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Simulation of Nonlinear Oscillations in a Micro-Generator of Clock Frequency. / Fadeev, S. I.; Kogai, V. V.

In: Numerical Analysis and Applications, Vol. 12, No. 4, 01.10.2019, p. 407-417.

Research output: Contribution to journal › Article › peer-review

Harvard

Fadeev, SI & Kogai, VV 2019, 'Simulation of Nonlinear Oscillations in a Micro-Generator of Clock Frequency', Numerical Analysis and Applications, vol. 12, no. 4, pp. 407-417. https://doi.org/10.1134/S1995423919040086

APA

Fadeev, S. I., & Kogai, V. V. (2019). Simulation of Nonlinear Oscillations in a Micro-Generator of Clock Frequency. Numerical Analysis and Applications, 12(4), 407-417. https://doi.org/10.1134/S1995423919040086

Vancouver

Fadeev SI, Kogai VV. Simulation of Nonlinear Oscillations in a Micro-Generator of Clock Frequency. Numerical Analysis and Applications. 2019 Oct 1;12(4):407-417. doi: 10.1134/S1995423919040086

Author

Fadeev, S. I. ; Kogai, V. V. / Simulation of Nonlinear Oscillations in a Micro-Generator of Clock Frequency. In: Numerical Analysis and Applications. 2019 ; Vol. 12, No. 4. pp. 407-417.

BibTeX

@article{2656ffb4063148f6979beebfbfb0e04a,
title = "Simulation of Nonlinear Oscillations in a Micro-Generator of Clock Frequency",
abstract = "In this paper, we consider a mathematical model of a new-type micro- generator. The model is based on excitation by electrostatic forces of oscillations of a mobile electrode in a micro gap. The principle of operation of the micro-generator is similar to the well-known theory of clock with a striking escapement mechanism. The difference is that in the equation of motion, the form of the right-hand side takes into account the electrostatic nature of the pulsed action. The numerical analysis shows that with time the bounded oscillations in the phase plane tend to a stable limit cycle, and thus the emerging oscillations are stable towards external perturbations. Studying periodic oscillations in dependence on model parameters relies on the boundary value problem solution for an equation with a discontinuous right-hand side transformed so that to enable application of the method of solution continuation with respect to a parameter. In this way, the domain in the plane of model parameters in which stable limit cycles exist is defined.",
keywords = "mathematical model, micro-generator, Cauchy problem, boundary value problem, periodic oscillations, limit cycle, phase plane, continuation of solution with respect to a parameter",
author = "Fadeev, {S. I.} and Kogai, {V. V.}",
year = "2019",
month = oct,
day = "1",
doi = "10.1134/S1995423919040086",
language = "English",
volume = "12",
pages = "407--417",
journal = "Numerical Analysis and Applications",
issn = "1995-4239",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "4",

}

RIS

TY - JOUR

T1 - Simulation of Nonlinear Oscillations in a Micro-Generator of Clock Frequency

AU - Fadeev, S. I.

AU - Kogai, V. V.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - In this paper, we consider a mathematical model of a new-type micro- generator. The model is based on excitation by electrostatic forces of oscillations of a mobile electrode in a micro gap. The principle of operation of the micro-generator is similar to the well-known theory of clock with a striking escapement mechanism. The difference is that in the equation of motion, the form of the right-hand side takes into account the electrostatic nature of the pulsed action. The numerical analysis shows that with time the bounded oscillations in the phase plane tend to a stable limit cycle, and thus the emerging oscillations are stable towards external perturbations. Studying periodic oscillations in dependence on model parameters relies on the boundary value problem solution for an equation with a discontinuous right-hand side transformed so that to enable application of the method of solution continuation with respect to a parameter. In this way, the domain in the plane of model parameters in which stable limit cycles exist is defined.

AB - In this paper, we consider a mathematical model of a new-type micro- generator. The model is based on excitation by electrostatic forces of oscillations of a mobile electrode in a micro gap. The principle of operation of the micro-generator is similar to the well-known theory of clock with a striking escapement mechanism. The difference is that in the equation of motion, the form of the right-hand side takes into account the electrostatic nature of the pulsed action. The numerical analysis shows that with time the bounded oscillations in the phase plane tend to a stable limit cycle, and thus the emerging oscillations are stable towards external perturbations. Studying periodic oscillations in dependence on model parameters relies on the boundary value problem solution for an equation with a discontinuous right-hand side transformed so that to enable application of the method of solution continuation with respect to a parameter. In this way, the domain in the plane of model parameters in which stable limit cycles exist is defined.

KW - mathematical model

KW - micro-generator

KW - Cauchy problem

KW - boundary value problem

KW - periodic oscillations

KW - limit cycle

KW - phase plane

KW - continuation of solution with respect to a parameter

UR - http://www.scopus.com/inward/record.url?scp=85079572867&partnerID=8YFLogxK

U2 - 10.1134/S1995423919040086

DO - 10.1134/S1995423919040086

M3 - Article

VL - 12

SP - 407

EP - 417

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 4

ER -

ID: 24302111