Parametric resonance of flexible footbridges under crowd-induced lateral excitation

The excessive lateral sway motion caused by crowds walking across footbridges has attracted great public attention in the past few years. Three possible mechanisms responsible for such lateral vibrations have been investigated in the literature: direct resonance, dynamic interaction, and internal resonance. In this paper, starting from a critical review of the mechanisms proposed in the literature, a parametric excitation mechanism is analyzed, based on a forcing model whose amplitude is a function of deck oscillations. A stability criterion is identified, depending on the ratio between the structural and excitation frequencies, on the ratio of the structural and pedestrian masses, and on the structural damping. The proposed mechanism can be achieved for very flexible footbridges, with a lateral natural frequency around 0.5 Hz, corresponding to a half of the lateral walking frequency. This situation can occur in modern structures, such as in the case of the London Millennium Footbridge.