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力学与实践 ›› 2015, Vol. 37 ›› Issue (6): 683-685,697.doi: 10.6052/1000-0879-14-288

• 应用研究 • 上一篇    下一篇

跳跃振子平衡及其分岔的能量分析

励轲1, 陈立群1,2,3   

  1. 1. 上海大学上海市应用数学和力学研究所, 上海 200072;
    2. 上海大学力学系, 上海 200444;
    3. 上海市力学在能源工程中的应用重点实验室, 上海 200072
  • 收稿日期:2014-09-05 修回日期:2014-09-27 出版日期:2015-12-15 发布日期:2015-12-17
  • 通讯作者: 陈立群,教授.E-mail:lqchen@staff.shu.edu.cn E-mail:lqchen@staff.shu.edu.cn
  • 基金资助:

    国家自然科学基金项目(11232009)和上海市重点学科建设项目(S30106)资助.

AN ENERGY ANALYSIS OF EQUILIBRIUM AND BIFURCATION OF A SNAP-THROUGH OSCILLATOR

LI Ke1, CHEN Liqun1,2,3   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
    2. Department of Mechanics, Shanghai University, Shanghai 200444, China;
    3. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
  • Received:2014-09-05 Revised:2014-09-27 Online:2015-12-15 Published:2015-12-17

摘要:

用能量方法研究了跳跃振子的平衡与分岔.用势能驻值条件确定了平衡位置所满足的方程,通过势能极值判断平衡的稳定性.在不同的弹簧构型下,数值计算了平衡随系统弹性刚度和质量比变化的分岔图.结果表明,弹性刚度和质量比较小时,系统只有一个稳定平衡点和一个不稳定平衡点;刚度和质量比充分大时,系统分岔出一个新的稳定平衡点和一个新的不稳定平衡点.

关键词:

能量采集器|跳跃振子|平衡|分岔|稳定性分析

Abstract:

An energy analysis is carried out for a snap-through oscillator to study its equilibrium and the bifurcation. The equilibrium equation is established based on the principle of the potential energy, and the stability of the equilibrium configurations can be determined via the extreme values of the potential energy. For different configurations of the spring, the equilibrium configurations and their bifurcation are numerically determined through the ratio of the spring stiffness to the mass changes. The results demonstrate that there are a stable equilibrium configuration and an unstable equilibrium one under the condition of a small control parameter. As the control parameter increases to a critical value, an additional stable equilibrium configuration and an additional unstable equilibrium bifurcation appear.

Key words:

energy harvesting|snap-through oscillator|equilibrium|bifurcation|stability analysis

中图分类号: 

  • O32