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不同索力斜拉索的主共振瞬时相频特性

邓正科 孙测世 杨汝东

邓正科,孙测世,杨汝东. 不同索力斜拉索的主共振瞬时相频特性 [J]. 应用数学和力学,2021,42(11):1126-1135 doi: 10.21656/1000-0887.420033
引用本文: 邓正科,孙测世,杨汝东. 不同索力斜拉索的主共振瞬时相频特性 [J]. 应用数学和力学,2021,42(11):1126-1135 doi: 10.21656/1000-0887.420033
DENG Zhengke, SUN Ceshi, YANG Rudong. Transient Primary Resonance Phase-Frequency Characteristics of Stay Cables With Different Tensions[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1126-1135. doi: 10.21656/1000-0887.420033
Citation: DENG Zhengke, SUN Ceshi, YANG Rudong. Transient Primary Resonance Phase-Frequency Characteristics of Stay Cables With Different Tensions[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1126-1135. doi: 10.21656/1000-0887.420033

不同索力斜拉索的主共振瞬时相频特性

doi: 10.21656/1000-0887.420033
基金项目: 国家自然科学基金(51808085)
详细信息
    作者简介:

    邓正科(1994—),男,硕士生(E-mail:1550487720@qq.com)

    孙测世(1985—),男,副教授,博士,硕士生导师(通讯作者. E-mail:suncs@hnu.edu.cn)

    杨汝东(1995—),男,硕士生(E-mail:1393977428@qq.com)

  • 中图分类号: U448.27; O322

Transient Primary Resonance Phase-Frequency Characteristics of Stay Cables With Different Tensions

  • 摘要: 考虑拉索垂度及几何非线性,研究了不同索力拉索的瞬时相频特性。利用斜拉索面内分布激励下的运动控制方程,采用多尺度法对微分方程进行摄动求解,分别得到面内、外主共振响应的近似解析式,再采用Hilbert变换得到响应与激励的瞬时相位差及其幅值。研究了不同索力下,响应与激励的瞬时相位差的变化规律及其原因。研究表明:面外主共振响应与激励间保持恒定的相位差,而面内响应与激励的瞬时相位差与索弹性参数和垂度等有关,微小的索力变化可能导致瞬时相频特性的明显改变。主要原因是面内响应的近似解中存在两倍频项和漂移项,前者使响应瞬时相位在单个周期内出现两次正负交替,后者决定面内响应与激励瞬时相位差的最大值及其变化规律。
  • 图  1  分布外激励下斜拉索振动简化模型

    Figure  1.  Simplified model of vibration of cable under distributed external excitation

    图  2  响应时程曲线

    Figure  2.  Response time history curves

    图  3  频谱图

    Figure  3.  Spectrum diagrams under different cable tensions

    图  4  瞬时相位差时程曲线

    Figure  4.  Time history curves of the transient phase difference

    图  5  pmaxH-Ωv平面投影

    Figure  5.  Projection of pmax in the H-Ωv plane

    图  6  pmax-Ωv曲线

    Figure  6.  The pmaxv curves

    图  7  pmax-H曲线(Ωv=1)

    Figure  7.  The pmax-H curve(Ωv=1)

    图  8  复平面投影曲线

    Figure  8.  Projection curves in the complex plane

    图  9  AvD复平面示意图

    Figure  9.  Illustration of AvD in the complex plane

    图  10  AvD$\beta $的变化曲线

    Figure  10.  Curves of AvD and $\; \beta$

    表  1  Normandie桥索参数

    Table  1.   Cable parameters of the Normandie bridge

    l/mm/(kg·m−1)H/kNA/m2E/Paθ/(°)C
    4401368 0001.53×10−21.9×101117.50.001
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-01-28
  • 修回日期:  2021-05-09
  • 网络出版日期:  2021-12-07
  • 刊出日期:  2021-11-30

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