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

D. Wei, S. Kadyrov, Z. Kazbek

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 languageEnglish
Pages (from-to)81-90
Number of pages10
JournalApplied and Computational Mechanics
Issue number1
Publication statusPublished - 2017


  • 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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