Parametric resonance in the Rayleigh-Duffing oscillator with time-delayed feedback

Siewe, M. Siewe; Tchawoua, C.; Rajasekar, S.

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dc.contributor.author	Siewe, M. Siewe
dc.contributor.author	Tchawoua, C.
dc.contributor.author	Rajasekar, S.
dc.date.accessioned	2012-10-05T14:31:06Z
dc.date.available	2012-10-05T14:31:06Z
dc.date.issued	2012-11
dc.description.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 obtain two slow flow equations on the amplitude and phase of the oscillator. We study the effects of the frequency detuning, the deterministic amplitude, and the time-delay on the dynamical behaviors, such as stability and bifurcation associated with the principal parametric resonance. Moreover, the appropriate choice of the feedback gain and the time-delay is discussed from the viewpoint of vibration control. It is found that the appropriate choice of the time-delay can broaden the stable region of the non-trivial steady-state solutions and enhance the control performance. Theoretical stability analysis is verified through a numerical simulation.	en_US
dc.description.librarian	ai2013
dc.description.sponsorship	The University of Pretoria	en_US
dc.description.uri	http://www.elsevier.com/locate/cnsns	en_US
dc.identifier.citation	Siewe M. Siewe, C. Tchawoua & S. Rajasekar, Parametric resonance in the Rayleigh-Duffing oscillator with time-delayed feedback, Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 11, pp. 4485-4493 (2012), doi: 10.1016/j.cnsns.2012.02.030.	en_US
dc.identifier.issn	1007-5704 (print)
dc.identifier.issn	1878-7274 (online)
dc.identifier.other	10.1016/j.cnsns.2012.02.030
dc.identifier.uri	http://hdl.handle.net/2263/20073
dc.language.iso	en	en_US
dc.publisher	Elsevier	en_US
dc.rights	© 2012 Elsevier. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Communications in Nonlinear Science and Numerical Simulation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Communications in Nonlinear Science and Numerical Simulation, vol 17, issue 11, November 2012, doi: 10.1016/j.cnsns.2012.02.030.	en_US
dc.subject	Delay feedback	en_US
dc.subject	Parametric excitation	en_US
dc.subject.lcsh	Parametric oscillators	en
dc.subject.lcsh	Parametric vibration	en
dc.subject.lcsh	Time delay systems	en
dc.subject.lcsh	Resonance	en
dc.subject.lcsh	Resonant vibration	en
dc.subject.lcsh	Oscillators, Electric	en
dc.subject.lcsh	Feedback (Electronics)	en
dc.title	Parametric resonance in the Rayleigh-Duffing oscillator with time-delayed feedback	en_US
dc.type	Postprint Article	en_US