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Resonances of a Harmonically Forced Duffing Oscillator with Time Delay State Feedback

Publication ,  Journal Article
Hu, H; Dowell, EH; Virgin, LN
Published in: Nonlinear Dynamics
January 1, 1998

The paper presents analytical and numerical studies of the primary resonance and the 1/3 subharmonic resonance of a harmonically forced Duffing oscillator under state feedback control with a time delay. By using the method of multiple scales, the first order approximations of the resonances are derived and the effect of time delay on the resonances is analyzed. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. In order to numerically solve the problem of history dependence prior to the start of excitation, the concepts of the Poincaré section and fixed points are generalized. Then, a modified shooting scheme associated with the path following technique is proposed to locate the periodic motion of the delayed system. The numerical results show the efficacy of the first order approximations of the resonances.

Duke Scholars

Published In

Nonlinear Dynamics

DOI

ISSN

0924-090X

Publication Date

January 1, 1998

Volume

15

Issue

4

Start / End Page

311 / 327

Related Subject Headings

  • Acoustics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

Citation

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Hu, H., Dowell, E. H., & Virgin, L. N. (1998). Resonances of a Harmonically Forced Duffing Oscillator with Time Delay State Feedback. Nonlinear Dynamics, 15(4), 311–327. https://doi.org/10.1023/A:1008278526811
Hu, H., E. H. Dowell, and L. N. Virgin. “Resonances of a Harmonically Forced Duffing Oscillator with Time Delay State Feedback.” Nonlinear Dynamics 15, no. 4 (January 1, 1998): 311–27. https://doi.org/10.1023/A:1008278526811.
Hu H, Dowell EH, Virgin LN. Resonances of a Harmonically Forced Duffing Oscillator with Time Delay State Feedback. Nonlinear Dynamics. 1998 Jan 1;15(4):311–27.
Hu, H., et al. “Resonances of a Harmonically Forced Duffing Oscillator with Time Delay State Feedback.” Nonlinear Dynamics, vol. 15, no. 4, Jan. 1998, pp. 311–27. Scopus, doi:10.1023/A:1008278526811.
Hu H, Dowell EH, Virgin LN. Resonances of a Harmonically Forced Duffing Oscillator with Time Delay State Feedback. Nonlinear Dynamics. 1998 Jan 1;15(4):311–327.
Journal cover image

Published In

Nonlinear Dynamics

DOI

ISSN

0924-090X

Publication Date

January 1, 1998

Volume

15

Issue

4

Start / End Page

311 / 327

Related Subject Headings

  • Acoustics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences