Abdulrehem Mahmoud M, Ott Edward
University of Maryland, College Park, Maryland 20742, USA.
Chaos. 2009 Mar;19(1):013129. doi: 10.1063/1.3087434.
When it opened to pedestrian traffic in the year 2000, London's Millennium Bridge exhibited an unwanted, large side-to-side oscillation, which was apparently due to a resonance between the stepping frequency of walkers and one of the bridge modes. Models for this event, and similar events on other bridges, have been proposed. The model most directly addressing the synchronization mechanism of individual walkers and the resulting global response of the bridge-pedestrian system is the one developed by Eckhardt et al. [Phys. Rev. E 75, 021110 (2007)]. This model treats individual walkers with a phase oscillator description and is inherently high dimensional with system dimensionality (N+2), where N is the number of walkers. In the present work we use a method proposed by Ott and Antonsen [Chaos 18, 037113 (2008)] to reduce the model of Eckhardt et al. to a low dimensional dynamical system, and we employ this reduced description to study the global dynamics of the bridge/pedestrian interaction. More generally, this treatment serves as an interesting example of the possibility of low dimensional macroscopic behavior in large systems of coupled oscillators.
2000年对行人开放时，伦敦千禧桥出现了意外的大幅度左右摆动，这显然是由于行人的步频与桥梁的一种模态发生共振所致。针对这一事件以及其他桥梁上类似事件的模型已被提出。最直接涉及个体行人同步机制以及由此产生的桥 - 行人系统全局响应的模型是由埃克哈特等人 [《物理评论E》75, 021110 (2007)] 开发的模型。该模型用相位振荡器描述个体行人，本质上是高维的，系统维度为 (N + 2)，其中N是行人数量。在本工作中，我们使用奥特和安东森 [《混沌》18, 037113 (2008)] 提出的方法将埃克哈特等人的模型简化为低维动力系统，并采用这种简化描述来研究桥梁/行人相互作用的全局动力学。更一般地说，这种处理是耦合振荡器大系统中低维宏观行为可能性的一个有趣例子。
