Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (1): 27-36.doi: https://doi.org/10.1007/s10483-013-1650-9

• 论文 • 上一篇    下一篇

Neimark-Sacker (N-S) bifurcation of oscillator with dry friction in 1:4 strong resonance

郭勇,谢建华   

  1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China
  • 收稿日期:2012-03-30 修回日期:2012-05-12 出版日期:2013-01-03 发布日期:2013-01-03
  • 通讯作者: 谢建华 E-mail:jhxie2000@126.com
  • 基金资助:

    the National Natural Science Foundation of China (No. 11172246) and the Fundamental Research Funds for the Central Universities of China (No. SWJTU11ZT15)

Neimark-Sacker (N-S) bifurcation of oscillator with dry friction in 1:4 strong resonance

Yong GUO, Jian-hua XIE   

  1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China
  • Received:2012-03-30 Revised:2012-05-12 Online:2013-01-03 Published:2013-01-03
  • Contact: Jian-hua XIE E-mail:jhxie2000@126.com
  • Supported by:

    the National Natural Science Foundation of China (No. 11172246) and the Fundamental Research Funds for the Central Universities of China (No. SWJTU11ZT15)

摘要: An oscillator with dry friction under external excitation is considered. The Poincar´e map can be established according to the series solution near equilibrium in the case of 1:4 resonance. Based on the theory of normal forms, the map is reduced into its normal form. It is shown that the Neimark-Sacker (N-S) bifurcations may occour. The theoretical results are verified with the numerical simulations.

关键词: analytical mechanics, nonholonomic system, inverse problem

Abstract: An oscillator with dry friction under external excitation is considered. The Poincar´e map can be established according to the series solution near equilibrium in the case of 1:4 resonance. Based on the theory of normal forms, the map is reduced into its normal form. It is shown that the Neimark-Sacker (N-S) bifurcations may occour. The theoretical results are verified with the numerical simulations.

Key words: analytical mechanics, nonholonomic system, inverse problem

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals