Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves. (4th August 2015)

• Record Type: Journal Article
• Authors: Hill, T.L.; Cammarano, A.; Neild, S.A.; Wagg, D.J.
• Is Part Of: Journal of sound and vibration. Volume 349(2015)
• Page Start: 276
• Page End: 288
• Publication Date: 2015-08-04
• Subjects: Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2015.03.030
• Languages: English
• ISSNs: 0022-460X

Abstract

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.