Hill, T.L., Cammarano, A., Neild, S.A. et al. (1 more author) (2015) Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves. Journal of Sound and Vibration, 349. 276 - 288. ISSN 0022-460X
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.
Metadata
Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015. T.L. Hill, A.Cammarano, S.A.Neild and D.J. Wragg This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Mechanical Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 03 Jul 2015 11:49 |
Last Modified: | 03 Jul 2015 11:49 |
Published Version: | http://dx.doi.org/10.1016/j.jsv.2015.03.030 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | https://doi.org/10.1016/j.jsv.2015.03.030 |