东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2012, Vol. 33 ›› Issue (5): 715-718.DOI: -

• 论著 • 上一篇    下一篇

原点反共振振动机1:3内共振动力学特性分析

李永强;李洁;刘杰;李小号;   

  1. 东北大学理学院;东北大学机械工程与自动化学院;
  • 收稿日期:2013-06-19 修回日期:2013-06-19 发布日期:2013-04-04
  • 通讯作者: -
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(51105066)

Analytic study on 1:3 internal resonance dynamics of driving point anti-resonant vibrating machine

Li, Yong-Qiang (1); Li, Jie (1); Liu, Jie (2); Li, Xiao-Hao (2)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110819, China; (2) School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China
  • Received:2013-06-19 Revised:2013-06-19 Published:2013-04-04
  • Contact: Li, Y.-Q.
  • About author:-
  • Supported by:
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摘要： 针对原点反共振振动机的力学模型,在考虑了立方非线性弹簧及弹簧静变形等因素后,建立二阶非线性系统动力学控制方程.由此得到系统产生内共振的条件并应用多尺度法建立了平均方程,研究了不同结构参数对系统非线性动力学特性的影响.研究结果表明:当激振力频率小于反共振频率时,非线性的影响可以忽略不计;当大于反共振频率时,非线性的影响增强,振幅出现分叉,并且这种影响随着激振力频率与反共振频率的偏离程度的增大而加强.

关键词: 反共振, 内共振, 非线性, 动力学特性, 多尺度

Abstract: In consideration of the cubic nonlinear spring and spring static deformation, the dynamic control equations of second order nonlinear system were established for the mechanical model of driving point anti-resonant vibrating machines. The condition of the system producing internal resonance was obtained and the average equation was established with the multi-scale method. Moreover, the effects of different structural parameters on the nonlinear dynamics characteristics were studied. The results showed that the influence of nonlinear can be ignored when the exciting force frequency is smaller than the anti-resonant one, on the contrary, the influence can be enhanced and the amplitude appear bifurcation which becomes larger with the increasing difference between exciting force and anti-resonant frequency.

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