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Title: Non-classical nonlinear normal vibration modes in mechanical systems
Authors: Mikhlin, Yuri V.
Plaksiy, Kateryna
Shmatko, Tatyana
Rudneva, Gayane
Keywords: mechanical systems; systems with a limited power-supply; nonlinear normal modes; chaotic vibrations
Issue Date: 2017
Publisher: Sapienza University of Rome
Citation: Non-classical nonlinear normal vibration modes in mechanical systems / Yuri V. Mikhlin [at al.] // Proceedings of 9th European Nonlinear Dynamics Conference (ENOC 2017), 25-30 June, 2017 / ed.: G. Stépán, G. Csernák ; Budapest University of Technology and Economics. – Budapest : CongressLine Ltd., 2017. – P. 305-306.
Abstract: Nonlinear normal modes (NNMs) of forced chaotic vibrations can be found in models which are obtained by digitization of some elastic systems that have lost stability under external compressive force. A system of non-autonomous Duffing equations can be obtained; chaotic motions appear as the force amplitude is slowly increased. A stability of periodic or chaotic vibration mode in a space with a greater dimension is studied. In non-ideal dissipative systems NNMs by Kauderer-Rosenberg cannot be realized due to exponential decrease of vibration amplitude. In such systems under the resonance conditions the transient nonlinear normal modes (TNNMs), which exist only for some levels of energy, can be found. These TNNMs temporarily attract other motions of the system near values of time, corresponding to the mentioned energy levels.
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