Lumped-parameter model for dynamic monolayer graphene sheets

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

Research output: Journal PublicationArticlepeer-review

1 Citation (Scopus)


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 languageEnglish
Article number117062
JournalJournal of Sound and Vibration
Publication statusPublished - 15 Sept 2022
Externally publishedYes


  • 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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