model. The synchronous locking model indicates that a crowd on a bridge gradually adjusts their walking frequency and synchronizes("lock-in") with the movement of the bridge, resulting in large lateral vibration of the bridge. By contrast, the inverted pendulum model supposes that the synchronization generated by the crowd adjusting the step frequency is not a prerequisite for the large lateral vibration of the bridge and asserts that the self-excited force caused by the pedestrian-bridge interaction is sufficient to cause vibrational instability, even if the pedestrians do not adjust the step frequency. Currently, the inverted pendulum model is considered more universal, but a debatable problem remains. The coefficient of component in phase with velocity c;under a normal walking frequency obtained by the inverted pendulum model is considerably less than the measured value.cpThe reason for this problem is most likely that the inverted pendulum model ignores the real synchronization effect in practice. On this basis, a novel model for the pedestrian-induced lateral vibration of footbridges, namely,the inverted pendulum–Kuramoto model, is proposed, in which the inverted pendulum model is regarded as the core framework and the Kuramoto model is introduced into the inverted pendulum model to consider the synchronization effect between the crowd and the bridge vibration. In such a manner, the inverted pendulum model is improved to be more reasonable and closer to reality. The proposed model is applied to the north span of the Millennium Bridge to verify its effectiveness. Meanwhile, the influences of crucial parameters, including the walking frequency distribution, the number of pedestrians, and the sensitivity coeffi

关 键 词：桥梁工程 人致横向振动 倒摆模型 Kuramoto模型 同步效应 

分 类 号：U441.3[建筑科学—桥梁与隧道工程]