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基于精确Cosserat模型的螺旋杆稳定性分析

刘延柱 薛纭

刘延柱, 薛纭. 基于精确Cosserat模型的螺旋杆稳定性分析[J]. 应用数学和力学, 2011, 32(5): 570-578. doi: 10.3879/j.issn.1000-0887.2011.05.007
引用本文: 刘延柱, 薛纭. 基于精确Cosserat模型的螺旋杆稳定性分析[J]. 应用数学和力学, 2011, 32(5): 570-578. doi: 10.3879/j.issn.1000-0887.2011.05.007
LIU Yan-zhu, XUE Yun. Stability Analysis of a Helical Rod Based on Exact Cosserat’s Model[J]. Applied Mathematics and Mechanics, 2011, 32(5): 570-578. doi: 10.3879/j.issn.1000-0887.2011.05.007
Citation: LIU Yan-zhu, XUE Yun. Stability Analysis of a Helical Rod Based on Exact Cosserat’s Model[J]. Applied Mathematics and Mechanics, 2011, 32(5): 570-578. doi: 10.3879/j.issn.1000-0887.2011.05.007

基于精确Cosserat模型的螺旋杆稳定性分析

doi: 10.3879/j.issn.1000-0887.2011.05.007
基金项目: 国家自然科学基金资助项目(10972143)
详细信息
    作者简介:

    刘延柱(1936- ),男,南京人,教授,博士生导师(联系人.E-mail:liuyzhc@online.sh.cn).

  • 中图分类号: O317;O343

Stability Analysis of a Helical Rod Based on Exact Cosserat’s Model

  • 摘要: 弹性杆的螺旋线平衡问题在DNA、纤维、海底电缆和输油管线等方面具有应用背景.Kirchhoff动力学比拟是分析弹性细杆平衡稳定性的有效方法.Kirchhoff模型中包括中心线无拉伸变形和截面无剪切变形的基本假定与生物大分子等软物质的实际状况有较大差异.基于精确Cosserat模型,考虑中心线的拉伸压缩变形和截面剪切变形,以及剪切变形引起杆中心线转动导致切线轴相对截面法线轴的偏离,以Euler角表达截面姿态,建立圆截面弹性杆的动力学普遍方程.在静力学范畴内讨论螺旋线平衡状态的Liapunov稳定性和Euler稳定性问题,导出稳定性条件及轴向力和扭矩的Euler临界值.证明螺旋杆平衡的静态Liapunov稳定性和Euler稳定性条件是动态Liapunov稳定性的必要条件.
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    [2] 刘延柱. 弹性细杆的非线性力学[M].北京: 清华大学出版社, Springer, 2006.(LIU Yan-zhu.Nonlinear Mechanics of Thin Elastic Rod[M]. Beijing: Tsinghua University & Springer, 2006.(in Chinese))
    [3] 刘延柱, 薛纭. 弹性细杆螺旋线平衡的动态稳定性[J]. 力学季刊,2005, 26(1): 1-7.(LIU Yan-zhu, XUE Yun. Dynamical stability of helical equilibrium of a thin elastic rod[J]. Chinese Quarterly of Mechanics, 2005, 26(1): 1-7.(in Chinese))
    [4] 刘延柱,盛立伟. 轴向受压螺旋杆的动态稳定性与振动[J]. 力学季刊,2006, 27(2): 190-195.(LIU Yan-zhu, SHENG Li-wei. Dynamical stability and vibration of an helical rod under axial compression[J]. Chinese Quarterly of Mechanics, 2006, 27(2): 190-195.(in Chinese))
    [5] 刘延柱,盛立伟. 圆截面弹性螺旋杆的稳定性与振动[J]. 物理学报,2007, 56(4):2305-2310.(LIU Yan-zhu, SHENG Li-wei. Stability and vibration of an elastic helical rod with circular cross section[J]. Acta Physica Sinica,2007, 56(4): 2305-2310.(in Chinese))
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出版历程
  • 收稿日期:  2011-02-21
  • 修回日期:  2011-03-23
  • 刊出日期:  2011-05-15

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