摘要
本文研究存在初始曲率或挠率的非圆截面弹性细杆的干衡及稳定性问题。在两端受力矩单独作用的条件下,杆的平衡微分方程可转换为用欧拉角表述的一阶自治系统,并有可能利用相平面的奇点理论分析弹性细杆平衡状态的稳定性。文中对杆截面的非对称性,以及杆的初始曲率和挠率对平衡状态稳定性的影响进行了定性分析,导出了解析形式的稳定性判据,揭示了杆平衡状态的静态分岔现象。
The problem on equilibrium of a thin elastic rod with noncircular cross-section and with initial curvature or twisting is discussed in this paper. The differential equation of equilibrium of the rod subjected to torques on both ends can be transformed to an autonomous system of Eulerian angles. The stability and bifurcation of the equilibrium states of the rod are analysed by using the singularity theory of phase plane. A qualitative analysis for the influence of the asymmetry of the cross-section, as well as the initial curvature and twisting is given, some stability criteria in analytical form are derived, and a phenomenon of static bifurcation is shown.
出处
《力学季刊》
CSCD
北大核心
2001年第2期147-153,共7页
Chinese Quarterly of Mechanics
关键词
弹性细杆
平衡稳定性
奇点理论
静态分岔
elastic thin rod
stability of equilibrium
singularity theory
static bifurcation
