Dynamics of the round sensing element of a nanoelectromechanical sensor

M. A. Barulina, I. V. Papkova, A. V. Krysko

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The theory of nonlinear dynamics of the circular sensing element of a nanoelectromechanical sensor in the form of flexible elastic axisymmetric nano plates is constructed. The developed theory is general. It is based on the kinematic model of the third approximation (Sheremetev-Pelekh-Reddy). Two other theories follow from it as a special case: the theory of nonlinear dynamics and flexible nano-plates, obtained on the basis of the kinematic model of the first approximation (Kirchhoff), the second approximation (Timoshenko). The general theory obtained follows from the variational principle of Hamilton. For each of the kinematic hypotheses, a system of nonlinear partial differential equations is obtained. Obtaining a 'true' solution is guaranteed using the methodology outlined in [1]. As an example, the model of the first approximation of the nonlinear dynamics of flexible elastic axisymmetric nano-plates is studied. In a numerical experiment, the required equations are solved by different methods, their convergence is investigated. It is shown that taking into account the size-dependent parameter significantly affects the character of plate oscillation and changes their character.

Original languageEnglish
Title of host publication25th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1-4
Number of pages4
ISBN (Electronic)9785919950578
DOIs
Publication statusPublished - 6 Jul 2018
Externally publishedYes
Event25th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018 - Saint Petersburg, Russian Federation
Duration: 28 May 201830 May 2018

Conference

Conference25th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018
CountryRussian Federation
CitySaint Petersburg
Period28.5.1830.5.18

Fingerprint

Kinematics
Sensing
Sensor
Nonlinear Dynamics
Sensors
Kinematic Model
Approximation
Partial differential equations
Nonlinear Partial Differential Equations
Variational Principle
Numerical Experiment
Oscillation
Experiments
Methodology
Dependent
Character
Model

Keywords

  • a modified couple stress theory
  • chaos
  • Fourier spectrum
  • geometric nonlinearity
  • Kirchhoff model (first approximation)
  • Lyapunov exponents
  • mathematical model
  • NEMS sensor
  • phase portrait
  • round axisymmetric size-dependent nanoplate
  • S.P. Timoshenko model (second approximation)
  • Sheremetev-Pelekh-Reddy model (third approximation)

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Aerospace Engineering
  • Automotive Engineering
  • Control and Optimization

Cite this

Barulina, M. A., Papkova, I. V., & Krysko, A. V. (2018). Dynamics of the round sensing element of a nanoelectromechanical sensor. In 25th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018 - Proceedings (pp. 1-4). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ICINS.2018.8405901

Dynamics of the round sensing element of a nanoelectromechanical sensor. / Barulina, M. A.; Papkova, I. V.; Krysko, A. V.

25th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2018. p. 1-4.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Barulina, MA, Papkova, IV & Krysko, AV 2018, Dynamics of the round sensing element of a nanoelectromechanical sensor. in 25th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc., pp. 1-4, 25th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018, Saint Petersburg, Russian Federation, 28.5.18. https://doi.org/10.23919/ICINS.2018.8405901
Barulina MA, Papkova IV, Krysko AV. Dynamics of the round sensing element of a nanoelectromechanical sensor. In 25th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2018. p. 1-4 https://doi.org/10.23919/ICINS.2018.8405901
Barulina, M. A. ; Papkova, I. V. ; Krysko, A. V. / Dynamics of the round sensing element of a nanoelectromechanical sensor. 25th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 1-4
@inproceedings{ab91899a2a124346ac13a6b6422ee803,
title = "Dynamics of the round sensing element of a nanoelectromechanical sensor",
abstract = "The theory of nonlinear dynamics of the circular sensing element of a nanoelectromechanical sensor in the form of flexible elastic axisymmetric nano plates is constructed. The developed theory is general. It is based on the kinematic model of the third approximation (Sheremetev-Pelekh-Reddy). Two other theories follow from it as a special case: the theory of nonlinear dynamics and flexible nano-plates, obtained on the basis of the kinematic model of the first approximation (Kirchhoff), the second approximation (Timoshenko). The general theory obtained follows from the variational principle of Hamilton. For each of the kinematic hypotheses, a system of nonlinear partial differential equations is obtained. Obtaining a 'true' solution is guaranteed using the methodology outlined in [1]. As an example, the model of the first approximation of the nonlinear dynamics of flexible elastic axisymmetric nano-plates is studied. In a numerical experiment, the required equations are solved by different methods, their convergence is investigated. It is shown that taking into account the size-dependent parameter significantly affects the character of plate oscillation and changes their character.",
keywords = "a modified couple stress theory, chaos, Fourier spectrum, geometric nonlinearity, Kirchhoff model (first approximation), Lyapunov exponents, mathematical model, NEMS sensor, phase portrait, round axisymmetric size-dependent nanoplate, S.P. Timoshenko model (second approximation), Sheremetev-Pelekh-Reddy model (third approximation)",
author = "Barulina, {M. A.} and Papkova, {I. V.} and Krysko, {A. V.}",
year = "2018",
month = "7",
day = "6",
doi = "10.23919/ICINS.2018.8405901",
language = "English",
pages = "1--4",
booktitle = "25th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018 - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
address = "United States",

