Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers

• Presenting the vibration behavior of the quadrilateral laminated plates based on the FSDT.
• Laminated plates with carbon nanotube reinforced composite layers are analyzed.
• Differential quadrature method is used to analyze plates with arbitrary boundary conditions.
• The effect of the carbon nanotubes distribution through the layer thickness is studied.
• The effects of geometrical shape parameters and thickness-to-length ratio are studied.

The free vibration behavior of quadrilateral laminated thin-to-moderately thick plates with carbon nanotube reinforced composite (CNTRC) layers is studied. The governing equations are based on the first-order shear deformation theory (FSDT). The solution procedure is based on transforming the governing differential equations from an arbitrary straight-sided physical domain to a regular computational one, and discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. Four different profiles of single walled carbon nanotubes (SWCNTs) distribution through the thickness of layers are considered, which are uniformly distributed (UD) and three others are functionally graded (FG) distributions. The fast rate of convergence of the presented approach is numerically demonstrated and to show its high accuracy, wherever possible comparison studies with the available results in the open literature are performed. Then, the effects of volume fraction of carbon nanotubes (CNTs), geometrical shape parameters, thickness-to-length and aspect ratios, different kinds of CNTs distribution along the layers thickness and different boundary conditions on the natural frequencies of laminated plates are studied.