Stability analysis on pedestrian-induced lateral vibration of footbridges considering pedestrian stochastic excitation

The infamous incident of large lateral vibration on the London Millennium Bridge in 2000 reveals that divergence of instability exists in pedestrian-induced vibration: a small increase in the number of pedestrians will cause the amplitude of vibration of the footbridge to become divergent. Such divergence of an instability phenomenon has been proven to be caused by the interaction between the pedestrian and the footbridge, although the mechanisms still have not been clearly explored. Most existing models are based on deterministic methods or results of a single test, ignoring the obvious randomness in the pedestrian load. In fact, pedestrian load is a complex stochastic process characteristized by narrow-band, including the large intra-subject and inter-subject randomness, which cause the real pedestrian load to be significantly different from that of a deterministic case. A nonlinear stochastic model for footbridges considering the pedestrian-bridge interaction and the randomness among the pedestrian lateral load was proposed. The pedestrian lateral load was considered as a narrow-band excitation process caused by the intra-subject variability, and was divided into a static load independent of footbridge vibration and vibration amplitude-dependent load. Based on the Itô equations derived by the stochastic averaging method, the stochastic P-bifurcation and stochastic D-bifurcation were analyzed to gain the critical condition for triggering a large lateral vibration of footbridge. Finally, through the case study of the northern span of the London Millennium Bridge, the availability of the proposed method was confirmed and meaningful conclusions were obtained. © 2019, Engineering Mechanics Press. All right reserved.