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

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 distri-butions (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 fre-quencies 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 con -figuration while the aspect ratio is set to 50.