A complex nonlinear system under state feedback control with a time delay corresponding to two coupled nonlinear oscillators with a parametric excitation is investigated by an asymptotic perturbation method based on Fourier expansion and time rescaling. Four coupled equations for the amplitude and the phase of solutions are derived. In the system without control, phase-locked solutions with period equal to the parametric excitation period are possible only if the oscillator amplitudes are equal, but they depend on the system parameters and excitation amplitude. In many cases, the amplitudes of periodic solutions do not correspond to the technical requirements. It is demonstrated that, if the vibration control terms are added, stable periodic solutions with arbitrarily chosen amplitude and phase can be accomplished. Therefore, an effective vibration control is possible if appropriate time delay and feedback gains are chosen.
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July 2008
Research Papers
Vibration Control for Parametrically Excited Coupled Nonlinear Oscillators
Attilio Maccari
Attilio Maccari
Via Alfredo Casella 3
, 00013 Mentana, Rome, Italy
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Attilio Maccari
Via Alfredo Casella 3
, 00013 Mentana, Rome, ItalyJ. Comput. Nonlinear Dynam. Jul 2008, 3(3): 031010 (8 pages)
Published Online: May 5, 2008
Article history
Received:
July 14, 2007
Revised:
October 23, 2007
Published:
May 5, 2008
Citation
Maccari, A. (May 5, 2008). "Vibration Control for Parametrically Excited Coupled Nonlinear Oscillators." ASME. J. Comput. Nonlinear Dynam. July 2008; 3(3): 031010. https://doi.org/10.1115/1.2908317
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