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Primary Resonance of a Duffing Oscillator With Two Distinct Time Delays in State Feedback Under Narrow-Band Random Excitation

[+] Author Affiliations
Yanfei Jin, Haiyan Hu

Nanjing University of Aeronautics and Astronautics, Nanjing, China

Paper No. DETC2007-35909, pp. 327-337; 11 pages
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME


The primary resonance of a Duffing oscillator with two distinct time delays in state feedback under narrow-band random excitation is investigated in detail by using the method of multiple scales. First, the equations of modulation of response amplitude and phase are determined. Then, the expressions of the first-order and the second-order steady-state moments and their stable regions are obtained by introducing the equivalent detuning frequency and the equivalent damping ratio. For the case of two distinct time delays, the appropriate choices of the combinations of the feedback gains and the difference between two time delays are discussed from the viewpoint of vibration control. Finally, the theoretical analyses are well verified through numerical simulations.

Copyright © 2007 by ASME



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