Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves
Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves
In this paper the backbone curves of a two-degree-of-freedom nonlinear oscillator are used to interpret its behaviour when subjected to external forcing. The backbone curves describe the loci of dynamic responses of a system when unforced and undamped, and are represented in the frequency–amplitude projection. In this study we provide an analytical method for relating the backbone curves, found using the second-order normal form technique, to the forced responses. This is achieved using an energy-based analysis to predict the resonant crossing points between the forced responses and the backbone curves. This approach is applied to an example system subjected to two different forcing cases: one in which the forcing is applied directly to an underlying linear mode and the other subjected to forcing in both linear modes. Additionally, a method for assessing the accuracy of the prediction of the resonant crossing points is then introduced, and these predictions are then compared to responses found using numerical continuation.
276-288
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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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)
Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves.
Journal of Sound and Vibration, 349, .
(doi:10.1016/j.jsv.2015.03.030).
Abstract
In this paper the backbone curves of a two-degree-of-freedom nonlinear oscillator are used to interpret its behaviour when subjected to external forcing. The backbone curves describe the loci of dynamic responses of a system when unforced and undamped, and are represented in the frequency–amplitude projection. In this study we provide an analytical method for relating the backbone curves, found using the second-order normal form technique, to the forced responses. This is achieved using an energy-based analysis to predict the resonant crossing points between the forced responses and the backbone curves. This approach is applied to an example system subjected to two different forcing cases: one in which the forcing is applied directly to an underlying linear mode and the other subjected to forcing in both linear modes. Additionally, a method for assessing the accuracy of the prediction of the resonant crossing points is then introduced, and these predictions are then compared to responses found using numerical continuation.
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Accepted/In Press date: 14 March 2015
e-pub ahead of print date: 21 April 2015
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Local EPrints ID: 490801
URI: http://eprints.soton.ac.uk/id/eprint/490801
ISSN: 0022-460X
PURE UUID: a8fd0385-3bf7-4197-b3d7-7210f46c0ca3
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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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