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Dynamic Analysis for Lateral Vibrations of Footbridges under Crowd Based on a Two-Degrees-of-Freedom Model

机译:基于两自由度模型的人群下人行天桥横向振动的动力分析

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摘要

Nakamura's model is widely used to describe lateral vibrations of a footbridge induced by crowd. The predicted responses of Nakamura's model were compared with measured data of T-bridge and M-bridge in Japan to demonstrate the validity. However, the predicted responses based on Nakamura's model almost always were stronger than measured data. Considering that both T-bridge and M-bridge are cable-stayed bridges, it seems to be not precise enough to simplify a cable-stayed bridge as a single degree of freedom system in Nakamura's model. In this paper, we establish a two-degrees-of-freedom model to describe lateral vibrations of a cable-stayed bridge. The cables have one degree, and the bridge deck has the other. Additionally, in this model we introduce a time delay in interaction between the bridge and pedestrians. By employing the center manifold theory, we find that a subcritical Hopf bifurcation occurs in the two-degrees-of-freedom model. We theoretically and numerically illustrate that the cables and time delay have significant influence on the lateral vibration amplitude of a footbridge under crowd. The appropriate increases of tension in the cables and time delay both can decrease the lateral vibration amplitude. The analysis for the proposed two-degrees-of-freedom model shows that the predicted responses of Nakamura's model can better agree with the measured date if we take the influence of cables and time delay into account.
机译:中村模型被广泛用于描述人群引起的人行天桥的横向振动。将中村模型的预测响应与日本T桥和M桥的测量数据进行比较,以证明其有效性。但是,基于Nakamura模型的预测响应几乎总是比实测数据强。考虑到T桥和M桥都是斜拉桥,在中村模型中将斜拉桥简化为单自由度系统似乎不够精确。在本文中,我们建立了一个两自由度模型来描述斜拉桥的横向振动。电缆具有一度,而桥面具有另一度。此外,在此模型中,我们引入了桥梁与行人之间互动的时间延迟。通过使用中心流形理论,我们发现在二自由度模型中发生了亚临界霍普夫分叉。我们从理论上和数值上说明,电缆和时间延迟对人群下人行天桥的横向振动幅度有显着影响。电缆中张力的适当增加和延时都会降低横向振动幅度。对所提出的两自由度模型的分析表明,如果考虑电缆和时延的影响,Nakamura模型的预测响应可以更好地与测量日期一致。

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  • 来源
    《Mathematical Problems in Engineering》 |2019年第4期|7452573.1-7452573.11|共11页
  • 作者单位

    Univ Shanghai Sci & Technol, Sch Environm & Architecture, Shanghai 200093, Peoples R China;

    Univ Shanghai Sci & Technol, Sch Environm & Architecture, Shanghai 200093, Peoples R China;

    Nanchang Hangkong Univ, Sch Civil Engn & Architecture, Nanchang 330063, Jiangxi, Peoples R China;

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