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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2013, Volume 13, Issue 3, Pages 122–140 (Mi vngu160)  
This article is cited in 2 scientific papers (total in 2 papers)

Researching of Periodic Solutions in a Mathematical Models of Micromechanics with Pulsed Periodic Impact

S. I. Fadeevab, D. O. Pimanovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
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Abstract: This paper considers results of the researching of nonlinear vibration in mathematical models of two microelectromechanical systems (MEMS). These models describe motion of moveable electrode in the micro-gap. The motion is due to the impact of repetitive pulse electrostatic field between the moveable and fixed electrodes. Thereby we formulate boundary value problems with periodicity conditions for the differential equation of motion of a point on plane and the hyperbolic equation. We found the range of parameters of models which consider a multiplicity of periodic solutions (two), one of which is stable and other — unstable.
Keywords: nonlinear vibration, electrostatic attraction, method of lines, boundary value problem, parameter continuation, multiplicity of solutions.
Received: 01.10.2012
English version:
Journal of Mathematical Sciences, 2015, Volume 205, Issue 3, Pages 473–489
DOI: https://doi.org/10.1007/s10958-015-2261-4
Document Type: Article
UDC: 519.63, 621.38
Language: Russian
Citation: S. I. Fadeev, D. O. Pimanov, “Researching of Periodic Solutions in a Mathematical Models of Micromechanics with Pulsed Periodic Impact”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 13:3 (2013), 122–140; J. Math. Sci., 205:3 (2015), 473–489
Citation in format AMSBIB
\Bibitem{FadPim13}
\by S.~I.~Fadeev, D.~O.~Pimanov
\paper Researching of Periodic Solutions in a Mathematical Models of~Micromechanics with Pulsed Periodic Impact
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2013
\vol 13
\issue 3
\pages 122--140
\mathnet{http://mi.mathnet.ru/vngu160}
\transl
\jour J. Math. Sci.
\yr 2015
\vol 205
\issue 3
\pages 473--489
\crossref{https://doi.org/10.1007/s10958-015-2261-4}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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