Nonlinear free and forced vibrations of graphene nanoplatelet reinforced microbeams with geometrical imperfection

  • Seyed Sajad Mirjavadi
  • Behzad Mohasel Afshari
  • Mohammad Reza Barati
  • A. M. S. Hamouda
Technical Paper


Nonlinear free/forced vibration of a functionally graded graphene nanoplatelet (GNP) reinforced microbeam having geometrical imperfection which is rested on a non-linear elastic substrate have been studied in the present research. Graphene Platelets have been uniformly and non-uniformly scattered in the cross section area of the microbeam. Non-uniform distribution of GNPs is considered to be linear or non-linear type. Geometric imperfection is considered similar to the first vibration mode of microbeam. Size effects due to micro-rotations are captured in this study by means of modified couple stress elasticity. In the case of forced vibration, a uniform harmonic load is exerted to the top surface of microbeam. Harmonic balance method has been implemented to solve the non-linear governing equation of microbeam having quadratic and cubic nonlinearities. In this regard, frequency-amplitude curves are obtained and their trends are studied by changing of GNP amount and distribution, geometric imperfection, forced amplitude and hardening foundation.



The first and second authors would like to thank FPQ (Fidar project Qaem) for providing the fruitful and useful help.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringQatar UniversityDohaQatar
  2. 2.School of Mechanical Engineering, College of EngineeringSharif University of TechnologyTehranIran
  3. 3.Fidar Project Qaem CompanyTehranIran

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