Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 471, Issue 2173, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rspa.2014.0659
Keywords
nonlinear oscillator; normal form; internal resonance; backbone curve
Categories
Funding
- Engineering and Physical Sciences Research Council
- EPSRC [EP/K005375/1, EP/K003836/1]
- Engineering and Physical Sciences Research Council [EP/K003836/1, EP/K005375/1, 1227535] Funding Source: researchfish
- EPSRC [EP/K005375/1, EP/K003836/1] Funding Source: UKRI
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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 degrees 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.
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