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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2018, Volume 22, Number 1, Pages 96–115 (Mi vsgtu1588)  

This article is cited in 3 scientific papers (total in 3 papers)

Mathematical Modeling, Numerical Methods and Software Complexes

Dynamic stability of deformable elements of designs at supersonic mode of flow

P. A. Vel'misov*, A. V. Ankilov

Ulyanovsk State Technical University, Ulyanovsk, 432027, Russian Federation

Abstract: The stability of deformable element of a construction in the form of a plate-strip with its flowing by supersonic flow of ideal gas is investigated. Adopted in paper definitions of stability are consistent with the concept of stability of dynamical systems by Lyapunov. For the description of dynamics of an elastic body the nonlinear mathematical model taking into account transverse and longitudinal deformations of the elastic plate is used. The model describes the associated system of partial differential equations for two unknown functions of deformations. Aerodynamic pressure upon a plate is defined according to Ilyushin's “piston” theory. On the base of the built functional for the case of hinged motionless fixing the ends of the plate the sufficient conditions of stability of the solution of the system of equations describing the length-cross oscillations of the plate are obtained. The estimation of the amplitude of deformations depending on initial conditions is made. On a specific example of one mechanical system the using of the proved theorems and estimates is shown.

Keywords: aerohydroelasticity, mathematical modeling, dynamic stability, elastic plate, supersonic flow of gas, system of the partial differential equations, functional

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-08599_
15-41-02455_--
This work was financially supported by the Russian Foundation for Basic Research (150108599_a and 154102455_r-povolzhe-a).

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1588

Full text: PDF file (718 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 533.6.013.4
MSC: 74F10
Received: December 12, 2017
Revised: February 17, 2018
Accepted: March 12, 2018
First online: March 28, 2018

Citation: P. A. Vel'misov, A. V. Ankilov, “Dynamic stability of deformable elements of designs at supersonic mode of flow”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 22:1 (2018), 96–115

Citation in format AMSBIB
\Bibitem{VelAnk18}
\by P.~A.~Vel'misov, A.~V.~Ankilov
\paper Dynamic stability of deformable elements of designs at supersonic mode of flow
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2018
\vol 22
\issue 1
\pages 96--115
\mathnet{http://mi.mathnet.ru/vsgtu1588}
\crossref{https://doi.org/10.14498/vsgtu1588}
\zmath{https://zbmath.org/?q=an:07038277}
\elib{https://elibrary.ru/item.asp?id=35246684}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. I. Eremeeva, P. A. Velmisov, “Dinamika vyazkouprugogo elementa protochnogo kanala”, Zhurnal SVMO, 21:4 (2019), 488–506  mathnet  crossref
    2. P. A. Velmisov, A. V. Ankilov, Yu. A. Tamarova, “Mathematical modeling in problems of dynamics and stability of some aeroelastic systems”, Proceedings of the 45Th International Conference on Application of Mathematics in Engineering and Economics (Amee'19), AIP Conf. Proc., 2172, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2019, 030010  crossref  isi  scopus
    3. P. A. Velmisov, A. V. Ankilov, Yu. V. Pokladova, “Matematicheskoe modelirovanie vibratsionnykh ustroistv”, MaterialyVserossiiskoinauchnoikonferentsii Differentsialnye uravneniyai ikh prilozheniya,posvyaschennoi 85-letiyu professoraM.T.Terekhina.Ryazanskii gosudarstvennyi universitet im. S.A. Esenina,Ryazan, 1718 maya2019 g. Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 185, VINITI RAN, M., 2020, 37–49  mathnet  crossref
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