全部

力学与实践 ›› 2019, Vol. 41 ›› Issue (6): 649-652.doi: 10.6052/1000-0879-19-276

• 应用研究 • 上一篇    下一篇

流动环现象的动力学分析

刘延柱*, 1), 张伟伟   

  1. * 上海交通大学工程力学系,上海 200240;
    太原科技大学应用科学院力学系, 太原 030024
  • 收稿日期:2019-07-29 发布日期:2019-12-27
  • 通讯作者: 1) 刘延柱,教授,主要研究方向为动力学与控制。E-mail: liuyzhc@163.com

DYNAMICAL EXPLANATION ON TOROFLUX'S PHENOMENA

LIU Yanzhu*, 1), ZHANG Weiwei   

  1. * Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai, 200240;
    * Department of Mechanics, Taiyuan University of Science and Technology, Taiyuan 030024
  • Received:2019-07-29 Published:2019-12-27

摘要: 本文分析了流动环特殊现象的力学原理。流动环是由细长钢带缠绕形成的环状螺旋玩具,具有瞬间几何形态突变和绕圆柱物体运动时迅速旋转两种独特现象。文中利用封闭曲杆的拓扑学规律确定其曲率和扭率,用于计算和比较流动环两种平衡状态的弹性变形势能。证实流动环的形态突变源于最小弹性势能原理。以组成流动环的单个圆环为分析对象,且考虑邻近圆环的牵拉效应。分析了流动环下落时相对圆柱体的滚动过程,以解释旋转现象的产生原因。导出了流动环下落旋转的角加速度公式。理论计算结果与实验数据较好吻合。

关键词: 流动环, White公式, 双稳态系统, 最小势能原理, 纯滚动

Abstract: The dynamic analysis of the toroflux, a toy with torus-spring winded by a steel ribbon, is given in this paper. As two special phenomena, the toroflux can suddenly change its geometrical form, and can rotate rapidly in falling process around a cylindrical body. The topological character of a closed bent rod is applied to determine the curvature and twist of the toroflux, and the elastic potential energies of two different equilibrium states of toroflux are calculated and compared. Then the phenomena of its shape mutation can be examined by the principal of minimal elastic potential energy. Taking a circle ring as an element of the toroflux, and the stretching effect of adjacent rings is considered. The pure rolling of the ring on the cylinder in falling process is analyzed to examine the occurrence of rapidly rotation, and the angular acceleration of the toroflux in falling process is derived. The theoretical results coincide with the data by experiment.

Key words: toroflux, White's formula, bistability system, principal of minimal elastic potential energy, pure rolling

中图分类号: 

  • O39