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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August 2012
Technical Briefs
Application of a Weakly Nonlinear Absorber to Suppress the Resonant Vibrations of a Forced Nonlinear Oscillator
J. C. Ji
J. C. Ji
School of Electrical, Mechanical and Mechatronic Systems, Faculty of Engineering and IT,
e-mail: jin.ji@uts.edu.au
University of Technology
, Sydney, PO Box 123, Broadway, NSW 2007, Australia
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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, Australia
e-mail: jin.ji@uts.edu.au
J. Vib. Acoust. Aug 2012, 134(4): 044502 (6 pages)
Published Online: May 29, 2012
Article history
Received:
June 9, 2011
Revised:
November 14, 2011
Online:
May 29, 2012
Published:
May 29, 2012
Citation
Ji, J. C. (May 29, 2012). "Application of a Weakly Nonlinear Absorber to Suppress the Resonant Vibrations of a Forced Nonlinear Oscillator." ASME. J. Vib. Acoust. August 2012; 134(4): 044502. https://doi.org/10.1115/1.4005839
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