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Synchronous lateral excitation

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When a pedestrian walks in sync with a ground oscillation, the lateral foot forces exacerbate already existing oscillations, leading to a positive feedback loop known as synchronous lateral excitation. Adapted from Figure 5-15 of Butz, C., et al. "Advanced load models for synchronous pedestrian excitation and optimized design guidelines for steel footbridges (SYNPEX)." RFCS-Research Project RFS-CR-03019 (2007).[1]

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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As the number of pedestrians on a footbridge increases (black line in steps), the lateral oscillations increase (gray area). After a critical number of pedestrians is reached (166 in this example), the bridge enters a stage of synchronous lateral excitation. Simplified graph based on page 37 of Parker, Matt. Humble Pi: A Comedy of Maths Errors. Penguin UK, 2019.[3]

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

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  • 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

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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

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  1. ↑ "Advanced load models for synchronous pedestrian excitation and optimised design guidelines for steel footbridges". Publications Office of the European Union. 2007.
  2. 1 2 Josephson, Brian (14 June 2000). "Out of step on the bridge". The Guardian. Retrieved 22 March 2018.
  3. 1 2 Parker, Matt (2019). Humble Pi: A Comedy of Maths Errors. Penguin UK.
  4. 1 2 3 "Stabilising the London Millennium Bridge". Ingenia. 2000-06-10. Retrieved 2025-04-21.
  5. 1 2 Venuti, Fiammetta; Bruno, Luca (2017). "Footbridge lateral vibrations induced by pedestrians" (PDF). Procedia Engineering. 199: 179–184. Retrieved 2025-04-21.
  6. ↑ Strogatz, Steven et al. (2005). "Theoretical mechanics: Crowd synchrony on the Millennium Bridge", Nature, Vol. 438, pp. 43–44.
  7. 1 2 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.
  8. ↑ "Modelling of lateral forces generated by pedestrians walking across footbridges" (PDF). Journal of Sound and Vibration. 528: 116938. 2022. Retrieved 2025-04-21.
  9. ↑ Julavitz, Robert. "Point of Collapse", Village Voice, 26 August 2003.
  10. ↑ 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.
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