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Technical Briefs

Application of a Weakly Nonlinear Absorber to Suppress the Resonant Vibrations of a Forced Nonlinear Oscillator

[+] Author and Article Information
J. C. Ji

School of Electrical, Mechanical and Mechatronic Systems, Faculty of Engineering and IT,  University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australiajin.ji@uts.edu.au

J. Vib. Acoust 134(4), 044502 (May 29, 2012) (6 pages) doi:10.1115/1.4005839 History: Received June 09, 2011; Revised November 14, 2011; Published May 29, 2012; Online May 29, 2012

A weakly nonlinear vibration absorber is used to suppress the primary resonance vibrations of a single degree-of-freedom weakly nonlinear oscillator with periodic excitation, where the two linearized natural frequencies of the integrated system are not under any internal resonance conditions. The values of the absorber parameters are significantly lower than those of the forced nonlinear oscillator, as such the nonlinear absorber can be regarded as a perturbation to the nonlinear primary oscillator. The characteristics of the nonlinear primary oscillator change only slightly in terms of its new linearized natural frequency and the frequency interval of primary resonances after the nonlinear absorber is added. The method of multiple scales is employed to obtain the averaged equations that determine the amplitudes and phases of the first-order approximate solutions. Selection criteria are developed for the absorber linear stiffness (linearized natural frequency) and nonlinear stiffness in order to achieve better performance in vibration suppression. Illustrative examples are given to show the effectiveness of the nonlinear absorber in suppressing nonlinear vibrations of the forced oscillator under primary resonance conditions.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Mechanical model of a nonlinear primary oscillator attached by a nonlinear vibration absorber, where m1 is the mass of the nonlinear primary oscillator, and m2 is the mass of the nonlinear vibration absorber.

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Figure 2

Variations of desensitization ratio with the absorber nonlinear stiffness k4

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Figure 3

Frequency-response curves of the nonlinear primary oscillator; (a) with and without nonlinear absorber for the amplitude of excitation f0=0.18 N; (b) with nonlinear and the corresponding linear absorber as well as without absorber for f0=0.37 N. Solid lines denote stable solutions and dashed-dotted lines represent unstable solutions.

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Figure 4

Time histories of the primary resonance response of the nonlinear primary oscillator under f1=0.5 N; (a) with and without nonlinear absorber, (b) nonlinear primary oscillator and nonlinear absorber; (c) with nonlinear absorber and the corresponding linear absorber.

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