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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 185, Pages 37–49
DOI: https://doi.org/10.36535/0233-6723-2020-185-37-49 (Mi into700) 		 
Mathematical modeling of vibration devices

P. A. Vel'misov, A. V. Ankilov, Yu. V. Pokladova

Ulyanovsk State Technical University
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DOI: https://doi.org/10.36535/0233-6723-2020-185-37-49
Abstract: Mathematical models of vibration devices designed to intensify technological processes are considered. Mathematical models are initial-boundary-value problems for coupled systems of partial differential equations for hydrodynamic functions and deformation functions of elastic elements. We examine the dynamics and dynamic stability of elastic elements. The study of dynamics is based of the Bubnov–Galerkin method. The study of dynamical stability is based on the construction of positive definite Lyapunov-type functionals.
Keywords: aerohydroelasticity, elastic plate, deformation, dynamics, stability, partial differential equation, Bubnov–Galerkin method, Lyapunov functional.
Funding agency Grant number
Russian Foundation for Basic Research 18-41-730015
This work was supported by the Russian Foundation for Basic Research and the Government of the Ulyanovsk Region (project No. 18-41-730015).
Document Type: Article
UDC: 517.9; 532.5; 539.3
MSC: 74F10
Language: Russian
Citation: P. A. Vel'misov, A. V. Ankilov, Yu. V. Pokladova, “Mathematical modeling of vibration devices”, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M.T.Terekhin. Ryazan State University named for S.A. Yesenin, Ryazan, May 17-18, 2019. Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 185, VINITI, Moscow, 2020, 37–49
Citation in format AMSBIB
\Bibitem{VelAnkPok20}
\by P.~A.~Vel'misov, A.~V.~Ankilov, Yu.~V.~Pokladova
\paper Mathematical modeling of vibration devices
\inbook Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M.T.Terekhin. Ryazan State University named for S.A. Yesenin, Ryazan, May 17-18, 2019. Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 185
\pages 37--49
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into700}
\crossref{https://doi.org/10.36535/0233-6723-2020-185-37-49}
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