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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 261, Pages 154–175
(Mi tm746)
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This article is cited in 4 scientific papers (total in 5 papers)
Resonance Dynamics of Nonlinear Flutter Systems
A. Yu. Kolesova, E. F. Mishchenkob, N. Kh. Rozovc a P. G. Demidov Yaroslavl State University
b Steklov Mathematical Institute, Russian Academy of Sciences
c M. V. Lomonosov Moscow State University
Abstract:
We consider a special class of nonlinear systems of ordinary differential equations, namely, the so-called flutter systems, which arise in Galerkin approximations of certain boundary value problems of nonlinear aeroelasticity and in a number of radiophysical applications. Under the assumption of small damping coefficient, we study the attractors of a flutter system that arise in a small neighborhood of the zero equilibrium state as a result of interaction between the $1:1$ and $1:2$ resonances. We find that, first, these attractors may be both regular and chaotic (in the latter case, we naturally deal with numerical results); and second, for certain parameter values, they coexist with the stable zero solution; i.e., the phenomenon of hard excitation of self-oscillations is observed.
Received in June 2007
Citation:
A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “Resonance Dynamics of Nonlinear Flutter Systems”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 261, MAIK Nauka/Interperiodica, Moscow, 2008, 154–175; Proc. Steklov Inst. Math., 261 (2008), 149–170
Linking options:
https://www.mathnet.ru/eng/tm746 https://www.mathnet.ru/eng/tm/v261/p154
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