Emergence of the London Millennium Bridge instability without synchronisation
Authors
Champneys, Alan R.
Jeter, Russell
McRobie, Allan
Publication Date
2021-12-10Journal Title
Nature Communications
Publisher
Nature Publishing Group UK
Volume
12
Issue
1
Language
en
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
Belykh, I., Bocian, M., Champneys, A. R., Daley, K., Jeter, R., Macdonald, J. H. G., & McRobie, A. (2021). Emergence of the London Millennium Bridge instability without synchronisation. Nature Communications, 12 (1) https://doi.org/10.1038/s41467-021-27568-y
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.
Keywords
Article, /639/166/986, /639/705/1041, /639/766/25, article
Sponsorship
National Science Foundation (NSF) (DMS-1909924)
Ministry of Education and Science of the Russian Federation (Minobrnauka) (0729-2020-0036)
Identifiers
s41467-021-27568-y, 27568
External DOI: https://doi.org/10.1038/s41467-021-27568-y
This record's URL: https://www.repository.cam.ac.uk/handle/1810/331868
Rights
Licence:
http://creativecommons.org/licenses/by/4.0/
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