非圆截面弹性细杆的平衡稳定性与分岔

本文研究存在初始曲率或挠率的非圆截面弹性细杆的平衡及稳定性问题，在两端受力矩单儿作用的条件下，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，文中对杆截面的对称性，以及杆的初始曲率和挠率对平衡状态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列态分岔现象。

Stability and Bifurcation of Equilibrium of a Thin Elastic Rod with Noncircular Cross-Section

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.