Synchronous lateral excitation
Synchronous lateral excitation is a dynamic phenomenon where pedestrians walking on a footbridge subconsciously synchronize their lateral footsteps with the bridge’s natural swaying motion, amplifying lateral vibrations.[2][3] First widely recognized during the 2000 opening of the London Millennium Bridge, synchronous lateral excitation has since become a critical consideration in the design of lightweight pedestrian structures.[4][5][6]
Mechanism
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Synchronous lateral excitation arises from two interrelated synchronization processes. The first is the pedestrian-structure synchronization, where slight lateral bridge movements (e.g., from wind or random pedestrian steps) prompt walkers to adjust their gait to match the bridge’s oscillation frequency, increasing lateral forces.[7] The second is pedestrian-pedestrian synchronization, where individuals unconsciously align their stepping patterns, further reinforcing the resonant force.[8][9]
Key cases
[edit]- The London Millennium Bridge experienced lateral vibrations up to 70 mm due to synchronous lateral excitation, requiring a £5M retrofit with dampers.[2][4]
- The Auckland Harbour Bridge experienced a lateral frequency of 0.67 Hz during a 1975 demonstration.[10]
- The Birmingham NEC Link bridge experienced a lateral frequency of 0.7 Hz.
- The Toda Park Bridge in Japan is an early documented case (1990s) studied by Fujino et al., informing later synchronous lateral excitation models.[7]
Mitigation strategies
[edit]Some ways to avoid synchronous lateral excitation are the implementation of tuned mass dampers, which were used in the Millennium Bridge to increase damping from 0.5% to 20% critical.[4] Other strategies involve designing bridges with lateral frequencies outside the 0.5–1.1 Hz range as well as managing crows by limiting pedestrian density during events.[5]
References
[edit]- ^ "Advanced load models for synchronous pedestrian excitation and optimised design guidelines for steel footbridges". Publications Office of the European Union. 2007.
{{cite web}}: CS1 maint: url-status (link) - ^ a b Josephson, Brian (14 June 2000). "Out of step on the bridge". The Guardian. Retrieved 22 March 2018.
- ^ a b Parker, Matt (2019). Humble Pi: A Comedy of Maths Errors. Penguin UK.
- ^ a b c "Stabilising the London Millennium Bridge". Ingenia. 2000-06-10. Retrieved 2025-04-21.
- ^ a b Venuti, Fiammetta; Bruno, Luca (2017). "Footbridge lateral vibrations induced by pedestrians" (PDF). Procedia Engineering. 199: 179–184. Retrieved 2025-04-21.
- ^ Strogatz, Steven et al. (2005). "Theoretical mechanics: Crowd synchrony on the Millennium Bridge", Nature, Vol. 438, pp. 43–44.
- ^ a b Venuti, Fiammetta; Bruno, Luca (2008). "The synchronous lateral excitation phenomenon: modelling framework and application" (PDF). Comptes Rendus Mécanique. 336 (1–2): 194–199. Retrieved 2025-04-21.
- ^ "Modelling of lateral forces generated by pedestrians walking across footbridges" (PDF). Journal of Sound and Vibration. 528: 116938. 2022. Retrieved 2025-04-21.
- ^ Julavitz, Robert. "Point of Collapse", Archived 17 June 2008 at the Wayback Machine Village Voice, 26 August 2003.
- ^ Dallard, P. et al. "The London Millennium Footbridge," Archived 27 September 2011 at the Wayback Machine Structural Engineer, 20 November 2001. 79:22, pp. 17–35.