人行天桥动力特性参数时变性分析及其TMD减振控制

人行天桥动力特性是影响桥上行人舒适度的主要因素。针对随机人群行走对人行天桥模态阻尼比和模态频率的影响,考虑人-人相互作用的行人步态主被动调整策略,基于考虑行人同步率的随机人群集中模型,推导了随机人群-人行天桥-TMD系统的耦合动力方程,分析了人行天桥动力特性参数时变规律,提出了基于人行天桥动力特性参数时变的TMD减振设计方法。结果表明:考虑人-人相互作用时,在随机人群行走下,人行天桥一阶瞬时阻尼比随人群密度的增大而大幅提高,提高的幅度与人行天桥基频和模态质量呈正相关;在随机人群行走下,人行天桥一阶瞬时频率随人群密度的增大而不断下降,降低的幅度与人行天桥基频呈负相关。基于人行天桥动力特性参数时变的减振设计方法能有效地减小单人定频行走、单人随机行走和随机人群行走下结构的竖向振动响应,其中0.6人/m²随机人群行走工况下,人行桥竖向振动加速度减振率达到72%。

Analysis of time-varying dynamic characteristic parameters of footbridge and TMD vibration control

Dynamic characteristics of footbridge are the main factors that affect the comfort level of pedestrian on the bridge. Based on the influence of random crowd walking on modal damping ratio and modal frequency of pedestrian bridge, considering the active and passive gait adjustment strategy of human-human interaction, a stochastic crowd concentration model dependent on the pedestrian synchronization rate was established. The coupling dynamic equation of random crowd-footbridge-TMD system was deduced. The time-varying law of dynamic characteristic parameters of footbridge was analyzed. The TMD vibration control design method based on time-varying dynamic characteristic parameters of footbridge was proposed. The results show that the first instantaneous damping ratio of the footbridge increases greatly with the increase of the crowd density under random crowd walking when the human-human interaction is considered, and the increment is positively correlated with the fundamental frequency and modal quality of the footbridge. The first instantaneous frequency of the footbridge decreases continuously with the increase of the crowd density under random crowd walking, and the decrement is negatively correlated with the fundamental frequency of the pedestrian bridge. The time-varying dynamic characteristic parameters of the footbridge based on vibration control design method can effectively reduce the vertical vibration response of single person walking at fixed frequency, single person randomly walking and random crowd walking. Under the case of 0.6 person/m² random crowd walking, the reduction rate of vertical footbridge vibration acceleration reaches 72%.