title: Bistable gaits and wobbling induced by pedestrian-bridge interactions.
abstract: 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.
authors.affiliation: Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, Georgia 30303, USA.
authors.forename: Igor V
authors.initials: IV
authors.lastname: Belykh
authors.affiliation: Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, Georgia 30303, USA.
authors.forename: Russell
authors.initials: R
authors.lastname: Jeter
authors.affiliation: Department of Control Theory, Lobachevsky State University of Nizhny Novgorod, 23, Gagarin Ave., Nizhny Novgorod 603950, Russia.
authors.forename: Vladimir N
authors.initials: VN
authors.lastname: Belykh