水平可动边界下张紧悬索参数振动建模及其共振分析

闵光云; 刘小会; 周晓慧; 蔡萌琦; 易航宇

doi:10.13204/j.gyjzG20030204

水平可动边界下张紧悬索参数振动建模及其共振分析

doi: 10.13204/j.gyjzG20030204

闵光云^1,3,
刘小会^2,3, ,,
周晓慧³,
蔡萌琦⁴,
易航宇³

1. 中山大学中法核技术与工程学院, 广东珠海 519082;
2. 重庆交通大学, 省部共建山区桥梁及隧道工程国家重点实验室, 重庆 400074;
3. 重庆交通大学土木工程学院, 重庆 400074;
4. 成都大学建筑与土木工程学院, 成都 610106

基金项目:

国家自然科学基金项目（51308570，51808085）；重庆市研究生科研创新项目（CYS19240）。

详细信息

作者简介:
闵光云,男,1995年出生,博士研究生。

通讯作者:
刘小会,男,1981年出生,博士,副教授,硕士生导师,cqdxlxh@126.com。

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出版历程
- 收稿日期: 2020-03-02
- 网络出版日期: 2021-08-19

PARAMETRIC VIBRATION MODELING AND RESONANCE ANALYSIS FOR TENSION SUSPENSION CABLE UNDER HORIZONTAL MOVABLE BOUNDARY

1. Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China;
2. State Key Laboratory of Bridge and Tunnel Engineering in Mountain Areas, Chongqing Jiaotong University, Chongqing 400074, China;
3. College of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, China;
4. School of Architecture and Civil Engineering, Chengdu University, Chengdu 610106, China

摘要

摘要: 建立了水平可动边界下张紧悬索参数振动模型，基于哈密顿变分准则推导了该模型下拉索的偏微分振动方程，根据边界约束条件、模态叠加法以及Galerkin法将该偏微分方程转化为常微分方程。通过摄动法分析了悬索的共振模式，利用四阶Runge-Kutta法求解了不同共振模式下悬索的位移响应，并评估了不同共振模式下水平激励的频率对张紧悬索位移响应的影响，最后进行了算例分析。分析表明：1：1：1：1共振模式下x轴方向的位移仅为1：1：2：1共振模式下的31.25%，1：1：1：1共振模式下z轴方向的位移仅为1：1：2：1共振模式下的2.181%，1：1：1：1共振模式相比1：1：2：1共振模式较为安全；水平激励的频率因尽量远离面内的自振频率，以保障悬索的幅值处于安全区间。
- 可动边界 /
- 悬索 /
- 参数振动 /
- 共振 /
- 多尺度法
Abstract: The model of parametric vibration for tension suspension cable with horizontal movable boundary is established, and the partial differential vibration equation was derived by Hamilton Principles. According to the boundary constraint, modal superposition method, and Galerkin method, the partial differential equation was transformed into an ordinary differential equation. The modes about resonance of the ordinary differential equation were analyzed by the perturbation method, and the displacement responses of the tension suspension cable under different resonance modes were solved by using the fourth-order Runge-Kutta function. Finally, the safety of the two resonance modes was evaluated by a specific numerical example. The results showed that the displacement of the x-axis in the 1:1:1:1:1 resonance mode was only 31.25% of that in the 1:1:2:1 resonance mode, and the displacement of the z-axis in the 1:1:1:1:1 resonance mode was only 2.181% of that in the 1:1:2:1 resonance mode. The frequency of horizontal excitation was far away from the in-plane natural frequency as far as possible to ensure that the amplitude of the cable was in a safe range.
- moving boundary /
- cable /
- parametric vibration /
- resonance /
- method of multiple scales

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参考文献(22)

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