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受力螺旋作用的非圆截面弹性直杆的Lyapunov稳定性
引用本文:薛纭,陈立群.受力螺旋作用的非圆截面弹性直杆的Lyapunov稳定性[J].动力学与控制学报,2008,6(3):198-201.
作者姓名:薛纭  陈立群
作者单位:1. 上海应用技术学院机械与自动化工程学院,上海,200235
2. 上海大学力学系,上海,200444
摘    要:基于Kirchhoff动力学比拟思想,研究非圆截面压扭弹性细直杆的Lyapunov稳定问题.用Cardano角表示截面的姿态,根据Kirchhoff方程建立杆的平衡微分方程,得到了两端受力螺旋作用时的直线平衡特解,导出了具有周期系数的线性化扰动方程,其周期与扭矩和杆长成正比,与抗扭刚度成反比,圆截面情形为其特例.用Floquet理论讨论了其Lyapunov稳定性,算例表明对于给定的弹性杆,扭矩和压力对稳定是有利的,而拉力是不稳定的主要因素.

关 键 词:压扭变形  弹性细杆  Kirchhoff方程  直杆  Lyapunov稳定性  Floquet理论
收稿时间:2008/1/26 0:00:00
修稿时间:2008/3/11 0:00:00

Lyapunov stability of a straight elastic rod with non circular cross section under force screw
Xue Yun and Chen Liqun.Lyapunov stability of a straight elastic rod with non circular cross section under force screw[J].Journal of Dynamics and Control,2008,6(3):198-201.
Authors:Xue Yun and Chen Liqun
Institution:1.Department of Mechanical Engineering;Shanghai Institute of Technology;Shanghai 200235;China;2.Department of Mechanics;Shanghai University;Shanghai 200444;China
Abstract:Lyapunov stability of an elastic rod with non circular cross section in straight equilibrium was studied based on the thought of Kirchhoff kinetic analogy in the paper.Expressing the attitude of a section of the rod by Cardano angles,the equilibrium differential equation was established in terms of Kirchhoff theory of the rod, and its special solution when two ends of the rod were acted by a pair of force screws was found which stands for straight equilibrium state.The linear perturbation equation with peri...
Keywords:axial and torsional deformation  thin elastic rod  Kirchhoff equation  straight rod  Lyapunov stability  Floquet theory  
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