A Suspension Footbridge Model under Crowd-Induced Lateral Excitation

Lijun Ouyang,Bin Ding,Tingting Li,Bin Zhen

doi:10.1155/2019/8058191

Lijun Ouyang, Bin Ding + Show 2 more

Open Access

https://doi.org/10.1155/2019/8058191

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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.

Highlights

It is observed that even if a footbridge is static at the beginning, excessive lateral vibrations still occur under crowd
There is no evidence that the structural characteristics of a footbridge have impact on dynamic interaction between pedestrians and the footbridge, McRobie et al [21] experimentally investigated the phenomenon of humanstructure lock in by using a section model consisting of two strings and a rigid body; Zhou and Ji [22] theoretically and experimentally analyzed dynamic characteristics of a generalized suspension system developed on the basis of the section model. eir research studies showed the parameters about strings have great influence on dynamic behaviour of the suspension system. is implies that we should not ignore structural characteristics in the analysis for mechanism of excessive lateral vibrations of suspension footbridges. e other motivation of our paper is to involve structural characteristic of the suspension bridge in the proposed model
E strings and the rigid body represent cables and bridge deck, respectively, as shown in Figure 1. e lateral force induced by crowd on the bridge here is expressed by a cosine function with random phase evaluating the effect of the moving bridge deck. e randomness of the phase reduces when the lateral bridge amplitude increases, because the swaying bridge always makes pedestrians synchronize with the moving deck

Summary

The Section Model for a Suspension Footbridge

O1A, O2B represent the cables and AB the bridge deck. Two symmetrically inclined cables are viewed as strings with in nite axial sti ness but without mass and transverse sti ness, and the bridge deck is simpli ed as a rigid body. E lengths of O1A and O2B both are L1; the width, mass, and lateral damping of AB are 2L2, M, and CL, respectively. The damping force applied on the bridge is assumed to be proportional to the lateral velocity of AB. E two inclined angles of the strings under gravity at static equilibrium state are the same and de ned by θ0; the rotations of the strings O1A and O2B are θ and ψ, respectively, when the bridge laterally sways. E lateral force induced by crowd is denoted by FL(t), which is assumed to act on point C

The Lateral Force Model of the Crowd Excitation

The Governing Equation

Conclusions