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Technical Brief

Vibration Suppression of Subharmonic Resonance Response Using a Nonlinear Vibration Absorber

[+] Author and Article Information
A. T. EL-Sayed

Department of Basic Sciences,
Modern Academy for Engineering and Technology,
Mokatem 11585, Egypt
e-mail: ashraftaha211@yahoo.com

H. S. Bauomy

Department of Mathematics,
Faculty of Science,
Zagazig University,
Zagazig 44516, Egypt
e-mail: hany_samih@yahoo.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 29, 2014; final manuscript received July 31, 2014; published online January 30, 2015. Assoc. Editor: Paul C.-P. Chao.

J. Vib. Acoust 137(2), 024503 (Apr 01, 2015) (6 pages) Paper No: VIB-14-1030; doi: 10.1115/1.4029268 History: Received January 29, 2014; Revised July 31, 2014; Online January 30, 2015

This paper is concerned with the vibration of a two degree-of-freedom (2DOF) nonlinear system subjected to multiparametric excitation forces. The vibrating motion of the system is described by the coupled differential equations having both quadratic and cubic terms. The aim of this work is to use a nonlinear absorber to control the vibration of the nonlinear system near the simultaneous subharmonic and internal resonances, where the vibrations are severe. Multiple scale perturbation technique (MSPT) is applied to obtain the averaged equations up to the second-order approximation. The steady-state response and their stability are studied numerically for the nonlinear system at the simultaneous subharmonic and internal resonances. Some recommendations regarding to the different system parameters are given following studying the effects of various parameters. Comparison with the available published work is made.

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Figures

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Fig. 1

Diagrammatic representation of the system

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Fig. 2

Response of the system without absorber at subharmonic resonance case (Ω1≅2ω1)

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Fig. 3

Response of the system with absorber at simultaneous subharmonic and internal resonance case (Ω1≅2ω1,ω1≅ω2)

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Fig. 4

Stability of the practical case, a1≠0,a2≠0 on steady-state amplitude a1 against σ1

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Fig. 5

Stability of the practical case, a1≠0,a2≠0 on steady-state amplitude a2 against σ2

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Fig. 6

(Dotted line) analytic solution (dashed line) numerical solution with the same values of the parameters at: (Ω1≅2ω1,ω1≅ω2)

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Fig. 7

Response of the natural and excitation frequency

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Fig. 8

Effect of linear damping parameters of the main system without absorber

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Fig. 9

Variations of amplitude of the main system and absorber

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