Foot force models of crowd dynamics on a wobbly bridge

Belykh, Igor; Jeter, Russell; Белых, В. Н.

doi:10.1126/sciadv.1701512

Cited by 43 publications

(34 citation statements)

References 48 publications

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“…[32][33][34] The use of the inverted pendulum models to describe pedestrian's gaits allowed us to predict the critical number of pedestrians required for the onset of wobbling of the London Millennium Bridge remarkably well. 31 Our results support the traditional observation that crowd synchrony was necessary for the London Millenium Bridge to experience large-amplitude wobbling. 31 Although, the exact cause of the initial onset of wobbling at least in the case of small amplitudes may be rooted into the ability of pedestrians to adapt their gait and maintain lateral balance while walking randomly.…”

Section: Introductionsupporting

confidence: 87%

“…31 Our results support the traditional observation that crowd synchrony was necessary for the London Millenium Bridge to experience large-amplitude wobbling. 31 Although, the exact cause of the initial onset of wobbling at least in the case of small amplitudes may be rooted into the ability of pedestrians to adapt their gait and maintain lateral balance while walking randomly.…”

Section: Introductionsupporting

confidence: 87%

“…We begin with the standard setup for modeling pedestrian-bridge interactions. 26,[29][30][31] The model describes pedestrian-induced lateral vibrations of the bridge by a massspring-damper system (Fig. 1).…”

Section: Pedestrian-bridge Interaction Modelmentioning

confidence: 99%

“…In our recent paper, 31 we developed a bio-mechanically inspired model of pedestrians' response which captures the key properties of pedestrian lateral balance and the resulting foot forces on the bridge. This model is an extension of the inverted pendulum model of human balance 29,30 which had been successfully used to analyze the whole body balance of bipedal walking.…”

Section: Introductionmentioning

confidence: 99%

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Bistable gaits and wobbling induced by pedestrian-bridge interactions

Belykh

Jeter

Белых

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Several modern footbridges around the world have experienced large lateral vibrations during crowd loading events. The onset of large-amplitude bridge wobbling has generally been attributed to crowd synchrony; although, its role in the initiation of wobbling has been challenged. To study the contribution of a single pedestrian into overall, possibly unsynchronized, crowd dynamics, we use a bio-mechanically inspired inverted pendulum model of human balance and analyze its bi-directional interaction with a lively bridge. We first derive analytical estimates on the frequency of pedestrian's lateral gait in the absence of bridge motion. Then, through theory and numerics, we demonstrate that pedestrian-bridge interactions can induce bistable lateral gaits such that switching between the gaits can initiate large-amplitude wobbling. We also analyze the role of stride frequency and the pedestrian's mass in hysteretic transitions between the two types of wobbling. Our results support a claim that the overall foot force of pedestrians walking out of phase can cause significant bridge vibrations.

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Section: Introductionsupporting

confidence: 87%

Section: Introductionsupporting

confidence: 87%

Section: Pedestrian-bridge Interaction Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bistable gaits and wobbling induced by pedestrian-bridge interactions

Belykh

Jeter

Белых

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Zhou Chen et al [13] studied the parameter vibration responses while considering the time-lag effect by taking the Millennium Bridge in London as an example, which shows that the time-lag has no effect on the amplitude of the parameter vibration response. Belykh, Igor et al [14] discussed parameter variation trends that were used to obtain coupled pedestrian-bridge oscillations, notably the influence of the mass ratio of pedestrians to the bridge mass in the mode considered, and the phase variation with the amplitude.…”

Section: Introductionmentioning

confidence: 99%

A Study on a Mechanism of Lateral Pedestrian-Footbridge Interaction

Zhou

Chen

et al. 2019

Applied Sciences

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Based on the pedestrian lateral force hybrid Van der Pol/Rayleigh model, this study investigates the interaction dynamic model of a pedestrian-flexible footbridge lateral coupling system. A multi scale method is adopted to decouple the equation. The paper also studies the nonlinear dynamic response of the pedestrian-footbridge coupling system as well as the relationship between the lateral displacement of pedestrians and flexible footbridges, and the lateral interaction of the two variables. The results show that with the same frequency tuning parameters, when the mass ratio of pedestrians and footbridges is very small, the larger the mass ratio is, the larger the lateral response amplitude of pedestrians becomes. Conversely, when the mass ratio of pedestrians and footbridges is much larger, the larger the mass ratio is, the smaller the response amplitude becomes. When the natural frequency of a footbridge is larger, its Phase Angle becomes larger. As the lateral amplitude of pedestrians increases, the Phase Angle approaches zero. Moreover, regarding the variation of the Phase Angle between the interaction force and footbridge lateral vibration speed based on the lateral relative displacement of pedestrians, of which the variation range is (0, π ), as the pedestrians’ lateral amplitude increases, the Phase Angle approaches − π / 2 . The dynamic load coefficient varies linearly with the lateral amplitude of pedestrian vibrations.

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