Eckhardt Bruno, Ott Edward, Strogatz Steven H, Abrams Daniel M, McRobie Allan
Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Feb;75(2 Pt 1):021110. doi: 10.1103/PhysRevE.75.021110. Epub 2007 Feb 12.
On its opening day the London Millennium footbridge experienced unexpected large amplitude wobbling subsequent to the migration of pedestrians onto the bridge. Modeling the stepping of the pedestrians on the bridge as phase oscillators, we obtain a model for the combined dynamics of people and the bridge that is analytically tractable. It provides predictions for the phase dynamics of individual walkers and for the critical number of people for the onset of oscillations. Numerical simulations and analytical estimates reproduce the linear relation between pedestrian force and bridge velocity as observed in experiments. They allow prediction of the amplitude of bridge motion, the rate of relaxation to the synchronized state and the magnitude of the fluctuations due to a finite number of people.
在伦敦千禧桥开放首日，行人走上桥后，该桥出现了意想不到的大幅摆动。将行人在桥上的行走建模为相位振荡器，我们得到了一个人和桥的组合动力学模型，该模型在分析上易于处理。它提供了对个体步行者相位动力学以及振荡开始时的临界人数的预测。数值模拟和分析估计重现了实验中观察到的行人作用力与桥速度之间的线性关系。它们能够预测桥运动的幅度、向同步状态的弛豫速率以及由于有限人数导致的波动大小。
