Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges

•Free vibration of CNT reinforced functionally graded plates is considered.•Plate edges are elastically restrained against translation and rotation.•The element-free IMLS-Ritz method is employed for the analysis.•The effect CNT distribution on the vibration behavior is examined.

For the first time, to the authors' knowledge, the problem of the free vibration of functionally graded carbon nanotube (FG-CNT) reinforced composite moderately thick rectangular plates with edges elastically restrained against transverse displacements and rotation of the plate cross section is considered. The element-free improved moving least-squares Ritz (IMLS-Ritz) method is employed for the analysis. The first-order shear deformation theory (FSDT), accounting for transverse shear strains and rotary inertia, is used in the theoretical formulation. The applicability of the formulation is illustrated by solving a selection of example problems. The numerical results are validated through comparison and convergence studies. The effect of elastically restrained edges on the vibration behavior of the FG-CNT reinforced composite plates is studied by taking into account the CNT volume fraction ratio, CNT distribution, plate thickness-to-width ratio and plate aspect ratio.