A size-dependent exact theory for thermal buckling, free and forced vibration analysis of temperature dependent FG multilayer GPLRC composite nanostructures restring on elastic foundation

  • Hamed SafarpourEmail author
  • Zanyar Esmailpoor Hajilak
  • Mostafa Habibi


In this paper, thermal buckling and free/forced vibration characteristics of size-dependent composite cylindrical nanoshell reinforced with graphene platelets (GPLs) is presented. Also, the nanoshell is embedded in an elastic pasternak medium, which is obtained by adding a shear layer to the Winkler model. The present nano-resonator is based on a vibrating first order nanoscale cylindrical shell subjected to transverse pressure. The temperature-dependent material properties of piece-wise functionally graded graphene-reinforced composites (FG-GRCs) are assumed to be graded in the thickness direction of a cylindrical nanoshell and are estimated through a nanomechanical model. Also, Halpin–Tsai nanomechanical model in used to surmise the effective material properties of each layer. The size-dependent FG-GRCs nanoshell is analyzed using modified couple stress parameter. The novelty of the current study is in considering the effects of FG-GRCs and thermal in addition of size effect on resonance frequencies, thermal buckling and dynamic deflections of the FG-GRCs nanoshell. The governing equations and boundary conditions have been developed using Hamilton’s principle and have been solved with the aid of analytical method. The results show that, GPL distribution pattern, modified couple stress parameter, length to radius ratio, mode number, winkler coefficient and thermal environment have important role on resonance frequency, relative frequency change, thermal buckling and dynamic deflections of the FG-GRCs cylindrical nanoshell in thermal environments.


Elastic foundation Forced vibration Graphene nanoplatelet Thermal buckling Analytical method Multilayer cylindrical nanoshell Modified couple stress parameter 


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mechanics, Faculty of EngineeringImam Khomeini International UniversityQazvinIran
  2. 2.Department of Mechanical EngineeringKN Toosi University of TechnologyTehranIran
  3. 3.Center of Excellence in Design, Robotics and Automation, School of Mechanical EngineeringSharif University of TechnologyTehranIran

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