Geodesic
The simulation of nonlinear oscillations in a micro clock generator
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 4, pp. 499-511 
S. I. Fadeev; V. V. Kogai. The simulation of nonlinear oscillations in a micro clock generator. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 4, pp. 499-511. http://geodesic.mathdoc.fr/item/SJVM_2019_22_4_a7/
@article{SJVM_2019_22_4_a7,
     author = {S. I. Fadeev and V. V. Kogai},
     title = {The simulation of nonlinear oscillations in a micro clock generator},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {499--511},
     year = {2019},
     volume = {22},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2019_22_4_a7/}
}
TY  - JOUR
AU  - S. I. Fadeev
AU  - V. V. Kogai
TI  - The simulation of nonlinear oscillations in a micro clock generator
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2019
SP  - 499
EP  - 511
VL  - 22
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJVM_2019_22_4_a7/
LA  - ru
ID  - SJVM_2019_22_4_a7
ER  - 
%0 Journal Article
%A S. I. Fadeev
%A V. V. Kogai
%T The simulation of nonlinear oscillations in a micro clock generator
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2019
%P 499-511
%V 22
%N 4
%U http://geodesic.mathdoc.fr/item/SJVM_2019_22_4_a7/
%G ru
%F SJVM_2019_22_4_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] E. G. Koscov, “Sostoyanie i perspektivy mikro- i nanoelektromekhaniki”, Avtometriya, 45:3 (2009), 3–52

[2] Younis M. I., MEMS Linear, Nonlinear Statics and Dynamics, Springer Science Business Media, 2011 | MR

[3] Ya. S. Grinberg, Yu. A. Pashkin, E. V. Il'ichev, “Nanomekhanicheskie rezonatory”, UFN, 182:4 (2012), 407–436 | DOI | MR

[4] E. G. Koscov, S. I. Fadeev, “Novye elektromekhanicheskie rezonatory dlya gigogercevykh chastot”, Avtometriya, 10:2 (2013), 115–122

[5] S. I. Fadeev, D. O. Pimanov, “Issledovanie periodicheskikh resheniy v matematicheskikh modelyakh mikromekhaniki pri impul'snom periodicheskom vozdeystvii”, Vestnik Novosibirskogo gosudarstvennogo universiteta. Seriya: Matematika, mekhanika, informatika, 13:3 (2013), 122–140 | Zbl

[6] A. A. Andronov, A. A. Vitt, S. E. Khaykin, Teoriya kolebaniy, FM, M., 1959

[7] V. V. Kogay, S. I. Fadeev, “Primenenie prodolzheniya po parametru na osnove metoda mnozhestvennoy strel'by dlya chislennogo issledovaniya nelineynykh kraevykh zadach”, Sib. zhurn. industr. matematiki., 4:1 (2001), 83–101 | MR