摘要
基于Kirchhoff理论讨论端部受轴向压力作用的圆截面弹性螺旋杆的动态稳定性问题。以杆中心线的Frenet坐标系为参考系,建立用欧拉角描述的弹性杆动力学方程。杆的螺旋线平衡状态由方程的特解确定。基于静力学分析的结论,在动力学范畴内继续讨论轴向受压螺旋杆平衡状态的稳定性。在一次近似意义下证明了螺旋杆在空间域内的欧拉稳定性条件为时域内的Lyapunov稳定性条件。从而进一步认识Lyapunov和欧拉两种不同稳定性概念之间的相互关系。导出轴向受压螺旋杆弯扭耦合振动固有频率的近似解析表达式。
The dynamical stability of an elastic helical rod with circular cross section under axial compression was discussed on the basis of Kirchhoff's dynamical analogy. The dynamical equations of the rod described by Euler's angles were established in the Frenet coordinates of the centerline. The helical equilibrium states were determined by the special solutions of the differential equations. Based on the conclusions of statical analysis, the discussion on the stability of helical equilibrium of the rod under axial compression was continued in the category of dynamics. It was proved in the sense of first approximation that Euler's stability condition of the helical rod in the space domain in Lyapunov's stability condition in the time domain. Then the relationship between different concepts of Lypunov's and Euler's stability can be further understood. The free frequency of flexural/torsional vibration of the helical rod under axial compression was derived in analytical form approximately.
出处
《力学季刊》
CSCD
北大核心
2006年第2期190-195,共6页
Chinese Quarterly of Mechanics
基金
国家自然科学基金资助项目(No.10472067)