• Corpus ID: 118221513

# Active Control of the Parametric Resonance in the Modified Rayleigh-Duffing Oscillator

@article{Miwadinou2013ActiveCO,
title={Active Control of the Parametric Resonance in the Modified Rayleigh-Duffing Oscillator},
author={Cl{\'e}ment Hod{\'e}v{\e}wan Miwadinou and Adjimon Vincent Monwanou and Jean Bio Chabi Orou},
journal={arXiv: Fluid Dynamics},
year={2013}
}`
• Published 3 March 2013
• Physics
• arXiv: Fluid Dynamics
The present paper examines the active control of parametric resonance in modified Rayleigh-Duffing oscillator. We used the method of averaging to obtain steady-state solutions. We have found the critical value of the parametrical amplitude which indicates the boundary layer where the control is efficient in reducing the amplitude vibration. We have also found the effects of excitation parameters and time-delay on dynamical of this system with the principal parametric resonance. We have obtained…
7 Citations

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## References

SHOWING 1-10 OF 34 REFERENCES
RESPONSE OF PARAMETRICALLY EXCITED DUFFING-VAN DER POL OSCILLATOR WITH DELAYED FEEDBACK
The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of
Dynamics of a Quasiperiodically Forced Rayleigh Oscillator
• Physics, Engineering
• 2006
This paper studies the dynamics of a self-excited oscillator with two external periodic forces. Both the nonresonant and resonant states of the oscillator are considered. The hysteresis boundaries
Application of He's method to the modified Rayleigh equation
• Physics
• 2011
In this work we analyze the application of He’s variational method for an estimation of limit cycles and oscillation periods for the class of self-sustained oscillations described by the modified
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
• Physics
Applied Mathematical Sciences
• 1983
The book surveys the theory and techniques needed to understand chaotic behavior of ODEs and considers four examples of chaotic systems: the forced van der Pol oscillator, Duffing's equation, the celebrated Lorenz equations, and Holmes' "bouncing ball map".
Hopf bifurcation in a disk-shaped NEMS
• Physics
• 2003
Self-sustained mechanical vibrations of a disc-type microfabricated resonator were experimentally observed when a continuous wave (CW) laser beam was focused on the periphery of the disc (for a 40 μm