19 - Free vibration analysis of microplates reinforced with functionally graded graphene nanoplatelets

Abstract

This chapter studies free vibration analysis of a functionally graded composite microplate reinforced with graphene nanoplatelets. The composite microplate is rested on Pasternak’s foundation. The microplate is subjected to thermal and mechanical loads. To account for size dependency in our formulation, the modified strain gradient theory is used which uses three microlength scale parameters in microscales. Graphene nanoplatelets are assumed to be distributed along the thickness direction based on regular patterns. A Halpin-Tsai micromechanical model and rule of mixture are used to compute the effective material properties such as effective modulus of elasticity and density or Poisson’s ratio. The kinematic relations of plate are developed based on a third-order shear deformation theory. The free vibration responses are investigated in terms of significant parameters such as weight fraction of GNPs, various distribution of GNPs, three microlength scale parameters, some nondimensional geometric parameters such as side length-to-thickness ratio and thickness-to-microlength scale ratio. To validate the present numerical results, two comparative studies are presented including the results based on modified couple stress theory and modified strain gradient theory.