Research On Human-induced Lateral Vibration Of Footbridges Under Different Pedestrian Models

Due to the use of new materials and more advanced construction and design methods,footbridges gradually develop to be light and flexible.However,under the dynamic excitation of pedestrians,excessive vibration is easy to occur,which may decrease of pedestrian comfort,cause economic losses.In recent years,many models of lateral pedestrian force have been proposed,but their vibration mechanism and response results are different.In this thesis,the lateral force model,the lateral inverted pendulum model,and the lateral Spring-Mass-Damping model(SMD model)are used respectively,with the Millennium Bridge as the main calculation example.At the same time,several other bridge examples are analyzed for lateral human-induced vibration.The main contents and conclusions are as follows:(1)Conducted the human induced vibration analysis under the lateral moving force model.Derived the motion equations of the bridge during the process of single pedestrain crossing the bridge,multiple pedestrains standing on the bridge,and multiple bridge getting on and off the bridge.The theoretical solution of human induced lateral vibration is obtained using Duhamel integral.It is found that due to the absence of the human bridge interaction,the vibration response increases linearly with the increase of the number of people;(2)The human induced lateral vibration analysis of the footbridge under the rigid ground inverted pendulum-R model and the vibrating ground inverted pendulum-V model was conducted using the Runge-Kutta method and Newmark-βmethod under different working conditions,respectively.The structural responses of the inverted pendulum-R model are the same as the harmonic force model.The inverted pendulum-V model contains self-excited components,and pedestrians are equivalent to additional mass and damping.When the additional negative damping exceeds the structural damping of the bridge,or the pedestrian input work continues to exceed the structural dissipated work,the response diverges and the bridge becomes unstable,but human-bridge resonance or pedestrians synchronization is not a necessary condition for lateral instability of the bridge;(3)Considering the pedestrian-footbridge interaction,the pedestrian-footbridge coupling dynamic equation under the lateral SMD model is established using Newmark-β.Under the SMD model,the vibration response increases nonlinearly as the number of people increases,with a larger increase when the number of people is small,and a slower increase when the number of people is large.Applying loads to the elastic mass is more realistic;(4)The main differences between the force model,the inverted pendulum-V model,and the SMD model are: the force model does not consider the human-bridge interaction,and the results under the pedestrians force model can be linearly superimposed;The inverted pendulum-V model has self-excited characteristics,which can better predict the lateral instability of bridges;The SMD model cannot simulate bridge instability through response divergence,but based on the pedestrian lateral SMD correction model and the suggested formula for synchronization probability proposed in this article,a relatively accurate maximum vibration response can be obtained,which is in good agreement with the measured data of several actual bridges.