Abstract:
In this article the dynamical stability of elastic walls of plane channels under flowing of the perfect liquid is investigated on the basis of mathematical models. Either the law of pressure change or the potential of liquid velocity or the longitudinal component of liquid velocity are applied on the input and output from the channels. The sufficient conditions of stability are obtained. These conditions impose a constraint on the velocity of the liquid homogeneous stream, on the compressing (decompressing) force and other parameters of mechanical system.
Citation:
A. V. Ankilov, P. A. Vel'misov, “On stability of solutions of equations of interaction between elastic walls of channels and affluent liquid”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 179–185
\Bibitem{AnkVel11}
\by A.~V.~Ankilov, P.~A.~Vel'misov
\paper On stability of solutions of equations of interaction between elastic walls of channels and affluent liquid
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 1(22)
\pages 179--185
\mathnet{http://mi.mathnet.ru/vsgtu869}
\crossref{https://doi.org/10.14498/vsgtu869}
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https://www.mathnet.ru/eng/vsgtu869
https://www.mathnet.ru/eng/vsgtu/v122/p179
This publication is cited in the following 9 articles:
P. A. Vel'misov, Yu. A. Tamarova, E. P. Semenova, “Asymptotic Equations of Gas Dynamics: Qualitative Analysis, Construction of Solutions, and Applications”, J Math Sci, 259:3 (2021), 309
P. A. Velmisov, Yu. A. Tamarova, E. P. Semenova, “Asimptoticheskie uravneniya gazovoi dinamiki: kachestvennyi analiz, postroenie reshenii, prilozheniya”, Materialy IV Mezhdunarodnoi nauchnoi konferentsii “Aktualnye problemy
prikladnoi matematiki”. Kabardino-Balkarskaya respublika, Nalchik, Prielbruse, 22–26 maya 2018 g. Chast I, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 165, VINITI RAN, M., 2019, 47–62
A. V. Ankilov, P. A. Velmisov, Yu. A. Tamarova, “Issledovanie dinamiki i ustoichivosti uprugogo elementa protochnogo kanala”, Zhurnal SVMO, 18:1 (2016), 94–107
P. A. Velmisov, A. V. Korneev, S. V. Kireev, “Issledovanie dinamicheskoi ustoichivosti truboprovoda”, Zhurnal SVMO, 18:2 (2016), 106–114
Petr A. Velmisov, Andrey V. Ankilov, Vsevolod A. Sudakov, “Mathematical modeling of the problem about dynamic stability of the shield in a supersonic gas flow”, ROMAI J., 1 (2014), 221–235https://rj.romai.ro/arhiva/2014/1/Velmisov2.pdf
P. A. Velmisov, V. A. Sudakov, A. V. Ankilov, “Chislennyi eksperiment v zadache o dinamike zaschitnogo ekrana pri sverkhzvukovom obtekanii potokom gaza”, Vestnik Ulyanovskogo gosudarstvennogo tekhnicheskogo universiteta, 2013, no. 3(63), 38–44
A. V. Ankilov, P. A. Velmisov, V. A. Sudakov, “Ob ustoichivosti reshenii nachalno-kraevoi zadachi o dinamike zaschitnogo ekrana pri vzaimodeistvii so sverkhzvukovym potokom gaza”, Vestnik Ulyanovskogo gosudarstvennogo tekhnicheskogo universiteta, 2013, no. 3(63), 45–52
P. A. Velmisov, Yu. A. Reshetnikov, V. V. Bogdanov, E. P. Semënova, “Matematicheskaya model gidrodinamicheskogo izluchatelya”, Vestnik Ulyanovskogo gosudarstvennogo tekhnicheskogo universiteta, 2013, no. 4(64), 31–39
P. A. Velmisov, Yu. A. Reshetnikov, E. P. Semënova, A. B. Zakharova, “Matematicheskaya model krylovogo profilya v aerodinamicheskoi trube”, Vestnik Ulyanovskogo gosudarstvennogo tekhnicheskogo universiteta, 2013, no. 4(64), 40–50
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