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)

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