Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6755695 | Journal of Sound and Vibration | 2015 | 13 Pages |
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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Authors
T.L. Hill, A. Cammarano, S.A. Neild, D.J. Wagg,