On the Dynamics of Pedestrians-Induced Lateral Vibrations of Footbridges

This chapter is concerned with the problem of the large horizontal oscillations induced on slender footbridges by the motion of pedestrians, a phenomenon which involves the synchronization between the motion of walkers and that of the bridge deck. We initially review the extensive technical and scientific literature, and then we focus on two models to detect numerically and analytically the phenomenon. A continuous-time bridge-pedestrians model initially developed by Strogatz et al. is improved to better understand some aspects of the underlying mechanical phenomena. We perform extensive parametric investigations by means of many numerical simulations. This permits to highlight the parameters which mainly affect the trigger and the development of the phenomenon of synchronous lateral excitations, thus allowing a good understanding of the physical event and an evaluation of the engineering reliability of the model. Then, in order to obtain analytical instead of numerical predictions, a nonlinear discrete-time model based on an appropriate ID map is considered. It is able to provide a reliable value of the number of pedestrians which trigger the synchronization, thus predicting the onset of instability which is also the onset of crowd synchronization. From a dynamical system point of view, the main result is that the model highlights how the phenomenon can be seen as a perturbation of a classical pitch-fork bifurcation, which is then shown to be the underlying dynamical event.