Pedestrian-Induced Bridge Instability: The Role of Frequency Ratios

The emergence of the pedestrian-induced bridge instability is conventionally associated with crowd synchrony; however, this view has been challenged. In this paper, we use a bio-mechanical pedestrian model in the form of an active inverted pendulum to analyze the average contribution of a single pedestrian to possibly uncorrelated crowd dynamics and bridge oscillations. We obtained that depending on the ratio of the bridge vibration and walking frequencies, the pedestrian can amplify bridge vibration or, surprisingly, extract energy from the bridge and damp bridge oscillations. In particular, we show that different combinations of the bridge and pedestrian step frequencies corresponding to the same or close frequency ratios can trigger two drastically different bridge dynamics, with enhanced or suppressed oscillations far from the resonances.