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Existence of nonlinear normal modes for coupled nonlinear oscillators

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Abstract

We prove the existence of nonlinear normal modes for general systems of two coupled nonlinear oscillators. Facilitating the comparison principle for ordinary differential equations, it is shown that there exist exact solutions representing a vibration in unison of the system. The associated spatially localised time-periodic solutions feature out-of-phase and in-phase motion of the oscillators.

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  1. Department of Mathematics, University of Portsmouth, Portsmouth, PO1 3HF, UK

    Dirk Hennig

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  1. Dirk Hennig
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Correspondence to Dirk Hennig.

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Hennig, D. Existence of nonlinear normal modes for coupled nonlinear oscillators. Nonlinear Dyn 80, 937–944 (2015). https://doi.org/10.1007/s11071-015-1918-3

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  • DOI: https://doi.org/10.1007/s11071-015-1918-3

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