A comprehensive study on the free vibration of arbitrary shaped thick functionally graded CNT-reinforced composite plates

The main objective of this paper is to analyze the free vibration of arbitrary shaped thick functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates based on the higher-order shear deformation theory (HSDT) using a variational differential quadrature approach. By means of the generalized differential quadrature (GDQ) numerical operators and Hamilton's principle, the discretized equations of motion are obtained. In order to use the GDQ differential and integral operators appropriately, the coordinate transformation is considered through the conventional finite element approach for transforming the irregular domain of the plate into the regular computational one. Employing a unified numerical approach to analyze different shapes of thick FG-CNTRC plates based on HSDT is the main novel aspect of the present study. To imply the accuracy of the present model, a wide range of comparison studies are presented. The results indicate the efficiency of the developed numerical methodology to study the vibration of arbitrary shaped thick FG-CNTRC plates. Several results are also given to investigate the impacts of geometrical parameters and material properties on the vibrational behavior of FG-CNTRC plates.