Pedestrian-structure synchronisation : application to swaying footbridges

Recently, the interest of researchers for the study of lateral oscillations of footbridges caused by pedestrian activity has increased. Numerous theoretical models found in literature try to reproduce the phenomenon while stressing the phenomenon of synchronization between pedestrians and the footbridge. However, the majority of these publications could not place the problem in a rigorous mathematical and physical form or neglect to study the behaviour of the pedestrians themselves. We propose here a continuous crowd-structure model which allows for the modelling of the lateral oscillations of the bridge and the behaviour of the crowd, taking into account the synchronization. Certain characteristics of the phenomenon can be determined using analytic development. A thorough numerical work supports an implementation of the model by limiting numerical errors. Application to real footbridges allows for a better understanding and a correct representatlon oftheir behaviour.