Mixed Navier-layerwise differential quadrature three-dimensional static and free vibration analysis of functionally graded carbon nanotube reinforced composite laminated plates

The three-dimensional free vibration and static analysis of the laminated plates with functionally graded (FG) carbon nanotube reinforced composite (CNTRC) layers is presented using a semi-analytical approach. The individual layers are assumed to be made from a mixture of aligned and straight single-walled carbon nanotubes (CNTs) with volume fractions graded in the thickness direction, and an isotropic matrix. The effective material properties of the resulting FG-CNTRC layers are estimated through a micromechanical model. The through-the-thickness variations of the displacement components are accurately modeled using a layerwise-differential quadrature method, and their in-plane variations are approximated using the trigonometric series. After demonstrating the convergence and accuracy of the method, the effects of geometrical parameters, type of CNTs distribution and volume fractions, and also lamination scheme on the natural frequencies, displacement and stress components of the FG-CNTRC layered plates are investigated.