On a model for the pedestrians-induced lateral vibrations of footbridges

Critical threshold and underlying dynamical phenomena in pedestrian-induced lateral vibrations of footbridges

“…Expression (35) is the same one obtained in [Lenci and Marcheggiani 2008] with a different model, and agrees with the predictions of the more sophisticated SAMEO model studied in [Marcheggiani and Lenci 2010]. The fact that it is a result of two different models supports its reliability.…”

“…• g > 0 is the dimensionless amplitude, such that G = gK ∼ = 30N is the maximum lateral force exerted by a pedestrian [Belli et al 2001;Marcheggiani and Lenci 2010];…”

“…where we have assumed 4ξ 2 − 4ξ 4 ∼ = 4ξ 2 due to the smallness of ξ , and where we remember that G av ∼ = 30N [Belli et al 2001;Marcheggiani and Lenci 2010].…”

“…have been the first, to the best of our knowledge, to mathematically describe and predict the simultaneous growth of bridge movement and crowd synchronization, an observation that was unexplained in previous models but that is confirmed by analyses of video footage [Arup 2000] recorded during overcrowding conditions on real footbridges [Fujino et al 1993;Dallard et al 2001a]. They proposed a model (called SAMEO in [Marcheggiani and Lenci 2010] from the initials of the authors) which is particularly interesting for its contribution to the physical-mathematical explanation of the underlying mechanical event, as well as for the reasonable description of the phenomenon itself.…”

“…The SAMEO model has been investigated in depth in [Marcheggiani and Lenci 2010], where extensive numerical simulations have been performed in order to detect the effects of the main parameters on the system's response, in particular on the critical threshold. Various extensions have been proposed to model some important aspects not considered in [Strogatz et al 2005], such as, for example, the self-interaction between pedestrians.…”