Model for the Lateral Vibration Of Footbridge Under the Parametric Resonance Stochastic Framework

The lateral vibration of footbridge is a complicated process governed by a number of coexisting mechanisms rather than a single one. So far, a number of models have been proposed. However, most of them are deterministic methods with ignoring the obvious randomness among the pedestrian load. On the basis of the parametric resonance model proposed by Piccard, a novel parametric resonance stochastic model is proposed, in which the narrow-band stochastic characteristic caused by the pedestrian intra-subject randomness is considered. Unlike the numerical simulation method that needs large amount of calculation, the proposed model is established in a theoretic framework of nonlinear stochastic vibration. Based on the Ito equations derived by the stochastic averaging method, the critical number of pedestrian needed to trigger large lateral vibration can be obtained by solving the stability problem. The case study of the Millennium Bridge confirms the effectiveness of the proposed model, and indicates that the proposed model is more suitable than the model proposed by Piccard.