弹性细杆的混沌形态

讨论端部受扭矩作用的非圆截面弹性杆平衡形态的混沌现象.混沌的产生来源于抗弯刚度的微幅周期变化.基于Kirchhoff动力学比拟理论列写弹性杆的平衡方程.应用Melnikov方法的解析预测以及Poincar啨截面和相轨?氖导扑阒っ鞯愿司哂蠸male马蹄意义下的混沌形态.给出混沌性态与规则性态所对应弹性杆几何形状的对照.

Chaotic configuration of a thin elastic rod

This paper discussed the chaotic phenomenon of equilibrium of a thin elastic rod with noncircular cross section under the action of torques on both ends. The equilibrium equations of the rod were written on the basis of Kirchhoff's kinetic analogy. The chaos was caused by the small periodic variation of the bending stiffness of the rod. The Melnikov's method was applied to predict the existence of the chaos, and the Poincaré sections, as well as the phase trajectory were given as numerical verification. It was shown that the rod had a chaotic configuration in the sense of Smale horseshoe. The geometric shapes of the rod with chaotic and regular behavior are presented.