A Study on a Mechanism of Lateral Pedestrian-Footbridge Interaction

Abstract

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.

Experimental Evaluation of Pedestrian-Induced Multiaxial Gait Loads on Footbridges: Effects of the Structure-to-Human Interaction by Lateral Vibrating Platforms

“…The coupling effects of anthropic loads with the vibrations of pedestrian bridges are due to the adaptive [ 41 ], random [ 42 , 43 ], and nonstationary conditions of the human gait [ 17 , 44 ]. HSI effects in flexible surfaces are configured as an advanced case of synchronization and are composed of three main important aspects: changes in the dynamic properties of the structure due to pedestrians, Human-to-Structure Interaction (H2SI) [ 45 , 46 , 47 ]; interactions between pedestrians in crowds, Human-to-Human Interaction (HHI) [ 48 , 49 , 50 ]; and changes in the pedestrian gait due to the structure’s vibration, Structure-to-Human Interaction (S2HI) [ 18 , 19 , 43 , 51 , 52 ]. Although many researchers have concluded that studies and interest in these topics have increased considerably in recent decades, aspects related to the behavior of the loads induced by the human gait in response to structural vibrations have not been fully detailed or understood [ 9 , 53 ]; for example, the effects of structural vibrations on pedestrian-induced gait loads in vertical and lateral directions simultaneously.…”

Fast-Slow Coupling Dynamics Behavior of the van der Pol-Rayleigh System

“…After adjusting the amplitude and phase shift, the vibration absorption and energy collection tasks were completed. Chen et al [15] used the multi-scale method to decouple the van der Pol-Rayleigh equation and applied the discussion results to the dynamic model of the side-coupling system of a footbridge-a flexible footbridge.…”

Experimental and Numerical Study on Dynamics of Two Footbridges with Different Shapes of Girders

“…It also depends mainly on synchronization with the structure and with other pedestrians. The human-structure interaction (HSI) phenomena were widely investigated in the literature [67][68][69][70][71][72]. Therefore, it is not easy to develop one universal model describing human-induced load [73].…”