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Linear Oscillations of Suspended Graphene

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Shell and Membrane Theories in Mechanics and Biology

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 45))

Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, St. Petersburg State Polytechnical University, Polytechnicheskaya 29, 195251, St. Petersburg, Russia

    Igor Berinskii & Anton Krivtsov

  2. Laboratory for Discrete Models in Mechanics, Institute for Problems in Mechanical Engineering, Bol’shoy Pr. V.O. 61, 199178, St. Petersburg, Russia

    Igor Berinskii & Anton Krivtsov

Authors
  1. Igor Berinskii
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  2. Anton Krivtsov
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Correspondence to Igor Berinskii .

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Editors and Affiliations

  1. Lehrstuhl für Technische Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Department of Bio- and Nanomechanics, Belarusian State University, Minsk, Belarus

    Gennadi I. Mikhasev

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Berinskii, I., Krivtsov, A. (2015). Linear Oscillations of Suspended Graphene. In: Altenbach, H., Mikhasev, G. (eds) Shell and Membrane Theories in Mechanics and Biology. Advanced Structured Materials, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-02535-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-02535-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02534-6

  • Online ISBN: 978-3-319-02535-3

  • eBook Packages: EngineeringEngineering (R0)

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