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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 8, Pages 1355–1365
DOI: https://doi.org/10.31857/S0044466924080026 (Mi zvmmf11805) 		 
General numerical methods

A method for separating the matrix spectrum by a straight line and an infinite strip flutter problem

È. A. Biberdorfa, A. S. Rudometovaa, Wang Lib, A. D. Zhumabaevb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 630090, Novosibirsk, Russia
b Novosibirsk State University, 630090, Novosibirsk, Russia
DOI: https://doi.org/10.31857/S0044466924080026
Abstract: A novel method for separating the matrix spectrum by a straight line based on a fractional linear transformation is proposed. This method has a number of advantages over the approaches based on an exponential transformation; more precisely, the range of its application is wider and the number of iterations needed for its convergence is much lower. The proposed method is used to study flutter problems for an infinite strip under various edge fastening conditions, which, after suitable discretization of differential operators, are reduced to spectral problems for linear operators. The study of stability regions by the method of spectrum dichotomy by the imaginary axis makes it possible to construct neutral curves in the plane of parameters of the flutter problem.
Key words: spectrum dichotomy, stability domain, flutter, discretization of differential operator, neutral curve.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022- 0008
This work was accomplished within the state assignment of the Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0008.
Received: 02.04.2024
Revised: 02.04.2024
Accepted: 02.05.2024
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 8, Pages 1704–1714
DOI: https://doi.org/10.1134/S0965542524700891
Bibliographic databases:
Document Type: Article
UDC: 519.61
Language: Russian
Citation: È. A. Biberdorf, A. S. Rudometova, Wang Li, A. D. Zhumabaev, “A method for separating the matrix spectrum by a straight line and an infinite strip flutter problem”, Zh. Vychisl. Mat. Mat. Fiz., 64:8 (2024), 1355–1365; Comput. Math. Math. Phys., 64:8 (2024), 1704–1714
Citation in format AMSBIB
\Bibitem{BibRudWan24}
\by \`E.~A.~Biberdorf, A.~S.~Rudometova, Wang~Li, A.~D.~Zhumabaev
\paper A method for separating the matrix spectrum by a straight line and an infinite strip flutter problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 8
\pages 1355--1365
\mathnet{http://mi.mathnet.ru/zvmmf11805}
\crossref{https://doi.org/10.31857/S0044466924080026}
\elib{https://elibrary.ru/item.asp?id=75224100}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 8
\pages 1704--1714
\crossref{https://doi.org/10.1134/S0965542524700891}
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