Multi-Agent Simlation Based Study On Pedestrian-Footbridge Coupling Vibration

In modern cities,footbridges have become an important walking facility.With the increasing maturity of engineering technology,footbridges have a large-span,lightweight development trend,and their natural vibration frequencies have dropped significantly,even within the pedestrians’walking frequency range.When there are many pedestrians,the synchronization of pedestrian-footbridge system may be triggered,resulting in large lateral vibrations.The large lateral vibration of the footbridge will reduce the walking comfort of the pedestrians,and even cause riots and vicious accidents such as pedaling and falling into the water.This thesis designed a single-degree-of-freedom vibration platform,with which a series of walking experiments were conducted to reproduce the dynamic process of pedestrian-footbridge coupling vibration.The relationship between pedestrian’s motion characteristics and lateral vibration of the footbridge was analyzed.The results showed that during the pedestrian walking process,the lateral walking force will provide the footbridge with power for lateral displacement,and the lateral vibration of the footbridge will in turn affect the pedestrians’gait.The interaction between the pedestrians and the footbridge makes pedestrian’s lateral frequency gradually deviate from his natural walking state and approach the lateral vibration frequency of the footbridge,which finally reaches a nearly synchronization state.In this process,there is a certain phase difference between the pedestrian’s lateral swing and the footbridge’s lateral vibration,which achieve relative motion.When the lateral frequency of the pedestrians is close to the frequency of the lateral vibration of the footbridge,it will cause a large lateral vibration of the footbridge.Under the influence of large lateral vibrations,the step length of pedestrians generally decreases,the step width becomes larger,and the time for bipedal support becomes longer.Lateral vibrations greatly affect pedestrians’walking balance,so pedestrians choose to walk with more cautious gait.There is a linear relationship between the step length and the velocity of a pedestrian,whether walking in a normal gait or in a lateral vibration environment.In addition,the research results also showed that the lateral vibration amplitude affects the linear relationship between the step length and the velocity:the larger the lateral amplitude,the constant the slope and the smaller the intercept.Summarizing the experimental results and related research results,this paper established a pedestrian-footbridge coupled vibration model based on multi-agent and conducts simulation analysis.The pedestrian’s phase difference dθ/dt is proposed as a criterion for the synchronization status of the pedestrian-footbridge system,and the pedestrian’s phase difference dθ/dt is used to find limit value of the order parameter R to indicate the synchronization status,i.e.,R=0.4,which can be used for the quick judgment of synchronization status.On this basis,the effects of changes in the state parameters of the footbridge agent and pedestrian agent on the dynamic state of the pedestrian-footbridge system were discussed,and the following conclusions were obtained:（1）Pedestrian arrival rate is quantified by t_brⁱ⁺¹（the interval time between two neighboring pedestrians going up the footbridge）.The larger value of t_brⁱ⁺¹ indicates that the pedestrian flow is smaller.The change in pedestrian flow will affect the critical number.For the t_brⁱ⁺¹ obeying the Poisson distribution P（?）,when the pedestrian flow is smaller,the critical number decreases,but at the same time the time to reach synchronization gradually increases.When the pedestrian flow is smaller than a certain value（?>0.4）,the pedestrian-footbridge system will not synchronize.（2）The value of C is used to quantify the sensitivity of the pedestrian to the amplitude and vibration phase of the footbridge.The larger value of C,the more sensitive the pedestrian is to the amplitude and vibration phase of the footbridge.As the value of C is larger,the critical number is smaller,because once a pedestrian is more sensitive to vibration,it is more susceptible to it,and the more disadvantageous is the structural stability.When the value of C is smaller than 8,synchronization will not occur in the pedestrian-footbridge system.（3）In the case of ensuring the ratio of the basic parameters of the footbridge agent,as the length of the footbridge increases,the critical number increases linearly,indicating that simply increasing the length of the footbridge will not bring unstable effects to the footbridge.（4）With a slight increase in the damping ratio,the critical number of people can be greatly improved.When the damping ratio is larger than 0.012,the critical number is larger than the number of people who can accumulate on the footbridge under certain arrival rate(t_brⁱ⁺¹ obeys the Poisson distribution P（?）,?=0.25),and the synchronization of pedestrian-footbridge system will not occur.（5）The phenomenon of hysteresis loop was found.That is,when the direction of the changes of crowd size is different,there is a lag between triggering the large lateral vibration of the footbridge and the large lateral vibration dissipation.The critical number of the weakening of large lateral vibration is much smaller than the large lateral vibration was triggered.Therefore,to avoid the occurrence of large lateral vibrations,on the one hand,we must strictly control the size of the crowd on the footbridge by controlling the pedestrian flow,which should not exceed the critical number.Reducing the size of the crowd on the footbridge when it triggered large lateral vibration is not a good way to ensure the safety of the system.On the other hand,we can certainly increase the damping ratio during design,or design some auxiliary facilities to help pedestrians reduce the sensitivity of the lateral vibration of the footbridge,which can provide pedestrians with a safer walking environment.In the process of design and management,the completed footbridge with the same proportion of basic parameters of the footbridge can be used as a reference.