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Numerical analysis of nonlinear modes of piecewise linear systems torsional vibrations

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Abstract

The nonlinear modes of essentially nonlinear piecewise-linear finite degrees of freedom systems are calculated by the numerical methods, which are suggested in this paper. The basis of these methods is numerical solutions of the equations of the systems motions in configuration space. The numerical method for the nonlinear modes of essentially nonlinear piecewise-linear systems forced vibrations is suggested. The basis of this approach is the combination of the Rauscher method and the calculations of the autonomous system nonlinear modes. The nonlinear modes of the diesel engine transmission torsional vibrations are analyzed numerically. The vibrations are described by essentially nonlinear piecewise-linear system with fifteen degrees of freedom. The NNMs of this system forced vibrations are observed in the resonance regions. Both NNMs and the motions, which are essentially differ from NNMs, are observed in the distance from the resonances. NNMs of the forced vibrations of the systems with dissipation are close to NNMs of the system without dissipation.

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Acknowledgements

Funding was provided by National Academy of Sciences of Ukraine (Grant No. II-67-14).

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Authors and Affiliations

  1. Department of Vibrations, The Podgorny Institute for Mechanical Engineering Problems of National Academy of Science of Ukraine, 2/10 Dm. Pozharskogo St., Kharkiv, 61046, Ukraine

    B. Uspensky & K. Avramov

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  1. B. Uspensky
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  2. K. Avramov
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Correspondence to K. Avramov.

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Uspensky, B., Avramov, K. Numerical analysis of nonlinear modes of piecewise linear systems torsional vibrations. Meccanica 52, 3743–3757 (2017). https://doi.org/10.1007/s11012-017-0677-2

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  • DOI: https://doi.org/10.1007/s11012-017-0677-2

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