Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves

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, pp. 276-288. (doi:10.1016/j.jsv.2015.03.030)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Cammarano, Dr Andrea
Authors: Hill, T.L., Cammarano, A., Neild, S.A., and Wagg, D.J.
College/School:College of Science and Engineering > School of Engineering > Systems Power and Energy
Journal Name:Journal of Sound and Vibration
Publisher:Elsevier Ltd.
ISSN:0022-460X
ISSN (Online):1095-8568
Copyright Holders:Copyright © 2015 The Authors
First Published:First published in Journal of Sound and Vibration 349:276-288
Publisher Policy:Reproduced under a Creative Commons License

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