Calculation for the Critical Number of Pedestrians on a Footbridge by Using the Modified Nakamura’s Model

Abstract:

The problem of the critical number of pedestrians is significant in the study of lateral vibrations of footbridges since it can cause serviceability for the footbridges. By considering the pedestrians mass on the footbridge increases slowly, the modified Nakamuras model can be regarded as a fast-slow system which can be used to calculate the critical number of pedestrians. The influence of the time delay of interaction between pedestrians and the footbridge on the critical number of pedestrians is analyzed. Comparison with other results indicates the correctness of our formula predicting the critical number of pedestrians. Furthermore, our research suggests that the existence of the time delay can make the critical number of pedestrians less, which means that the time delay helps to improve the safety of the footbridge.

• Periodical: Applied Mechanics and Materials (Volumes 427-429)
• Pages: 408-411
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.427-429.408
• Online since: September 2013
• Authors: Rui Lin*, Bin Zhen, Zhong Yang Ren
• Keywords: Delayed Hopf Bifurcation, Fast-Slow Time-Delay System, Modified Nakamura’s Model

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