Research On Crowd-footbridge Coupled Vibration Based On Social Force Model

While carrying pedestrians,modern footbridges must also meet people’s artistic and aesthetic requirements for bridge architecture.Therefore,in recent years,footbridges have gradually developed towards the trend of large span,slenderness and light weight.The damping of the footbridge structure decreases as the mass decreases,and its resonance frequency also decreases.When it is close to the lateral swaying frequency of pedestrians,if the number of pedestrians reach a certain amount,it will result in large amplitude lateral vibration of the footbridge,which further threats pedestrians’ walking comfort and safety.In order to reproduce the crowd-footbridge coupled vibration phenomenon,this thesis selects the social force model as a basic model,takes the pedestrian’s walking velocity and dynamic step frequency as the coupling input parameter,and establishes a crowd-footbridge coupled vibration model.The interaction between pedestrians and footbridges,as well as the dynamic characteristics of the crowd-footbridge model have been analyzed under different crowd sizes.The results show that for the low pedestrian density cases,the movement of pedestrians and the vibration of the footbridge show random features,the footbridge does not vibrate laterally and the crowd-footbridge system does not evolve into obvious synchronization characteristics.For high pedestrian density scenarios,the crowd-footbridge system shows obvious synchronized features,i.e.,large amplitude lateral vibration of the bridge can be observed.Base on the simulations results,it is proposed to use the pedestrian phase difference dθdt to define synchronization.By comparing the relationship between dθdt and the order parameter R,it was proposed to use the pedestrian phase difference when lower limit value R=0.6 as a criterion to determine synchronization in a quick way.It was also found that the pedestrian’s walking velocity and the phase difference dθdt show similar development trend.The pedestrian’s walking velocity decreases with the increase of crowd density,and finally tends to a constant value.On the basis of the proposed model,in order to find effective vibration reduction measures,the relevant parameters of the footbridge and pedestrian were controlled,the influence on the crowd-footbridge system was explored,and the critical number of people under the influence of different parameters was revealed.The results show that when the time interval between two pedestrians stepping onto the bridge one after another obeys the Poisson distribution,with the increase of mean,the critical number of pedestrians gradually decreases,however,the time to achieve synchronization tends to increase.When the mean step frequency of pedestrians is a constant,the larger the standard deviation,the smaller the dynamic response of the footbridge,and the longer it takes for the crowd-footbridge system to reach synchronization.If the interval time doesn’t change,the increasing of C meaning pedestrian sensitivity to the vibration of the footbridge,will result in almost the same critical number of pedestrian.However,the time required to achieve synchronization tends to decrease.When other parameters remain the same,the change of the initial phase distribution of control pedestrian has almost no effect on the crowd-footbridge system.When the ratio of the basic parameters of the footbridge remains unchanged,the change of controlling footbridge length will have an impact on the critical number of people.By changing the damping ratio of the structure,the additional damping will also change.As the damping ratio increases,critical pedestrian number show barely no difference,while the dynamic response of the footbridge gradually decreases,which prolongs the time for the footbridge to evolve into giant lateral vibrations.When the damping ratio≥1.5%,the crowd-footbridge system will not synchronize.Based on the above research findings,a method of placing temporary obstacles to control the crowd-footbridge vibration is proposed,and the effect of changing the size and placement of obstacles on the vibration of the footbridge is discussed.The results show that when the size of the obstacle remains unchanged,the vibration can be well-controlled when the obstacles were placed near the entrance of the footbridge.When the obstacle placed near the mid-span and the exit of the footbridge,the vibration amplitude cannot be efficiently controlled.Under this situation,with the increase of obstacle size,the critical number of people to trigger vibration and the dynamic response of the footbridge tend to increase,too.When placed near the entrance of the footbridge,the larger the size of the obstacle,the more obvious the vibration reduction effect on the crowd-footbridge system can be observed.When the obstacle size is 3m*2.0m,the average number of pedestrians and lateral acceleration are reduced by 39.8% and 86.5%,respectively,and the average amplitude reduced by 86.7%compared with the absence of obstacles.In addition,the lateral displacement of the footbridge gradually decreases,but the time for the footbridge to undergo a large lateral vibration gradually increases,indicating that increasing the size of the obstacle can prolong the time the crowd-footbridge system evolves into synchronization and control vibration.In summary,in the design and operation of the footbridge,in order to avoid the obvious synchronization of the crowd-footbridge system and the large lateral vibration of the footbridge,the damping ratio of the structure should be set large during the design stage,or some auxiliary equipment and facilities can be used to control the sensitivity of pedestrians to the dynamic response of the footbridge to a certain range.In addition,in the operational phase,during holidays or large-scale events,equipment and facilities such as seats,traffic cones or water horses can be used to build obstacles to temporary control the vibration and provide a safer walking environment for pedestrians.