千禧桥行人诱发振动的低维描述
Low Dimensional Description of Pedestrian-Induced Oscillation of the Millennium Bridge
摘要：
当它在2000年向行人开放时，伦敦的千禧桥表现出不必要的，大的，左右摆动，这显然是由于步行者的脚步频率和桥梁模式之间的共振。已经提出了这种事件以及其他桥梁上类似事件的模型。Eckhardt等人开发的模型最直接地解决了单个步行者的同步机制和由此产生的桥梁-行人系统的全局响应。该模型用相位振荡器描述对待单个步行者，并且固有地具有系统维数（N+2）的高维性，其中N是步行者的数量。在目前的工作中，我们使用的方法提出的Ott和Antonsen减少Eckhartt等人的模型。一个低维的动力系统，我们采用这种减少的描述来研究桥梁/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，低维宏观行为的可能性，在大型系统的耦合振子。
英文摘要：
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 one developed by Eckhardt et al. 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 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.
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