Nonlinear vibration and of the Duffing oscillator to parametric excitation with time delay feedback

Kotb, A. A; EL-Sayed, A. T; Amer, Y. A

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Nonlinear vibration and of the Duffing oscillator to parametric excitation with time delay feedback

Kotb, A. A; EL-Sayed, A. T; Amer, Y. A

Full Text link: https://link.springer.com/article/10.1007/s11071-016-2840-z

Date issued: 2016-09

Doi: https://doi.org/10.1007/s11071-016-2840-z

Publisher: Springer

Series Info: NONLINEAR DYNAMICS;Volume: 85 Issue: 4 Pages: 2497-2505

Type: Article

Keywords: University for CHAOS , ABSORBER , SUPPRESSION , SYSTEM , Stability , Time delay , Sub-harmonic resonance , Multiple scales perturbation , Duffing oscillator

Abstract:

The aim of this paper was to study the nonlinear vibrations of a parametric excited Duffing oscillator with time delay feedback. At some values of the time delay can be used to suppress the vibration of the nonlinear system. The method of multiple scales perturbation is applied to obtain the analytical solution of the system and the frequency response equation near sub-harmonic resonance case. The stability of the obtained nonlinear solution is studied and solved numerically. The effects of the different parameters of the system behavior are investigated. Analytical solution in this paper is in good agreement with the numerical simulation.