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Regular and Chaotic Dynamics, 2012, Volume 17, Issue 6, Pages 506–511
DOI: https://doi.org/10.1134/S1560354712060032 (Mi rcd418) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the Probability of the Outcomes in Buckling of an Elastic Beam

Michail Pivovarov

Technische Universität Ilmenau, PF 10 05 65, 98684 Ilmenau, Germany
Citations (1)
DOI: https://doi.org/10.1134/S1560354712060032
Abstract: A nonlinear time-varying one-degree-of-freedom system, which is used for the modelling of the buckling of a loaded beam in Euler’s problem, is considered. For a slowly changing load, the deterministic approach in this problem fails if the trajectories pass through the separatrix. An expression for the probability of possible outcomes of the evolution of the oscillations is obtained. The analytical and numerical results are compared.
Keywords: deterministic chaos, separatrix crossing, buckling of beams.
Received: 25.09.2012
Accepted: 25.10.2012
Bibliographic databases:
Document Type: Article
MSC: 70K55, 70H14, 37N15
Language: English
Citation: Michail Pivovarov, “On the Probability of the Outcomes in Buckling of an Elastic Beam”, Regul. Chaotic Dyn., 17:6 (2012), 506–511
Citation in format AMSBIB
\Bibitem{Piv12}
\by Michail Pivovarov
\paper On the Probability of the Outcomes in Buckling of an Elastic Beam
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 6
\pages 506--511
\mathnet{http://mi.mathnet.ru/rcd418}
\crossref{https://doi.org/10.1134/S1560354712060032}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3001097}
\zmath{https://zbmath.org/?q=an:1344.70040}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012RCD....17..506P}
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    • This publication is cited in the following 1 articles:
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