Design of a nonlinear vibration absorber using three-to-one internal resonances

Ji, JC

Design of a nonlinear vibration absorber using three-to-one internal resonances

Ji, JC

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Publication Type:: Journal Article
Citation:: Mechanical Systems and Signal Processing, 2014, 42 (1-2), pp. 236 - 246
Issue Date:: 2014-01-01

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Field	Value	Language
dc.contributor.author	Ji, JC https://orcid.org/0000-0003-3280-5463	en_US
dc.date.issued	2014-01-01	en_US
dc.identifier.citation	Mechanical Systems and Signal Processing, 2014, 42 (1-2), pp. 236 - 246	en_US
dc.identifier.issn	0888-3270	en_US
dc.identifier.uri	http://hdl.handle.net/10453/35581
dc.description.abstract	A weakly nonlinear vibration absorber is designed to attenuate the primary resonance vibrations of a single-degree-of-freedom weakly nonlinear oscillator having cubic nonlinearity. The linearised natural frequency of the nonlinear absorber is tuned to be approximately one-third the linearised natural frequency of the primary nonlinear oscillator. The low frequency mode for the absorber is favourably considered based on the fact that the nonlinear absorber can be easily realised in practice by using a light-weight mass attachment with small values of linear and nonlinear stiffness of coupling. For a given primary nonlinear oscillator and absorber mass, implementation of three-to-one internal resonances requires the smallest value of the absorber linear stiffness among three options for utilising internal resonances to design nonlinear absorber. The method of multiple scales is used to obtain the averaged equations that determine the amplitudes and phases of the first-order approximate solutions to the vibrations of the primary nonlinear oscillator and nonlinear absorber. It is found that the absorber response may admit either forced vibration having the forcing frequency or a combination of forced vibration and free-oscillation term having one third the forcing frequency. The nonlinear absorber can effectively suppress the amplitude of primary resonance response and eliminate saddle-node bifurcations occurring in the frequency-response curves of the primary nonlinear oscillator. Numerical results are given to show the effectiveness of the nonlinear absorber for suppressing nonlinear vibrations of the primary nonlinear oscillator under primary resonance conditions. © 2013 Elsevier Ltd. All rights reserved.	en_US
dc.relation.ispartof	Mechanical Systems and Signal Processing	en_US
dc.relation.isbasedon	10.1016/j.ymssp.2013.06.019	en_US
dc.subject.classification	Acoustics	en_US
dc.title	Design of a nonlinear vibration absorber using three-to-one internal resonances	en_US
dc.type	Journal Article
utslib.citation.volume	1-2	en_US
utslib.citation.volume	42	en_US
utslib.for	091304 Dynamics, Vibration and Vibration Control	en_US
utslib.for	0905 Civil Engineering	en_US
utslib.for	0913 Mechanical Engineering	en_US
utslib.for	0915 Interdisciplinary Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	closed_access
pubs.issue	1-2	en_US
pubs.publication-status	Published	en_US
pubs.volume	42	en_US

Abstract:

A weakly nonlinear vibration absorber is designed to attenuate the primary resonance vibrations of a single-degree-of-freedom weakly nonlinear oscillator having cubic nonlinearity. The linearised natural frequency of the nonlinear absorber is tuned to be approximately one-third the linearised natural frequency of the primary nonlinear oscillator. The low frequency mode for the absorber is favourably considered based on the fact that the nonlinear absorber can be easily realised in practice by using a light-weight mass attachment with small values of linear and nonlinear stiffness of coupling. For a given primary nonlinear oscillator and absorber mass, implementation of three-to-one internal resonances requires the smallest value of the absorber linear stiffness among three options for utilising internal resonances to design nonlinear absorber. The method of multiple scales is used to obtain the averaged equations that determine the amplitudes and phases of the first-order approximate solutions to the vibrations of the primary nonlinear oscillator and nonlinear absorber. It is found that the absorber response may admit either forced vibration having the forcing frequency or a combination of forced vibration and free-oscillation term having one third the forcing frequency. The nonlinear absorber can effectively suppress the amplitude of primary resonance response and eliminate saddle-node bifurcations occurring in the frequency-response curves of the primary nonlinear oscillator. Numerical results are given to show the effectiveness of the nonlinear absorber for suppressing nonlinear vibrations of the primary nonlinear oscillator under primary resonance conditions. © 2013 Elsevier Ltd. All rights reserved.

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http://hdl.handle.net/10453/35581