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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2019, Volume 22, Number 4, Pages 499–511
DOI: https://doi.org/10.15372/SJNM20190408
(Mi sjvm728)
 

This article is cited in 2 scientific papers (total in 2 papers)

The simulation of nonlinear oscillations in a micro clock generator

S. I. Fadeevab, V. V. Kogaiab

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia
References:
Abstract: In this paper, we consider a mathematical model of a new type of a microgenerator, based on generating the oscillations of a mobile electrode in a micro-gap due to electrostatic forces. The principle of operation of the generator is analogous to the well-known theory of the clock-escapement mechanism, with the difference that in the equation of motion the form of the right-hand side corresponds to the electrostatic nature of the impulse action. The numerical analysis shows that the bounded oscillations with an increase in time tend towards a stable limit cycle in the phase plane and, thereby, the emerging oscillations are stable with respect to external perturbations. In studying periodic oscillations, depending on the parameters of a model, we use the solution of the boundary value problem for the equation with a discontinuous right-hand side, transformed to a form allowing the application of the numerical continuation method. In this way, the area in the plane of the model parameters is defined, in which stable limit cycles exist.
Key words: mathematical model, microgenerator, Cauchy problem, boundary value problem, periodic oscillations, limit cycle, phase plane, continuation of the solution with respect to the parameter.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences 273
This work was supported by the SB RAS Comprehensive Fundamental Research Program “Interdisciplinary integration studies” for 2018–2020 (project no. 273).
Received: 28.09.2018
Revised: 20.11.2018
Accepted: 25.07.2019
English version:
Numerical Analysis and Applications, 2019, Volume 12, Issue 4, Pages 407–417
DOI: https://doi.org/10.1134/S1995423919040086
Bibliographic databases:
Document Type: Article
UDC: 519.62, 621.38
Language: Russian
Citation: S. I. Fadeev, V. V. Kogai, “The simulation of nonlinear oscillations in a micro clock generator”, Sib. Zh. Vychisl. Mat., 22:4 (2019), 499–511; Num. Anal. Appl., 12:4 (2019), 407–417
Citation in format AMSBIB
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\by S.~I.~Fadeev, V.~V.~Kogai
\paper The simulation of nonlinear oscillations in a micro clock generator
\jour Sib. Zh. Vychisl. Mat.
\yr 2019
\vol 22
\issue 4
\pages 499--511
\mathnet{http://mi.mathnet.ru/sjvm728}
\crossref{https://doi.org/10.15372/SJNM20190408}
\transl
\jour Num. Anal. Appl.
\yr 2019
\vol 12
\issue 4
\pages 407--417
\crossref{https://doi.org/10.1134/S1995423919040086}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000513714900008}
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  • This publication is cited in the following 2 articles:
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