Vibration behaviors of two-directional carbon nanotube reinforced functionally graded composite plates.

• A CNT distribution model in two directions is proposed. • Free vibration behaviors of 2D-FG CNTRC plates are studied. • Various CNT volume fractions are employed in the analysis. • Third order shear deformation theory with finite element formulation is employed. • The results obtained by using 1D-FG CNTRC and 2D-FG CNTRC models are discussed. The dynamical analysis of two directional functionally graded carbon nanotube reinforced composite (2DFG-CNTRC) plates are studied for various boundary conditions. The effects of the CNT distribution in the two directions on the dimensionless frequencies are investigated and compared with the unidirectional CNT distributions (1DFG-CNTRC) with respect to the variation of the CNT configuration, volume fraction and aspect ratio. Based on the variational formulation, the numerical results are obtained by using a finite element model. It is found that the volume fraction of the CNTs is affected with respect to the y direction and the difference between the dimensionless fundamental frequencies calculated based on the 2DFG-CNTRC and 1DFG-CNTRC configurations is significant. Moreover, for CFFF plates, the difference between the dimensionless frequencies obtained based on the 2DFG-CNTRC and 1DFG-CNTRC configurations is approximately 43.5% and 39% for 5th mode of the "U" and "V" type CNT configurations and 42% for 6th mode of the "X" type CNT configuration while the aspect ratio is set to 50. [ABSTRACT FROM AUTHOR]