Nonlinear Analysis for the Lateral Vibration of Footbridges Induced by Pedestrians
Publication: Journal of Bridge Engineering
Volume 18, Issue 2
Abstract
In this paper, the factors and variables that affect the amplitude of the lateral vibration of the footbridge induced by pedestrians in Nakamura’s model are investigated in the aspect of nonlinear dynamics. Nakamura’s model is based on the motion of equations including coefficients of the rate of a pedestrian’s lateral force, the pedestrian density, the rate of synchronized pedestrians, the function describing how pedestrians synchronize with the bridge natural frequency, and the pedestrians’ attitude to large vibration amplitude. The important coefficient cannot be decided in this model because of the lack of data available on the lateral load behaviors of walking people. Nakamura assumed that in his model by considering that pedestrians are most likely to synchronize at the bridge frequency around 1.0 Hz. The analysis results presented in this paper demonstrate that the amplitude of the lateral vibration increases when the function increases. This suggests may not be the worst case scenario for the lateral vibration of footbridges. Assuming may be one reason why most of the predicted results of Nakamura are on the large side. Through modifying Nakamura’s model, an equation of motion including the time delay of the interaction between the pedestrians and the footbridge is proposed to preferably agree with the measure data. The analysis shows that the amplitude of the lateral vibration of the footbridge decreases as the time delay increases. The ignored time delay of the interaction between pedestrians and the footbridge in Nakamura’s model is another reason why the numerical results of Nakamura are larger than the measured data. From the analysis, appropriately increasing the time delay of the interaction between pedestrians and the footbridge is a possible way to reduce the lateral vibration induced by pedestrians.
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Acknowledgments
The authors thank the reviewers for valuable suggestions to improve the paper, the National Natural Science Foundation of China (Grant No. 11002103), the State Key Program of National Natural Science of China (Grant No. 11032009), the National Science Foundation for Distinguished Young Scholars of China (Grant No. 10625211), the China Postdoctoral Science Fund (Grant No. 20100480888), and the Fundamental Research Funds for the Central Universities (Grant No. 2010-IV-019).
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Published In
Journal of Bridge Engineering
Volume 18 • Issue 2 • February 2013
Pages: 122 - 130
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Feb 15, 2011
Accepted: Sep 22, 2011
Published online: Sep 26, 2011
Published in print: Feb 1, 2013
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