Invariant torus break-down in vibroimpact system – route to crisis ?

dc.contributor.authorBazhenov, V. A.
dc.contributor.authorPogorelova, O. S.
dc.contributor.authorPostnikova, T. G.
dc.date.accessioned2020-05-27T07:13:16Z
dc.date.available2020-05-27T07:13:16Z
dc.date.issued2018
dc.description.abstractChaotic vibrations of dynamical systems and their routes to chaos are interesting and investigated subjects in nonlinear dynamics. Particularly the routes to chaos in non-smooth dynamical systems are of the special scientists’ interest. In this paper we study quasiperiodic route to chaos in nonlinear non-smooth discontinuous 2-DOF vibroimpact system. The break-down of invariant torus or of the closed curve occurs just under the quasiperiodic route to chaos. Is it route to crisis? 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, the zones of prechaotic and postchaotic motion. The hysteresis effects (jump phenomena) occurred for increasing and decreasing frequencies. The observed chaos was the transient one.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. These investigations confirm the theory by Newhouse, Ruelle, and Takens who suggested a new bifurcation scenario where a periodic solution produces subsequently a torus and then a strange attractor.uk_UA
dc.identifier.citationBazhenov V. A. Invariant torus break-down in vibroimpact system – route to crisis ? / V. A. Bazhenov, O. S. Pogorelova, T. G. Postnikova // Опір матеріалів і теорія споруд : наук.- техн. зб. / Київ. нац. ун-т буд-ва і архітектури ; відп. ред. В. А. Баженов. – Київ, 2018. – Вип. 100. – С. 3 - 17. - Бібліогр. : 30 назв.uk_UA
dc.identifier.issn2410-2547
dc.identifier.urihttps://repositary.knuba.edu.ua/handle/987654321/4285
dc.language.isoenuk_UA
dc.publisherКНУБАuk_UA
dc.subjectvibroimpact systemuk_UA
dc.subjectdynamical behaviouruk_UA
dc.subjectquasiperiodicuk_UA
dc.subjectchaoticuk_UA
dc.subjectsubharmonicsuk_UA
dc.subjectPoincaré mapuk_UA
dc.subjectFourier spectrumuk_UA
dc.subjectLyapunov exponentuk_UA
dc.subjectfractal structureuk_UA
dc.subjectthe department building mechanicsuk_UA
dc.subject.udc539.3uk_UA
dc.subject.udc534.1uk_UA
dc.titleInvariant torus break-down in vibroimpact system – route to crisis ?uk_UA
dc.typeArticleuk_UA
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