受拉扭弹性细杆超螺旋形态的定性分析

基于弹性杆的Kirchhoff模型讨论受拉扭弹性细杆的超螺旋形态.导出细长螺旋杆的等效抗弯和抗扭刚度.分析受拉扭弹性细杆的稳定性和分岔，且利用等效刚度概念将弹性杆的稳定性条件应用于对细长螺旋杆稳定性的判断.在扭矩不变条件下增加拉力至极限值时，直杆平衡状态失稳转为螺旋杆状态.继续增加拉力，直螺旋杆平衡状态失稳卷绕为超螺旋杆.从而对Thompson/Champney实验中受拉扭弹性细杆形成超螺旋形态的多次卷绕现象作出定性的理论解释. 关键词： 弹性细杆 Kirchhoff动力学比拟 等效刚度 超螺旋形态

Qualitive analysis of supercoiling configuration of a thin elastic rod under tension and twist

The supercoiling configuration of a thin elastic rod is discussed on the basis of Kirchhoff’s model. The equivalent twisting stiffness and bending stiffness of a thin helical rod are derived. The stability and bifurcation of a thin elastic rod under tension and twist are analyzed, and the results can be applied to determine the stability of a thin helical rod by use of the equivalent stiffness. In the case when the rod is under constant twist and increasing tension force the straight equilibrium can be unstable and transfers to helical equilibrium. When the tension force increases further the straight thin helical rod can be unstable and twins to a supercoiling state. Therefore the forming process of supercoiling configuration of a rod under tension and twist observed in Thompson/Champney experiment can be explained qualitatively.