Hybrid Model for Pedestrian-Induced Lateral Vibrations of Footbridge Based on Pedestrian Phase Evolution and Inverted Pendulum Model: Simulation and Validation

Abstract

The inverted pendulum model is currently a widely accepted pedestrian lateral force model in the study of pedestrian-induced lateral vibration. The inverted pendulum model proposes that pedestrians walking on a laterally vibrating structure maintain their balance and comfort by adjusting their lateral foot position rather than their stride frequency. In other words, the stride frequency of a pedestrian is unaffected by the lateral vibration of the structure. This viewpoint directly contradicts the synchronization theory, which suggests that pedestrians adjust their stride frequency to adapt to the lateral vibration of the structure. The observed phenomenon of phase drift in Bocian's experiments provided validation for the effectiveness of the inverted pendulum model. However, the simultaneous observation of phase pulling indirectly refuted the underlying assumption of the inverted pendulum model: that pedestrians' stride frequency remains unaffected by the lateral vibration of the structure. Bocian's experimental findings shattered the artificial boundary between the inverted pendulum model and the synchronization theory, indicating the existence of a hybrid mechanism in the pedestrian lateral force model. Regrettably, to date, no specific model for this hybrid mechanism has been developed. This study employs the Kuramoto model to describe the phase evolution of a pedestrian under the influence of structural lateral vibration. Based on the traditional inverted pendulum model (IPM), the phase evolution inverted pendulum model (PE-IPM), which takes into account the adjustment of pedestrian lateral stride frequency (or stride time), is developed to explain the potential hybrid mechanism in the pedestrian lateral force model. To validate the effectiveness of PE-IPM, detailed comparisons are made between its numerical simulation results of pedestrian lateral gait and Bocian's experimental findings, the results of which are in good agreement. The validation demonstrates that PE-IPM can capture the detailed characteristics of pedestrian lateral gait well and effectively address the issue of an underestimated equivalent damping coefficient in IPM, confirming that PE-IPM can be used as an improved pedestrian lateral force model for further investigations into pedestrian-induced lateral vibration.