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Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (4): 423-436.doi: https://doi.org/10.1007/s10483-014-1802-9

• 论文 • 上一篇    下一篇

Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

张智勇 陈予恕   

  1. School of Astronautics, Harbin Institute of Technology, Harbin 150001, P. R. China
  • 收稿日期:2013-03-08 修回日期:2013-06-13 出版日期:2014-04-09 发布日期:2014-04-01
  • 通讯作者: Zhi-yong ZHANG, Ph. D. E-mail:zhiyzhang@126.com

Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

 ZHANG Zhi-Yong, CHEN Yu-Shu   

  1. School of Astronautics, Harbin Institute of Technology, Harbin 150001, P. R. China
  • Received:2013-03-08 Revised:2013-06-13 Online:2014-04-09 Published:2014-04-01
  • Contact: Zhi-yong ZHANG, Ph. D. E-mail:zhiyzhang@126.com

PDF

960

被引次数

20

摘要：

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time (HB-AFT) domain technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

关键词: global response, stability, harmonic balance method with alternating frequency/time (HB-AFT) domain technique, fractional exponential nonlinearity

Abstract:

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time (HB-AFT) domain technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

Key words: stability, global response, harmonic balance method with alternating frequency/time (HB-AFT) domain technique, fractional exponential nonlinearity

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