}

TY - GEN

T1 - Dynamics of the round sensing element of a nanoelectromechanical sensor

AU - Barulina, M. A.

AU - Papkova, I. V.

AU - Krysko, A. V.

PY - 2018/7/6

Y1 - 2018/7/6

N2 - The theory of nonlinear dynamics of the circular sensing element of a nanoelectromechanical sensor in the form of flexible elastic axisymmetric nano plates is constructed. The developed theory is general. It is based on the kinematic model of the third approximation (Sheremetev-Pelekh-Reddy). Two other theories follow from it as a special case: the theory of nonlinear dynamics and flexible nano-plates, obtained on the basis of the kinematic model of the first approximation (Kirchhoff), the second approximation (Timoshenko). The general theory obtained follows from the variational principle of Hamilton. For each of the kinematic hypotheses, a system of nonlinear partial differential equations is obtained. Obtaining a 'true' solution is guaranteed using the methodology outlined in [1]. As an example, the model of the first approximation of the nonlinear dynamics of flexible elastic axisymmetric nano-plates is studied. In a numerical experiment, the required equations are solved by different methods, their convergence is investigated. It is shown that taking into account the size-dependent parameter significantly affects the character of plate oscillation and changes their character.

AB - The theory of nonlinear dynamics of the circular sensing element of a nanoelectromechanical sensor in the form of flexible elastic axisymmetric nano plates is constructed. The developed theory is general. It is based on the kinematic model of the third approximation (Sheremetev-Pelekh-Reddy). Two other theories follow from it as a special case: the theory of nonlinear dynamics and flexible nano-plates, obtained on the basis of the kinematic model of the first approximation (Kirchhoff), the second approximation (Timoshenko). The general theory obtained follows from the variational principle of Hamilton. For each of the kinematic hypotheses, a system of nonlinear partial differential equations is obtained. Obtaining a 'true' solution is guaranteed using the methodology outlined in [1]. As an example, the model of the first approximation of the nonlinear dynamics of flexible elastic axisymmetric nano-plates is studied. In a numerical experiment, the required equations are solved by different methods, their convergence is investigated. It is shown that taking into account the size-dependent parameter significantly affects the character of plate oscillation and changes their character.

KW - a modified couple stress theory

KW - chaos

KW - Fourier spectrum

KW - geometric nonlinearity

KW - Kirchhoff model (first approximation)

KW - Lyapunov exponents

KW - mathematical model

KW - NEMS sensor

KW - phase portrait

KW - round axisymmetric size-dependent nanoplate

KW - S.P. Timoshenko model (second approximation)

KW - Sheremetev-Pelekh-Reddy model (third approximation)

UR - http://www.scopus.com/inward/record.url?scp=85050666161&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050666161&partnerID=8YFLogxK

U2 - 10.23919/ICINS.2018.8405901

DO - 10.23919/ICINS.2018.8405901

M3 - Conference contribution

SP - 1

EP - 4

BT - 25th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

ER -