title: Out-of-unison resonance in weakly nonlinear coupled oscillators.
abstract: Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs-a type of system where out-of-unison resonance has not previously been identified-is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems.
authors.affiliation: Department of Mechanical Engineering , University of Bristol , Bristol BS8 1TR, UK.
authors.forename: T L
authors.initials: TL
authors.lastname: Hill
authors.affiliation: Department of Mechanical Engineering , University of Bristol , Bristol BS8 1TR, UK.
authors.forename: A
authors.initials: A
authors.lastname: Cammarano
authors.affiliation: Department of Mechanical Engineering , University of Bristol , Bristol BS8 1TR, UK.
authors.forename: S A
authors.initials: SA
authors.lastname: Neild
authors.affiliation: Department of Mechanical Engineering , University of Sheffield , Sheffield S1 3JD, UK.
authors.forename: D J
authors.initials: DJ
authors.lastname: Wagg
keywords: backbone curve; internal resonance; nonlinear oscillator; normal form