The influence of phase-locking on internal resonance from a nonlinear normal mode perspective
The influence of phase-locking on internal resonance from a nonlinear normal mode perspective
When a nonlinear system is expressed in terms of the modes of the equivalent linear system, the nonlinearity often leads to modal coupling terms between the linear modes. In this paper it is shown that, for a system to exhibit an internal resonance between modes, a particular type of nonlinear coupling term is required. Such terms impose a phase condition between linear modes, and hence are denoted phase-locking terms. The effect of additional modes that are not coupled via phase-locking terms is then investigated by considering the backbone curves of the system. Using the example of a two-mode model of a taut horizontal cable, the backbone curves are derived for both the case where phase-locked coupling terms exist, and where there are no phase-locked coupling terms. Following this, an analytical method for determining stability is used to show that phase-locking terms are required for internal resonance to occur. Finally, the effect of non-phase-locked modes is investigated and it is shown that they lead to a stiffening of the system. Using the cable example, a physical interpretation of this is provided.
135-149
Hill, T.L.
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Neild, S.A.
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Cammarano, A.
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Wagg, D.J.
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24 June 2016
Hill, T.L.
96922dda-e993-4889-a519-5f89fe6ebca8
Neild, S.A.
e11b68bb-ddff-4cac-a8a7-798cc3cc3891
Cammarano, A.
c0c85f55-3dfc-4b97-9b79-e2554406a12b
Wagg, D.J.
7aa7d661-df7e-4ecc-86b1-823d4adaf05f
Hill, T.L., Neild, S.A., Cammarano, A. and Wagg, D.J.
(2016)
The influence of phase-locking on internal resonance from a nonlinear normal mode perspective.
Journal of Sound and Vibration, 379, .
(doi:10.1016/j.jsv.2016.05.028).
Abstract
When a nonlinear system is expressed in terms of the modes of the equivalent linear system, the nonlinearity often leads to modal coupling terms between the linear modes. In this paper it is shown that, for a system to exhibit an internal resonance between modes, a particular type of nonlinear coupling term is required. Such terms impose a phase condition between linear modes, and hence are denoted phase-locking terms. The effect of additional modes that are not coupled via phase-locking terms is then investigated by considering the backbone curves of the system. Using the example of a two-mode model of a taut horizontal cable, the backbone curves are derived for both the case where phase-locked coupling terms exist, and where there are no phase-locked coupling terms. Following this, an analytical method for determining stability is used to show that phase-locking terms are required for internal resonance to occur. Finally, the effect of non-phase-locked modes is investigated and it is shown that they lead to a stiffening of the system. Using the cable example, a physical interpretation of this is provided.
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Accepted/In Press date: 16 May 2016
e-pub ahead of print date: 6 June 2016
Published date: 24 June 2016
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Local EPrints ID: 490797
URI: http://eprints.soton.ac.uk/id/eprint/490797
ISSN: 0022-460X
PURE UUID: af3b7453-a458-4ce2-96ca-6a0decc0f4e4
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Date deposited: 06 Jun 2024 16:53
Last modified: 07 Jun 2024 02:08
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Author:
T.L. Hill
Author:
S.A. Neild
Author:
A. Cammarano
Author:
D.J. Wagg
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