Study on nonlinear parametric vibration of footbridge considering time-lag effect

Abstract

Under the action of pedestrian dynamic load, a pedestrian bridge with large span and light flexibility will show the nonlinear characteristics of the structure, and there is a time lag phenomenon in the feedback of the pedestrian’s force on the pedestrian bridge. Therefore, based on the derivation of the nonlinear dynamic model of the parametric vibration of pedestrian bridge, the time lag effect is introduced. Taking the Millennium Bridge of London as an example, the influence of time-lag on parametric vibration of pedestrian bridge is analyzed. By using Galerkin method and multi-scale perturbation method, theoretical and numerical analysis of large vibration induced by parametric vibration and forced vibration of pedestrian bridge is carried out. The amplitude frequency curve of nonlinear parametric vibration with time-lag effect is obtained, and it is concluded that the time-lag of nonlinear parametric vibration in Millennium Bridge has no effect on the amplitude of the structure, but only affects the peak arrival time and the time of stable amplitude. And the conclusion is proved by the numerical analysis.