A New Model for Excessive Lateral Vibration of a Footbridge Induced by Pedestrians

Abstract

In this paper, a new model is proposed to describe the phenomena of the excessive lateral vibration induced by pedestrians walking on a flexible footbridge. The lateral vibration of footbridges is considered, in most existing literature, to be caused by the directly lateral forces induced by crowds on the footbridge. However, the vertical vibration of the mass centre of human bodies may also affect its lateral vibration because of the internal resonant between lateral and vertical modes. The lateral vibration of most footbridges is like a restricted pendulum, and the vertical vibration of human bodies excites the footbridge to vibrate laterally in a way of parametric excitation. This model was obtained by taking into account the parametric excitation between pedestrians and the footbridge. The model shows that when the number of pedestrians walking on the footbridge reaches a threshold, the equilibrium position of lateral vibration of the footbridge loses its stability and the amplitude of the lateral vibration increases rapidly very quickly, which coincides with the observations of the London Millennium Bridge.