基于行人动力学模型的人桥竖向动力相互作用

基于行人动力学模型,研究了人-桥竖向动力相互作用。行人动力学模型采用以行人步频和体重表示的刚度-质量-阻尼(SMD)模型,人行桥假定为Euler-Bernoulli梁模型,建立人-桥竖向动力相互作用控制方程。采用状态空间法进行非比例阻尼系统瞬时模态的求解,得到系统的时变频率和阻尼比;利用变步长四阶五级Runge-Kutta-Felhberg算法求解时变控制方程,对比分析考虑人-桥竖向动力相互作用和只在人行荷载作用下人行桥的动力响应。结果表明:考虑人-桥动力相互作用,人行桥自振频率略有降低,阻尼有显著增大;当行人以人行桥的频率行走时,考虑人-桥竖向动力相互作用结构的动力响应比不考虑人-桥相互作用显著降低。

Pedestrian-bridge dynamic interaction in the vertical based on biodynamic model

The vertical dynamic interaction of pedestrian-bridge is studied by using biodynamic model. The biodynamic model adopts the stiffness-mass-damping (SMD) model expressed by pedestrian''s step frequency and weight, under the assumption that the foot bridge is of Euler-Bernoulli model, and the control equation of pedestrian-bridge dynamic interaction in the vertical is established. The state-space method is used to solve the instantaneous model of non-proportionally damped system, and the time-varying frequency and damping ratio are obtained. The time-varying control equation is determined by using variable step four-level-five-order Runge-Kutta-Felhberg algorithm, and the dynamic responses of pedestrian bridge were compared with considering pedestrian-bridge vertical dynamic interaction and under the action of the pedestrian load. The calculated results show that with considering the pedestrian-bridge dynamic interaction in the vertical, the frequency of the foot bridge is lowered slightly, and the damping is increased significantly. When pedestrians walk at the frequency of foot bridge, the dynamic response with considering the Pedestrian-bridge dynamic interaction in the vertical should be obviously lower than that without considering pedestrian-bridge interaction.