A Suspension Footbridge Model under Crowd‐Induced Lateral Excitation

Abstract

In this paper, a plane pendulum model is proposed to investigate the lateral vibration of a suspension bridge under crowd excitation. The plane model consists of two strings and a rigid body, which represent cables and the bridge deck, respectively. The lateral force induced by crowd is expressed as a cosine function with random phase. Comparing with other existing pedestrian-footbridge interaction models, the proposed model has two features: one is that the structural characteristics of the suspension bridge are taken into account. The other is that the expression of the lateral force induced by crowd has a unified form for different lateral bridge amplitudes. By numerically analyzing the solution stability of the plane model, we exhibit the whole changing process how a suspension bridge increases its lateral amplitude from small to large. It is shown that the worst case occurs when the lateral natural frequency of the bridge is half the lateral step frequency of the pedestrians. Based on the analysis results, the plane pendulum model can be easily used to explain why the central span of the London Millennium Bridge has large lateral oscillations at about 0.48 Hz.

Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time‐Delay Effect

“…It is related to the number of pedestrians on the footbridge. Given that pedestrians will exert vertical and horizontal harmonic effects on footbridge during the walking process, the longitudinal harmonic forces show parametric excitations on the vibration of footbridge, such as the fourth term in equation (18). However, due to the limitation of pedestrian load, the parametric excitation of longitudinal load is considerably weak.…”

“…Resonance. e multi-scale approach is employed to solve equation (18). Since the pedestrian excitation frequency is not close to ω 1 , small parameters are applied into the damping term, parametric excitation term, and nonlinear term, and the following scaling transformations are given by…”

“…e analysis found that when the lateral frequency of the pedestrian load is twice the lateral natural frequency of the bridge, intense parametric vibration will occur [17]. Based on previous studies, Wang showed that the process of continuous walking can be regarded as a periodic process, which can be expressed in the form of a Fourier series [18]. In order to predict the effect of vertical pedestrian dynamics on footbridges, Bassoli proposed two simulation models to evaluate the structure's response to pedestrian loads [19].…”

Dynamic Analysis of Suspension Footbridges Using an Actual Pedestrian Load Model Compared with EUR23984 EN Requirements

“…Based on literature review, the research works conducted by researchers can be categorized into two main fields of investigation: (a) Interaction mechanisms between the pedestrians and the bridges (b) Characterizing the human body motions during passing the bridges As the first field, some significant studies and their results are as follows. A plane pendulum model was proposed in order to characterize the lateral lock-in phenomenon of the suspension footbridges under the crowd excitation, where the hangers are assumed as the rope and the bridge deck as the rigid body [4]. Also, as a result of a study, it is found out that the dynamic excitations induced by people walking together are not periodic but are narrow-band random phenomena and varies significantly not only among different people but also for a single person who cannot repeat two identical steps [5].…”