Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device

D. Wei; S. Kadyrov; Z. Kazbek

doi:10.24132/acm.2017.322

Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device

D. Wei
, S. Kadyrov
, Z. Kazbek

Department of Mathematics

Nazarbayev University

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

5 Citations (Scopus)

2 Downloads (Pure)

Abstract

Phase plane analysis of the nonlinear spring-mass equation arising in modeling vibrations of a lumped mass attached to a graphene sheet with a fixed end is presented. The nonlinear lumped-mass model takes into account the nonlinear behavior of the graphene by including the third-order elastic stiffness constant and the nonlinear electrostatic force. Standard pull-in voltages are computed. Graphic phase diagrams are used to demonstrate the conclusions. The nonlinear wave forms and the associated resonance frequencies are computed and presented graphically to demonstrate the effects of the nonlinear stiffness constant comparing with the corresponding linear model. The existence of periodic solutions of the model is proved analytically for physically admissible periodic solutions, and conditions for bifurcation points on a parameter associated with the third-order elastic stiffness constant are determined.

Original language	English
Pages (from-to)	81-90
Number of pages	10
Journal	Applied and Computational Mechanics
Volume	11
Issue number	1
DOIs	https://doi.org/10.24132/acm.2017.322
Publication status	Published - 2017

Funding

The authors thank the School of Science and Technology, Nazarbayev University for supporting capstone research projects like the one that produced the part of results in this paper and also thank the three anonymous reviewer’s valuable comments and suggestions which helped us to improve the presentations in the paper significantly. The first author is thankful for the support of the Nazarbayev University ORAU grant which helped completing this paper.

Keywords

Electrostatic pull-in stability
Graphene
Lumped-mass model
Nonlinear spring
Periodic solutions

ASJC Scopus subject areas

Biophysics
Computational Mechanics
Civil and Structural Engineering
Fluid Flow and Transfer Processes
Computational Mathematics

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Cite this

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title = "Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device",

abstract = "Phase plane analysis of the nonlinear spring-mass equation arising in modeling vibrations of a lumped mass attached to a graphene sheet with a fixed end is presented. The nonlinear lumped-mass model takes into account the nonlinear behavior of the graphene by including the third-order elastic stiffness constant and the nonlinear electrostatic force. Standard pull-in voltages are computed. Graphic phase diagrams are used to demonstrate the conclusions. The nonlinear wave forms and the associated resonance frequencies are computed and presented graphically to demonstrate the effects of the nonlinear stiffness constant comparing with the corresponding linear model. The existence of periodic solutions of the model is proved analytically for physically admissible periodic solutions, and conditions for bifurcation points on a parameter associated with the third-order elastic stiffness constant are determined.",

keywords = "Electrostatic pull-in stability, Graphene, Lumped-mass model, Nonlinear spring, Periodic solutions",

author = "D. Wei and S. Kadyrov and Z. Kazbek",

note = "Funding Information: The authors thank the School of Science and Technology, Nazarbayev University for supporting capstone research projects like the one that produced the part of results in this paper and also thank the three anonymous reviewer{\textquoteright}s valuable comments and suggestions which helped us to improve the presentations in the paper significantly. The first author is thankful for the support of the Nazarbayev University ORAU grant which helped completing this paper. Publisher Copyright: {\textcopyright} 2017 University of West Bohemia. All rights reserved.",

year = "2017",

doi = "10.24132/acm.2017.322",

language = "English",

volume = "11",

pages = "81--90",

journal = "Applied and Computational Mechanics",

issn = "1802-680X",

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TY - JOUR

T1 - Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device

AU - Wei, D.

AU - Kadyrov, S.

AU - Kazbek, Z.

N1 - Funding Information: The authors thank the School of Science and Technology, Nazarbayev University for supporting capstone research projects like the one that produced the part of results in this paper and also thank the three anonymous reviewer’s valuable comments and suggestions which helped us to improve the presentations in the paper significantly. The first author is thankful for the support of the Nazarbayev University ORAU grant which helped completing this paper. Publisher Copyright: © 2017 University of West Bohemia. All rights reserved.

PY - 2017

Y1 - 2017

N2 - Phase plane analysis of the nonlinear spring-mass equation arising in modeling vibrations of a lumped mass attached to a graphene sheet with a fixed end is presented. The nonlinear lumped-mass model takes into account the nonlinear behavior of the graphene by including the third-order elastic stiffness constant and the nonlinear electrostatic force. Standard pull-in voltages are computed. Graphic phase diagrams are used to demonstrate the conclusions. The nonlinear wave forms and the associated resonance frequencies are computed and presented graphically to demonstrate the effects of the nonlinear stiffness constant comparing with the corresponding linear model. The existence of periodic solutions of the model is proved analytically for physically admissible periodic solutions, and conditions for bifurcation points on a parameter associated with the third-order elastic stiffness constant are determined.

AB - Phase plane analysis of the nonlinear spring-mass equation arising in modeling vibrations of a lumped mass attached to a graphene sheet with a fixed end is presented. The nonlinear lumped-mass model takes into account the nonlinear behavior of the graphene by including the third-order elastic stiffness constant and the nonlinear electrostatic force. Standard pull-in voltages are computed. Graphic phase diagrams are used to demonstrate the conclusions. The nonlinear wave forms and the associated resonance frequencies are computed and presented graphically to demonstrate the effects of the nonlinear stiffness constant comparing with the corresponding linear model. The existence of periodic solutions of the model is proved analytically for physically admissible periodic solutions, and conditions for bifurcation points on a parameter associated with the third-order elastic stiffness constant are determined.

KW - Electrostatic pull-in stability

KW - Graphene

KW - Lumped-mass model

KW - Nonlinear spring

KW - Periodic solutions

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DO - 10.24132/acm.2017.322

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VL - 11

SP - 81

EP - 90

JO - Applied and Computational Mechanics

JF - Applied and Computational Mechanics

IS - 1

ER -

Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device

Abstract

Funding

Keywords

ASJC Scopus subject areas

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