• Corpus ID: 118221513

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

title={Active Control of the Parametric Resonance in the Modified Rayleigh-Duffing Oscillator},
author={Cl{\'e}ment Hod{\'e}v{\`e}wan Miwadinou and A. V. Monwanou and J. B. 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

Figures from this paper

Melnikov Chaos in a Modified Rayleigh-Duffing Oscillator with ϕ6 Potential
• Computer Science, Mathematics
Int. J. Bifurc. Chaos
• 2016
The chaotic behavior of the modified Rayleigh–Duffing oscillator with ϕ6 potential and external excitation is investigated both analytically and numerically and it is pointed out that certain quadratic damping effects are contrary to cubic damping effect.
Effect of Nonlinear Dissipation on the Basin Boundaries of a Driven Two-Well Modified Rayleigh-Duffing Oscillator
• Mathematics, Computer Science
Int. J. Bifurc. Chaos
• 2015
The Melnikov criterion is used to examine a global homoclinic bifurcation and transition to chaos in the case of the Modified Rayleigh-Duffing Oscillator and it is found the effects of unpure quadratic parameter and amplitude of parametric excitation on the critical Melnikov amplitude $\mu_{cr}$.
Hysteresis, Quasiperiodicity and Chaoticity in a Nonlinear Dissipative Hybrid Oscillator
• Physics
• 2017
Hysteresis, quasi-periodicity and chaoticity in a nonlinear dissipative hybrid oscillator are studied. The modified Rayleigh-Duffing oscillator is considered. We simultaneously take into account the
Effect of nonlinear dissipation on the basin boundaries of a driven two-well or catastrophic single-well Modified Rayleigh-Duffing Oscillator
• Mathematics
• 2013
This paper considers effect of nonlinear dissipation on the basin boundaries of a diven two-well Modified Rayleigh-Duffing Oscillator where pure and unpure quadratic and cubic nonlinearities are
Nonlinear dynamics of a $$\varvec{\phi ^6}-$$ϕ6- modified Duffing oscillator: resonant oscillations and transition to chaos
• Physics
• 2017
The nonlinear dynamics of a hybrid Rayleigh–Van der Pol–Duffing oscillator includes pure and impure quadratic damping are investigated. The multiple timescales method is used to study exhaustively
Modeling nonlinear dissipative chemical dynamics by a forced modified Van der Pol-Duffing oscillator with asymmetric potential: Chaotic behaviors predictions
• Physics
• 2018
Abstract This paper addresses the issues of nonlinear chemical dynamics modeled by a modified Van der Pol-Duffing oscillator with asymmetric potential. The Melnikov method is utilized to analytically
Nonlinear dynamics of system oscillations modeled by a forced Van der Pol generalized oscillator
• Mathematics, Physics
• 2014
This paper considers the oscillations modeled by a forced Van der Pol generalized oscillator. These oscillations are described by a nonlinear differential equation of the form \$

References

SHOWING 1-10 OF 34 REFERENCES
Parametric resonance in the Rayleigh–Duffing oscillator with time-delayed feedback
• Mathematics
• 2012
Abstract We investigate the principal parametric resonance of a Rayleigh–Duffing oscillator with time-delayed feedback position and linear velocity terms. Using the asymptotic perturbation method, we
Dynamics of a Quasiperiodically Forced Rayleigh Oscillator
• Physics
• 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
• Mathematics
• 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
Active control with delay of catastrophic motion and horseshoes chaos in a single well Duffing oscillator
• Mathematics
• 2005
Abstract In this paper, the control of escape and Melnikov chaos of an harmonically excited particle from a catastrophic (unbounded) single well φ4 potential is considered. In the linear limit, the
Stability, bifurcation and chaos of non-linear structures with control—II. Non-autonomous case
• Mathematics
• 1993
Abstract We study a class of structural models with non-linear soft spring and active control subjected to simple harmonic excitations. The first of the two parts deals with the analysis of stability
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
• Computer Science, 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".
Linear feedback and parametric controls of vibrations and chaotic escape in a Φ6 potential
• Physics
• 2003
Abstract The control of vibration amplitude and chaotic escape of an harmonically excited particle in a single well Φ 6 potential is considered. The linear feedback and parametric control strategies
Chatter suppression by parametric excitation: Model and experiments
• Physics
• 2011
Abstract Chatter vibration leads to challenges in precise machining due to its harmful effect on productivity and surface quality. In this study, a chatter suppression method based on parametric
Hopf bifurcation in a disk-shaped NEMS
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
Perturbation analysis of entrainment in a micromechanical limit cycle oscillator
• Physics
• 2007
Abstract We study the dynamics of a thermo-mechanical model for a forced disc shaped, micromechanical limit cycle oscillator. The forcing can be accomplished either parametrically, by modulating the