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Izvestiya: Mathematics, 1999, Volume 63, Issue 2, Pages 219–244
DOI: https://doi.org/10.1070/im1999v063n02ABEH000237
(Mi im237)
 

This article is cited in 23 scientific papers (total in 23 papers)

Oscillations of von Karman's plate in a potential flow of gas

L. Boutet de Monvela, I. D. Chueshovb

a Université Pierre & Marie Curie, Paris VI
b V. N. Karazin Kharkiv National University
References:
Abstract: The paper deals with the problem of non-linear oscillations of a clamped plate in a flow of gas. The dynamics of the plate is described by a modification of von Karman's evolution equations, in which the rotatory inertia of the elements of the plate is taken into account. To describe the influence of the gas flow we apply the linearized theory of potential flows. We prove the global existence and uniqueness of weak solutions of the problem under investigation and study their properties. We show that under certain conditions on the initial data the problem can be reduced to a retarded non-linear partial differential equation for the displacement of the plate. We justify certain heuristic formulae for aerodynamic pressure. Our approach is a general one and enables us to consider both subsonic and supersonic flows.
Received: 12.03.1997
Bibliographic databases:
Language: English
Original paper language: Russian
Citation: L. Boutet de Monvel, I. D. Chueshov, “Oscillations of von Karman's plate in a potential flow of gas”, Izv. Math., 63:2 (1999), 219–244
Citation in format AMSBIB
\Bibitem{BouChu99}
\by L.~Boutet de Monvel, I.~D.~Chueshov
\paper Oscillations of von Karman's plate in a~potential flow of gas
\jour Izv. Math.
\yr 1999
\vol 63
\issue 2
\pages 219--244
\mathnet{http://mi.mathnet.ru//eng/im237}
\crossref{https://doi.org/10.1070/im1999v063n02ABEH000237}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1701819}
\zmath{https://zbmath.org/?q=an:0948.74017}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000082449800001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-3142669983}
Linking options:
  • https://www.mathnet.ru/eng/im237
  • https://doi.org/10.1070/im1999v063n02ABEH000237
  • https://www.mathnet.ru/eng/im/v63/i2/p3
  • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:402
    Russian version PDF:188
    English version PDF:8
    References:38
    First page:1
     
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