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 | |
| Publication status | Published - Jan 1 2017 |
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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
Cite this
Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device. / Wei, D.; Kadyrov, S.; Kazbek, Z.
In: Applied and Computational Mechanics, Vol. 11, No. 1, 01.01.2017, p. 81-90.Research output: Contribution to journal › Article
}
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.
PY - 2017/1/1
Y1 - 2017/1/1
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
UR - http://www.scopus.com/inward/record.url?scp=85021762297&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85021762297&partnerID=8YFLogxK
U2 - 10.24132/acm.2017.322
DO - 10.24132/acm.2017.322
M3 - Article
AN - SCOPUS:85021762297
VL - 11
SP - 81
EP - 90
JO - Applied and Computational Mechanics
JF - Applied and Computational Mechanics
SN - 1802-680X
IS - 1
ER -