Effects of Stochastic Excitation and Phase Lag of Pedestrians on Lateral Vibration of Footbridges

Incidents of pedestrian-induced large lateral vibrations of footbridges reveal the occurrence of an instability-type phenomenon in pedestrian-induced vibration. However, the mechanism involved has yet to be clearly explained. In this work, a novel model for predicting the lateral vibration of footbridges is proposed. Under an algebraic framework of nonlinear stochastic vibration, the narrow-band vibration caused by the pedestrian intra-subject randomness and the phase lag between the footbridge motion and the pedestrian load are considered. The critical condition that triggers the large lateral vibration of the footbridge is identified using the stochastic averaging method and the concept of stability based on the Lyapunov exponent. The validity of the proposed method is confirmed through case studies of three bridges. Through a parametric analysis, the effects of several crucial parameters on the stability/instability of vibration are discussed. Finally, conclusions are drawn regarding insights that can be useful to the future designs of footbridges.