Low dimensional description of pedestrian-induced oscillation of the Millennium Bridge
Low dimensional description of pedestrian-induced oscillation of the Millennium Bridge
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DOI：
10.1063/1.3087434
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发表时间：
2009-03-01
期刊：
影响因子：
2.9
通讯作者：
Ott, Edward
中科院分区：
文献类型：
--
作者：
Abdulrehem, Mahmoud M.;Ott, Edward
2000年，伦敦千禧桥向行人开放时，它表现出了一种不受欢迎的、巨大的左右摆动，这显然是由于步行者的步伐频率与桥梁的一种模式之间的共振。这一事件的模型，以及其他桥梁上类似的事件，已经被提出。最直接地解决单个步行者的同步机制和由此产生的桥-行人系统的整体响应的模型是由Eckhardt [Phys]开发的。[j].农业工程学报，2014,27(2)。该模型用相位振荡器描述单个行走者，具有固有的高维系统维数（N+2），其中N为行走者的数量。在本研究中，我们使用了Ott和Antonsen [Chaos 18, 037113(2008)]提出的方法，将Eckhardt模型简化为低维动力系统，并使用这种简化的描述来研究桥梁/行人相互作用的全局动力学。更一般地说，这种处理作为一个有趣的例子，说明了耦合振荡器大系统中低维宏观行为的可能性。
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 [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 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.