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Quasiperiodic Route to Transient Chaos in Vibroimpact System

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Nonlinear Dynamics, Chaos, and Complexity

Part of the book series: Nonlinear Physical Science ((NPS))

Abstract

Dynamic behaviour of the nonsmooth systems is interesting and explored subject in nonlinear science. We studied quasiperiodic route to chaos in nonlinear nonsmooth discontinuous vibroimpact system. In narrow frequency range different oscillatory regimes have succeeded each other many times under very small control parameter varying. There were periodic subharmonic regimes—chatters, quasiperiodic, and chaotic regimes. There were the zones of transition from one regime to another, the zones of prechaotic or postchaotic motion. The hysteresis effects (jump phenomena) occurred for increasing and decreasing frequencies. The chaoticity of obtained regime has been confirmed by typical views of Poincaré map and Fourier spectrum, by the positive value of the largest Lyapunov exponent, and by the fractal structure of Poincaré map. Discontinuous bifurcations are also described—it is phenomenon unique for nonsmooth systems. It is discussed the largest Lyapunov estimation for nonsmooth vibroimpact system.

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Notes

  1. 1.

    We consider hysteresis effect as dependence of the system state on its history (the system manifests hysteretic features in the transition between different types of motion) [12, 16].

  2. 2.

    The mark (n,k) means nT-periodic vibration with k impacts per cycle [32], T is period of external loading \(T=2\pi /\omega \).

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Authors and Affiliations

  1. Kyiv National University of Construction and Architecture, 31, Povitroflotskiy avenu, Kyiv, Ukraine

    Victor Bazhenov, Olga Pogorelova & Tatiana Postnikova

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  1. Victor Bazhenov
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  2. Olga Pogorelova
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  3. Tatiana Postnikova
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Correspondence to Victor Bazhenov .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA

    Dimitri Volchenkov

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Bazhenov, V., Pogorelova, O., Postnikova, T. (2021). Quasiperiodic Route to Transient Chaos in Vibroimpact System. In: Volchenkov, D. (eds) Nonlinear Dynamics, Chaos, and Complexity. Nonlinear Physical Science. Springer, Singapore. https://doi.org/10.1007/978-981-15-9034-4_3

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  • DOI: https://doi.org/10.1007/978-981-15-9034-4_3

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