Out-of-unison resonance in weakly nonlinear coupled oscillators
Out-of-unison resonance in weakly nonlinear coupled oscillators
Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems.
Hill, T.L.
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Cammarano, A.
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Neild, S.A.
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Wagg, D.J.
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8 January 2015
Hill, T.L.
96922dda-e993-4889-a519-5f89fe6ebca8
Cammarano, A.
c0c85f55-3dfc-4b97-9b79-e2554406a12b
Neild, S.A.
e11b68bb-ddff-4cac-a8a7-798cc3cc3891
Wagg, D.J.
7aa7d661-df7e-4ecc-86b1-823d4adaf05f
Hill, T.L., Cammarano, A., Neild, S.A. and Wagg, D.J.
(2015)
Out-of-unison resonance in weakly nonlinear coupled oscillators.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471 (2173).
(doi:10.1098/rspa.2014.0659).
Abstract
Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems.
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hill-et-al-2015-out-of-unison-resonance-in-weakly-nonlinear-coupled-oscillators
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Accepted/In Press date: 17 October 2014
e-pub ahead of print date: 8 January 2015
Published date: 8 January 2015
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Local EPrints ID: 490799
URI: http://eprints.soton.ac.uk/id/eprint/490799
ISSN: 1364-5021
PURE UUID: c7a9ad84-58b3-4122-b363-de57c28ef867
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Date deposited: 06 Jun 2024 16:54
Last modified: 07 Jun 2024 02:08
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Author:
T.L. Hill
Author:
A. Cammarano
Author:
S.A. Neild
Author:
D.J. Wagg
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