Abstract
In this paper, to investigate the lateral vibrations of a footbridge under crowd excitation Nakamura’s model and its modified version are studied by using the energy method. The periodic solutions of Nakamura’s model and its modified version are obtained analytically, the efficiency of which is demonstrated by comparing with numerical results. Our analytical solutions are very convenient to apply to the structural calculation and design of footbridges. Our analysis shows that the introduction of the time delay of interaction between pedestrians and the bridge in Nakamura’s model makes the model accord better with the measurement data. From the modified Nakamura’s model, the increase in the time delay decreases the lateral amplitude of a footbridge under crowd excitation, which suggests us that increasing the time delay of the interaction between pedestrians and the bridge maybe a new approach to reduce the lateral vibrations of a footbridge. In addition, our calculations indicate that delay differential equations can be solved more simply by using the energy method than the Galerkin method.
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Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11472160, 11302126, 11272236 and 11572224). We appreciate the referees for their valuable suggestions and questions.
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Zhen, B., Xu, J. & Song, Z. Lateral periodic vibrations of footbridges under crowd excitation. Nonlinear Dyn 86, 1701–1710 (2016). https://doi.org/10.1007/s11071-016-2987-7
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DOI: https://doi.org/10.1007/s11071-016-2987-7