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.
Highlights
The vertical vibrations of a pedestrian-footbridge coupling have attracted considerable and increasing attention [1,2,3,4,5]
From Equation (58), it can be known that the absolute displacement amplitude of pedestrians is related to the following parameters: lateral response amplitude of the footbridge, relative displacement of pedestrians, Phase Angle, frequency difference, and the time of footbridge displacement, which in turn has nothing to do with the mass of the footbridge and pedestrians
This paper presents research on a pedestrians’ lateral force model of the hybrid Van der Pol/Rayleigh
Summary
The vertical vibrations of a pedestrian-footbridge coupling have attracted considerable and increasing attention [1,2,3,4,5]. Bocian considered pedestrians using a linear inverted pendulum model and studied the changes in parameters such as mass, damping, and force in the case of pedestrian-footbridge laterally coupled vibrations [15,16,17]. Among these studies, most researchers did not highlight the importance of pedestrians’ vibration responses, but focused on the vibration responses of the footbridge. Its vibration amplitude and frequency were assumed to be a constant value [18] In this case, this assumption is not reasonable because the lateral vibration response of pedestrians and footbridges interacts mutually. The study obtains a dynamic response of interactions between pedestrians and footbridges through an example
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