Numerical Study of Nonlinear Oscillations in a Clock Frequency MEMS-Generator

Standard

Numerical Study of Nonlinear Oscillations in a Clock Frequency MEMS-Generator. / Fadeev, S. I.

In: Journal of Applied and Industrial Mathematics, Vol. 14, No. 2, 01.05.2020, p. 296-307.

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

Harvard

Fadeev, SI 2020, 'Numerical Study of Nonlinear Oscillations in a Clock Frequency MEMS-Generator', Journal of Applied and Industrial Mathematics, vol. 14, no. 2, pp. 296-307. https://doi.org/10.1134/S1990478920020088

APA

Fadeev, S. I. (2020). Numerical Study of Nonlinear Oscillations in a Clock Frequency MEMS-Generator. Journal of Applied and Industrial Mathematics, 14(2), 296-307. https://doi.org/10.1134/S1990478920020088

Vancouver

Fadeev SI. Numerical Study of Nonlinear Oscillations in a Clock Frequency MEMS-Generator. Journal of Applied and Industrial Mathematics. 2020 May 1;14(2):296-307. doi: 10.1134/S1990478920020088

Author

Fadeev, S. I. / Numerical Study of Nonlinear Oscillations in a Clock Frequency MEMS-Generator. In: Journal of Applied and Industrial Mathematics. 2020 ; Vol. 14, No. 2. pp. 296-307.

BibTeX

@article{839a03285e3d4e3482da68b7f3fcd56e,

title = "Numerical Study of Nonlinear Oscillations in a Clock Frequency MEMS-Generator",

abstract = "Under consideration is some mathematical model of a clock frequency generator, a deviceof the MEMS class (microelectromechanical systems). We numerically study the solution of thecorresponding second-order ordinary differential equation with nonlinear right-hand side and showthat there is a region of the model parameters in which the bounded solutions tend to a stablelimit cycle in the phase plane and, therefore, the periodic oscillations are stable with respectto the external perturbations. To determine the boundary of the region, we use the parametercontinuation method of the solution of the boundary value problem defining the limit cycle. Themodel leads to the numerical identification of the region of generator operability.",

keywords = "boundary value problem, frequency generator, limit cycle, mathematical model, parameter continuation method, periodic oscillations, phase plane, stability",

author = "Fadeev, {S. I.}",

year = "2020",

month = may,

day = "1",

doi = "10.1134/S1990478920020088",

language = "English",

volume = "14",

pages = "296--307",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Numerical Study of Nonlinear Oscillations in a Clock Frequency MEMS-Generator

AU - Fadeev, S. I.

PY - 2020/5/1

Y1 - 2020/5/1

N2 - Under consideration is some mathematical model of a clock frequency generator, a deviceof the MEMS class (microelectromechanical systems). We numerically study the solution of thecorresponding second-order ordinary differential equation with nonlinear right-hand side and showthat there is a region of the model parameters in which the bounded solutions tend to a stablelimit cycle in the phase plane and, therefore, the periodic oscillations are stable with respectto the external perturbations. To determine the boundary of the region, we use the parametercontinuation method of the solution of the boundary value problem defining the limit cycle. Themodel leads to the numerical identification of the region of generator operability.

AB - Under consideration is some mathematical model of a clock frequency generator, a deviceof the MEMS class (microelectromechanical systems). We numerically study the solution of thecorresponding second-order ordinary differential equation with nonlinear right-hand side and showthat there is a region of the model parameters in which the bounded solutions tend to a stablelimit cycle in the phase plane and, therefore, the periodic oscillations are stable with respectto the external perturbations. To determine the boundary of the region, we use the parametercontinuation method of the solution of the boundary value problem defining the limit cycle. Themodel leads to the numerical identification of the region of generator operability.

KW - boundary value problem

KW - frequency generator

KW - limit cycle

KW - mathematical model

KW - parameter continuation method

KW - periodic oscillations

KW - phase plane

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=85087670488&partnerID=8YFLogxK

U2 - 10.1134/S1990478920020088

DO - 10.1134/S1990478920020088

M3 - Article

AN - SCOPUS:85087670488

VL - 14

SP - 296

EP - 307

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 2

ER -

ID: 24769494