Title: Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device
Authors: Wei, Dongming
Kadyrov, Shirali
Kazbek, Zhassulan
Citation: Applied and Computational Mechanics. 2017, vol. 11, no. 1, p. 1-10.
Issue Date: 2017
Publisher: University of West Bohemia
Document type: článek
URI: http://hdl.handle.net/11025/26120
ISSN: 1802-680X (Print)
2336-1182 (Online)
Keywords: soustředěný model;nelineární pružina;grafen;elektrostatická zátěžová stabilita;periodická řešení
Keywords in different language: lumped-mass model;nonlinear spring;graphene;electrostatic pull-in stability;periodic solutions
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.
Rights: © 2017 University of West Bohemia. All rights reserved.
Appears in Collections:Volume 11, number 1 (2017)
Volume 11, number 1 (2017)

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