Emergence of the London Millennium Bridge instability without synchronisation

Igor Belykh (), Mateusz Bocian, Alan R. Champneys, Kevin Daley, Russell Jeter, John H. G. Macdonald and Allan McRobie
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Igor Belykh: Georgia State University
Mateusz Bocian: Wrocław University of Science and Technology
Alan R. Champneys: University of Bristol
Kevin Daley: Georgia State University
Russell Jeter: Georgia State University
John H. G. Macdonald: University of Bristol
Allan McRobie: University of Cambridge

Nature Communications, 2021, vol. 12, issue 1, 1-14

Abstract: Abstract The pedestrian-induced instability of the London Millennium Bridge is a widely used example of Kuramoto synchronisation. Yet, reviewing observational, experimental, and modelling evidence, we argue that increased coherence of pedestrians’ foot placement is a consequence of, not a cause of the instability. Instead, uncorrelated pedestrians produce positive feedback, through negative damping on average, that can initiate significant lateral bridge vibration over a wide range of natural frequencies. We present a simple general formula that quantifies this effect, and illustrate it through simulation of three mathematical models, including one with strong propensity for synchronisation. Despite subtle effects of gait strategies in determining precise instability thresholds, our results show that average negative damping is always the trigger. More broadly, we describe an alternative to Kuramoto theory for emergence of coherent oscillations in nature; collective contributions from incoherent agents need not cancel, but can provide positive feedback on average, leading to global limit-cycle motion.

Date: 2021
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DOI: 10.1038/s41467-021-27568-y

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