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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 5967491, 12 pages
Research Article

Nonlinear Stochastic Analysis for Lateral Vibration of Footbridge under Pedestrian Narrowband Excitation

School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, China

Correspondence should be addressed to Yu Xiao-lin

Received 11 March 2017; Revised 14 May 2017; Accepted 7 June 2017; Published 9 July 2017

Academic Editor: Roman Lewandowski

Copyright © 2017 Jia Bu-yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


During the lateral vibration of footbridge, the pedestrian lateral load shows two distinct features: one is the vibration-dependency; another is the narrowband randomness caused by the variability between two subsequent walking steps. In this case, the lateral vibration of footbridge is actually a complicated, nonlinear stochastic system. In this paper, a novel nonlinear stochastic model for lateral vibration of footbridge is proposed, in which a velocity-dependent load model developed from Nakamura model is adopted to represent the pedestrian-bridge interaction and the narrowband stochastic characteristic is considered. The amplitude and phase involved Itô equations are established using the multiscale method. Based on the maximal Lyapunov exponent derived from these equations, the critical condition for triggering a large lateral vibration can be obtained by solving the stability problem. The validity of the proposed method is confirmed, based on performing the case studies of two bridges. Meanwhile, through parameter analysis, the influences of several crucial parameters on the stability of vibration are discussed.