Linear Oscillations of Suspended Graphene

  • Igor BerinskiiEmail author
  • Anton Krivtsov
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 45)


Due to their excellent mechanical properties and extra high electroconductivity, suspended graphene sheets recently were proposed as perspective working elements of nanosystems. This work is devoted to derivation of natural frequencies of such sheets. Two different approaches are proposed. The first one is based on representation of the graphene sheet as a thin rectangular membrane. In this case the transversal oscillations are described with the classical one-dimensional wave equation. Evaluation of the tension force in the membrane is performed basing on the misfit between the graphene and silicon substrate crystal lattices. As a result, the natural frequencies are found as the functions of the membrane length. Another approach is to represent a graphene sheet as a thin plate. In this case a bending rigidity of graphene has to be taken into account. As a result, it is shown that the bending rigidity is more significant for the short resonators and leads to the higher frequencies in comparison the long resonators.


Graphene Sheet Graphene Layer Linear Density Plate Model Silicon Oxide Substrate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The work is supported by RFBR grant 14-01-802 and the President’s of Russian Federation grant MK–4873.2014.1.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Theoretical and Applied MechanicsSt. Petersburg State Polytechnical UniversitySt. PetersburgRussia
  2. 2.Laboratory for Discrete Models in MechanicsInstitute for Problems in Mechanical EngineeringSt. PetersburgRussia

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