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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 3, Pages 133–145 (Mi sjim799)  
This article is cited in 1 scientific paper (total in 1 paper)

Numerical study of mathematical models of micromechanics with periodic impulse action

S. I. Fadeevab, D. O. Pimanovb

a Sobolev Institute of Mathematics SD RAS, 4 Koptyug av., 630090 Novosibirsk
b Novosibirsk State University, 2 Pirogova st., 630090, Novosibirsk
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Abstract: We consider the results of the numerical study of mathematical models of two microelectromechanical systems (MEMS). We formulate matematical models as initial boundary value problems describing the cylindrical flexure of the elastic beam as a movable electrode under the action of a repetitive intensity impulse of the electrostatic field between the movable and fixed electrodes in a microgap. In the first problem, both ends of the beam are rigidly fixed, and in the second problem, we consider a cantilever beam. The range of the parameters is found for a model having two periodic solutions with periods of impulse interaction one of which is stable and the other is unstable.
Keywords: nonlinear oscillation, electrostatic attraction, method of lines, boundary value problem, continuation with respect to a parameter, nonuniqueness of solutions.
Received: 13.03.2013
English version:
Journal of Applied and Industrial Mathematics, 2013, Volume 7, Issue 4, Pages 503–514
DOI: https://doi.org/10.1134/S1990478913040054
Bibliographic databases:
Document Type: Article
UDC: 519.63:621.38
Language: Russian
Citation: S. I. Fadeev, D. O. Pimanov, “Numerical study of mathematical models of micromechanics with periodic impulse action”, Sib. Zh. Ind. Mat., 16:3 (2013), 133–145; J. Appl. Industr. Math., 7:4 (2013), 503–514
Citation in format AMSBIB
\Bibitem{FadPim13}
\by S.~I.~Fadeev, D.~O.~Pimanov
\paper Numerical study of mathematical models of micromechanics with periodic impulse action
\jour Sib. Zh. Ind. Mat.
\yr 2013
\vol 16
\issue 3
\pages 133--145
\mathnet{http://mi.mathnet.ru/sjim799}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3234780}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 4
\pages 503--514
\crossref{https://doi.org/10.1134/S1990478913040054}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский журнал индустриальной математики
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