Nonlinear thermal vibration analysis of refined shear deformable FG nanoplates: two semi-analytical solutions

  • Mohammad Reza Barati
  • Hossein Shahverdi
Technical Paper


This paper deals with the semi-analytical nonlinear thermal vibration analysis of functionally graded (FG) nanoplates modeled by four-variable refined plate theory. The nanoplate is resting on a nonlinear hardening elastic medium and subjected to uniform and nonlinear temperature rises. Temperature-dependent gradient material properties of the nanoplate are described via simple power-law model. A closed-form expression for nonlinear frequency is presented using a novel Hamiltonian approach as well as He’s variational method. To the best of the author’s knowledge, the nonlinear governing equations and their solution for a refined four-variable nanoplate are very rare in the literature. It is seen that the nonlinear vibration frequency is affected by the uniform temperature rise, nonlinear temperature rise, scale parameter, maximum amplitude, material gradation, foundation parameters and temperature-dependency. The presented formulation and solution approaches can be used in future investigations on macro to nanoscale plates.


Nonlinear vibration Hamiltonian method Four-variable plate theory Nonlocal elasticity 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Aerospace Engineering Department and Center of Excellence in Computational AerospaceAmirKabir University of TechnologyTehranIran

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