Belykh 2021 - Emergence of the London Millennium Bridge instability without synchronisation.pdf (4.68 MB)
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Emergence of the London Millennium Bridge instability without synchronisation

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journal contribution
posted on 14.01.2022, 15:09 by Igor Belykh, Mateusz Bocian, Alan R Champneys, Kevin Daley, Russell Jeter, John HG Macdonald, Allan McRobie
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.

Funding

U.S. National Science Foundation under grant No. DMS-1909924 (to I.B., K.D., and R.J.); the Ministry of Science and Higher Education of the Russian Federation under grant No. 0729-2020-0036 (to I.B.); the Polish National Agency for Academic Exchange (NAWA) under grant No. PPN/PPO/2019/1/00036 (to M.B.).

History

Citation

Belykh, I., Bocian, M., Champneys, A.R. et al. Emergence of the London Millennium Bridge instability without synchronisation. Nat Commun 12, 7223 (2021). https://doi.org/10.1038/s41467-021-27568-y

Author affiliation

School of Engineering

Version

VoR (Version of Record)

Published in

Nature Communications

Volume

12

Pagination

7223

Publisher

Springer Science and Business Media LLC

eissn

2041-1723

Acceptance date

26/11/2021

Copyright date

2021

Available date

10/12/2021

Language

en

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