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]

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]

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