Transitional regimes under route to chaos in vibroimpact system

Authors

DOI:

https://doi.org/10.32347/2410-2547.2019.102.37-45

Keywords:

vibroimpact system, route to chaos, transitional regime, Poincaré map, Fourier spectrum, continuous wavelet transform

Abstract

In recent years in nonlinear dynamics particular attention was paid to studying the chaotic behaviour of dynamical systems and their routes to chaos. Sometimes this route may be intricate. We watched such intricate route to chaos when studying the quasi-periodic route to chaos in strongly nonlinear non-smooth discontinuous vibroimpact system that was two-body 2-DOF one. After Neimark-Sacker bifurcation many different regimes replace each other. There are transitional regimes with inconsistent characteristics among them. We analyze these regimes with continuous wavelet transform CWT applying. CWT plots confirm just their transition kind and give clear picture of different frequencies presence in time series and their distribution in time.

Author Biographies

Viktor Bazhenov, Kyiv National University of Construction and Architecture

Doctor of Technical Sciences, Professor, Academician of the National Academy of Pedagogical Sciences of Ukraine, Head of the Department of Structural Mechanics

Olga Pogorelova, Kyiv National University of Construction and Architecture

Candidate of Sciences (Physics and Mathematics), Senior Researcher at the Institute of Structural Mechanics

Tatiana Postnikova, Kyiv National University of Construction and Architecture

Candidate of Technical Sciences, Senior Researcher at the Institute of Structural Mechanics

References

Moon F.C. Chaotic vibrations: an introduction for applied scientists and engineers. – New York : Wiley, 1987. – 219 P.

Kuznetsov S.P. Dynamical chaos //Moscow: Fizmatlit.-2006.-356 P. – 2001.

Schuster H.G. Deterministic Chaos. An Introduction 2nd Revised Edition. – 1988.

Bazhenov V.A., Pogorelova O.S. & Postnikova T.G. Invarient Torus break-down in vibroimpact system – route to crisis?. //Strength of Materials and Theory of Structures. – 2018. – V. 100. – P. 3-17.

Bazhenov V.A., Pogorelova O.S., Postnikova T.G. & Lukianchenko O.O. Wavelet transform using for analysis of vibroimpact system chaotic behavior. //Strength of Materials and Theory of Structures. – 2018. – V.101. – P. 14-25.

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Published

2019-07-12

Issue

No. 102 (2019)

Section

Статті

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Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.