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Russian Academy of Sciences
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IssuesArchive of Issues2013-2pp.225-229

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I.L. Antonov, "The use of Markov chain theory in the problem of the dynamic stability of an elastic rod," J. Appl. Math. Mech. 77 (2), 225-229 (2013)
Year 2013 Volume 77 Issue 2 Pages 225-229
Title The use of Markov chain theory in the problem of the dynamic stability of an elastic rod
Author(s) I.L. Antonov (Moscow, Russia, ilanto@yandex.ru)
Abstract The stability of the vertical position of an elastic rods, hinged at the ends and loaded at the upper end with a time-dependent longitudinal force containing a stochastic component, is considered. A homogeneous Markov chain is used to model the stochastic component. An inequality is obtained that depends on the characteristics of the stochastic force and the damping factor of the bar and, depending on whether this inequality is satisfied, the above equilibrium position will either be attracting or unstable.
Received 18 May 2011
Link to Fulltext http://www.sciencedirect.com/science/article/pii/S0021892813000889
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