In this paper, a statistical analysis was performed on free vibration characteristics of functionally graded graphene reinforced composite (FG-GRC) plates. The effective mechanical properties of the graphene based polymer nanocomposite plates were estimated based on the modified Halpin-Tsai micromechanical model to account for the weak load transfer between the matrix and the reinforcement. Free vibration analysis was performed using higher order shear deformation theory. Then, analysis of variance (ANOVA) was carried out for comprehensive investigation of the parameters effect on vibration behavior of nanocomposites. The parameters under investigation were thickness ratio, volume fraction of graphene nanoplatelets (GPLs), distribution pattern of GPLs and boundary condition. The importance degree and contribution percentage of these parameters on natural frequency were calculated based on the ANOVA results. Followed by statistical analysis, an empirical/mathematical model was developed to express the natural frequency of the FG-GRC plates as a function of input parameters. The obtained results revealed that boundary condition and volume fraction of GPLs were the most significant parameters affecting the vibration characteristics of GPL/polymer nanocomposite plates, followed by thickness ratio and distribution pattern of GPLs, respectively. The regression models showed a quadratic relationship between the natural frequency and the involved input parameters.
