Control for the lateral vibration of footbridges induced by pedestrians

This paper presents a nonlinear analysis for the motion of equations proposed by Nakamura [8] to predict the lateral vibration induced by pedestrians on footbridges, in which the influence of crowd on the footbridge is considered as a velocity feedback with a time delay to it. The relationship between the lateral vibration of footbridge and the coefficients in Nakamura´s model, including the rate of a pedestrian´s lateral force, pedestrian density, rate of synchronized pedestrians, and pedestrians´ attitude to large vibration amplitude, is revealed. The influence of time delay on the dynamics of the footbridge is discussed. Our results show that time delay always prevents the lateral vibration of the footbridge, which is demonstrated by the numerical simulations.