Free vibration analysis of micro plate reinforced with functionally graded graphene nanoplatelets based on modified strain-gradient formulation

Abstract

In this paper, modified strain-gradient theory is developed for size-dependent formu- lation of micro plate reinforced with functionally graded graphene nanoplatelets. The reinforced micro plate is subjected to thermal and mechanical loads. The functionally graded graphene nanoplatelets are distributed along the thickness direction based on various patterns. The effective material properties of reinforced structure including modulus of elasticity and density or Poisson’s ratio are calculated based on Halpin– Tsai model and rule of mixture, respectively. The kinematic relations are developed based on third-order shear deformation theory. The solution procedure is proposed based on analytical work for custom boundary condition. Before presentation of numerical results, a comprehensive comparative study is performed for validation of present formulation. The numerical results are presented to investigate the influence of important parameters such as weight fraction of GNPs, various distribution of GNPs, three micro length scale parameters and some non-dimensional geometric parameters on the vibration responses.