基于社会力模型的人群-桥梁竖向动力耦合效应研究

针对越来越多的轻质柔性人行桥在随机人群荷载作用下的结构振动问题,为了能够获得更为真实、精细的振动响应,建立考虑人群-结构相互作用的随机人群荷载模型尤为重要。首先利用移动弹簧-质量-阻尼模型模拟单人的动力学行为,并基于社会力模型,建立人群的随机运动模型,进而建立考虑人群-结构耦合振动的随机人群荷载模型。根据任意时刻人行桥和随机人群动力平衡,建立随机人群-人行桥耦合振动的控制方程。利用状态空间法求解人行桥动力参数随随机人群运动的变化情况,利用振型分解法求解耦合振动控制方程,探讨考虑人群-结构耦合振动的随机人群荷载对人行桥模态以及振动响应的影响。分析结果表明耦合系统模态变化量随着人数增加而增加。行人随机性与人群-结构相互作用对轻质结构的竖向动力响应影响很大,故在计算轻质结构振动响应时不可忽略。相比于加速度峰值,均方根加速度能够弱化随机波动的干扰作用,因此也采用了1-s均方根加速度更合理地衡量了结构的振动响应。

Analysis on the vertical coupled dynamic effect of a crowd-bridge system based on the social force model

For more and more structural vibration problems of lightweight flexible footbridges under random crowd loading, it is particularly important to establish a stochastic crowd model considering the crowd-structure interaction in order to obtain more realistic and accurate vibration responses.A moving spring-mass-damping model was used to simulate the dynamical characters of a single pedestrian, and the movement model of a random crowd was established based on the social force model.Then a random crowd load model considering the crowd-structure coupled vibration was built.According to the dynamic balance of the pedestrian bridge and the random crowd at any time, the control equation for the coupled vibration of the crowd and the bridge was established.The variation of footbridge dynamic parameters in pace with the crowd motion was solved by the state space method and the control equation for the coupled vibration was solved by the mode decomposition method.The influence of random crowd load on the modal and vibration responses of the pedestrian bridge considering crowd-structure coupled vibration was discussed.The results show that the modal variation of the coupled system increases along with the increase of pedestrians.The pedestrian-structure interaction and pedestrian randomness are of marked effect on vertical dynamic responses so they should not be ignored while analysing the vibration of light-weight footbridges.Compared with the peak acceleration, the RMS acceleration can weaken the disturbance of random fluctuation, so 1-s RMS acceleration is more reasonable to be used in measuring structural vibration responses.