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Title: Bifurcation of a Duffing oscillator having nonlinear fractional derivative feedback
Author(s): Leung, Andrew Yee Tak 
Author(s): Yang, H. X.
Zhu, P.
Issue Date: 2014
Publisher: World Scientific Publishing Company
Journal: International Journal of Bifurcation and Chaos 
Volume: 24
Issue: 3
Active feedback control is commonly used to attenuate undesired vibrations in vibrating machineries and structures, such as bridges, highways and aircrafts. In this paper, we investigate the primary resonance and 1/3 subharmonic resonance of a harmonically forced Duffing oscillator under fractional nonlinear feedback control. By means of the first order averaging method, slow flow equations governing the modulations of amplitude and phase of the oscillator are obtained. An approximate solution for the steady state periodic response is derived and its stability is determined by the Routh–Hurwitz criterion. We demonstrate that appropriate choices on the control strategies and feedback gains can delay or eliminate the undesired bifurcations and reduce the amplitude peak both of the primary and subharmonic resonances. Analytical results are verified by comparisons with the numerical integration results.
DOI: 10.1142/S021812741450028X
CIHE Affiliated Publication: No
Appears in Collections:CIS Publication

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