Lumped-parameter model for dynamic monolayer graphene sheets

Dongming Wei; Daulet Nurakhmetov; Almir Aniyarov; Dichuan Zhang; Christos Spitas

doi:10.1016/j.jsv.2022.117062

Lumped-parameter model for dynamic monolayer graphene sheets

Dongming Wei
, Daulet Nurakhmetov
, Almir Aniyarov
, Dichuan Zhang
, Christos Spitas

Nazarbayev University

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

3 Citations (Scopus)

Abstract

In this paper, the dynamic Euler–Bernoulli PDE model based on the quadratic constitutive law are used for modeling of monolayer graphene sheets suspended in free vibration. The PDE model and corresponding lumped-parameter model are introduced. Analytical formulas for the lumped-parameter model and semi-analytic/numerical solutions of the model are presented by using several techniques of approximations. It is demonstrated analytically and numerically that the nonlinear quadratic term has a significant impact on the resonant frequency of the vibrating system. In additions to the numerical solution, the analytic solution obtained by the variational iteration method with Pade approximations indicates the existence of several natural frequencies of nonlinear models.

Original language	English
Article number	117062
Journal	Journal of Sound and Vibration
Volume	534
DOIs	https://doi.org/10.1016/j.jsv.2022.117062
Publication status	Published - Sept 15 2022

Funding

The lumped-parameter model (11) was developed by the first three authors and supported by the Nazarbayev University research grant SST2016024 . These three authors acknowledge for helpful discussion and suggestion of Remark 1 with Piotr Skrzypacz. The other sections of this work were supported by the Nazarbayev University research grant OPCRP2020002 “Rapid response fixed astronomical telescope for gamma ray bust observation”. Authors are grateful to the anonymous referees for their invaluable suggestions and comments for the improvement of the paper. All authors have read and agreed to the published version of the manuscript.

Keywords

Graphene sheet
Lumped-parameter model
Natural frequency
Stiffness coefficient

ASJC Scopus subject areas

Condensed Matter Physics
Mechanics of Materials
Acoustics and Ultrasonics
Mechanical Engineering

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10.1016/j.jsv.2022.117062

Cite this

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title = "Lumped-parameter model for dynamic monolayer graphene sheets",

abstract = "In this paper, the dynamic Euler–Bernoulli PDE model based on the quadratic constitutive law are used for modeling of monolayer graphene sheets suspended in free vibration. The PDE model and corresponding lumped-parameter model are introduced. Analytical formulas for the lumped-parameter model and semi-analytic/numerical solutions of the model are presented by using several techniques of approximations. It is demonstrated analytically and numerically that the nonlinear quadratic term has a significant impact on the resonant frequency of the vibrating system. In additions to the numerical solution, the analytic solution obtained by the variational iteration method with Pade approximations indicates the existence of several natural frequencies of nonlinear models.",

keywords = "Graphene sheet, Lumped-parameter model, Natural frequency, Stiffness coefficient",

author = "Dongming Wei and Daulet Nurakhmetov and Almir Aniyarov and Dichuan Zhang and Christos Spitas",

note = "Funding Information: The lumped-parameter model (11) was developed by the first three authors and supported by the Nazarbayev University research grant SST2016024 . These three authors acknowledge for helpful discussion and suggestion of Remark 1 with Piotr Skrzypacz. The other sections of this work were supported by the Nazarbayev University research grant OPCRP2020002 “Rapid response fixed astronomical telescope for gamma ray bust observation”. Authors are grateful to the anonymous referees for their invaluable suggestions and comments for the improvement of the paper. All authors have read and agreed to the published version of the manuscript. Publisher Copyright: {\textcopyright} 2022 Elsevier Ltd",

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doi = "10.1016/j.jsv.2022.117062",

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AU - Wei, Dongming

AU - Nurakhmetov, Daulet

AU - Aniyarov, Almir

AU - Zhang, Dichuan

AU - Spitas, Christos

N1 - Funding Information: The lumped-parameter model (11) was developed by the first three authors and supported by the Nazarbayev University research grant SST2016024 . These three authors acknowledge for helpful discussion and suggestion of Remark 1 with Piotr Skrzypacz. The other sections of this work were supported by the Nazarbayev University research grant OPCRP2020002 “Rapid response fixed astronomical telescope for gamma ray bust observation”. Authors are grateful to the anonymous referees for their invaluable suggestions and comments for the improvement of the paper. All authors have read and agreed to the published version of the manuscript. Publisher Copyright: © 2022 Elsevier Ltd

PY - 2022/9/15

Y1 - 2022/9/15

N2 - In this paper, the dynamic Euler–Bernoulli PDE model based on the quadratic constitutive law are used for modeling of monolayer graphene sheets suspended in free vibration. The PDE model and corresponding lumped-parameter model are introduced. Analytical formulas for the lumped-parameter model and semi-analytic/numerical solutions of the model are presented by using several techniques of approximations. It is demonstrated analytically and numerically that the nonlinear quadratic term has a significant impact on the resonant frequency of the vibrating system. In additions to the numerical solution, the analytic solution obtained by the variational iteration method with Pade approximations indicates the existence of several natural frequencies of nonlinear models.

AB - In this paper, the dynamic Euler–Bernoulli PDE model based on the quadratic constitutive law are used for modeling of monolayer graphene sheets suspended in free vibration. The PDE model and corresponding lumped-parameter model are introduced. Analytical formulas for the lumped-parameter model and semi-analytic/numerical solutions of the model are presented by using several techniques of approximations. It is demonstrated analytically and numerically that the nonlinear quadratic term has a significant impact on the resonant frequency of the vibrating system. In additions to the numerical solution, the analytic solution obtained by the variational iteration method with Pade approximations indicates the existence of several natural frequencies of nonlinear models.

KW - Graphene sheet

KW - Lumped-parameter model

KW - Natural frequency

KW - Stiffness coefficient

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UR - https://www.scopus.com/pages/publications/85131671062#tab=citedBy

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DO - 10.1016/j.jsv.2022.117062

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AN - SCOPUS:85131671062

SN - 0022-460X

VL - 534

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

M1 - 117062

ER -

Lumped-parameter model for dynamic monolayer graphene sheets

Abstract

Funding

Keywords

ASJC Scopus subject areas

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