RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Tr. Mat. Inst. Steklova, 2008, Volume 261, Pages 154–175 (Mi tm746)  

This article is cited in 3 scientific papers (total in 4 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.

Full text: PDF file (672 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 261, 149–170

Bibliographic databases:

UDC: 517.957
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, Tr. Mat. Inst. Steklova, 261, MAIK Nauka/Interperiodica, Moscow, 2008, 154–175; Proc. Steklov Inst. Math., 261 (2008), 149–170

Citation in format AMSBIB
\Bibitem{KolMisRoz08}
\by A.~Yu.~Kolesov, E.~F.~Mishchenko, N.~Kh.~Rozov
\paper Resonance Dynamics of Nonlinear Flutter Systems
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2008
\vol 261
\pages 154--175
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm746}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2489703}
\zmath{https://zbmath.org/?q=an:1239.34053}
\elib{http://elibrary.ru/item.asp?id=11032693}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2008
\vol 261
\pages 149--170
\crossref{https://doi.org/10.1134/S0081543808020120}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000262227900012}
\elib{http://elibrary.ru/item.asp?id=13585680}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-48849101291}


Linking options:
  • http://mi.mathnet.ru/eng/tm746
  • http://mi.mathnet.ru/eng/tm/v261/p154

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. V. Anosov, S. M. Aseev, R. V. Gamkrelidze, S. P. Konovalov, M. S. Nikol'skii, N. Kh. Rozov, “Evgenii Frolovich Mishchenko (on the 90th anniversary of his birth)”, Russian Math. Surveys, 67:2 (2012), 385–402  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Ob odnom mekhanizme zhestkogo vozbuzhdeniya kolebanii v nelineinykh flatternykh sistemakh”, Model. i analiz inform. sistem, 21:1 (2014), 32–44  mathnet
    3. Sadovnichii V.A., Kolesov A.Yu., Rozov N.Kh., “Parametric Chaos in Nonlinear Flutter Systems”, Dokl. Math., 89:3 (2014), 382–386  crossref  mathscinet  zmath  isi  elib  scopus
    4. Grushkovskaya V., “Asymptotic decay of solutions to an essentially nonlinear system with two-frequency resonances”, Appl. Anal., 95:11 (2016), 2501–2516  crossref  mathscinet  zmath  isi  elib  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:281
    Full text:31
    References:47
    First page:14

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019