On the free vibration behavior of nanocomposite laminated plates contained piece-wise functionally graded graphene-reinforced composite plies

The numerical answer to the free vibration behavior of laminated plate structure contained piece-wise carbonbased nanocomposites plies is investigated. Plies are made from a combination of an isotropic polymer matrix and a nanoscale carbon-based reinforcements namely graphene. The graphene reinforcements are dispersed across the plate thickness either in uniform or non-uniform fashion according to four different distribution patterns. To assess the effect of the grading graphene patterns five types of lay-up arrangements are comparatively investigated. The effective elastic moduli of the laminated nanocomposite including Young's and shear moduli are obtained by using the so-called extended Halpin-Tsai model. Theoretical approaches are based on the first-order shear deformation theory (FSDT), while Lagrange's equation and a finite element formulation are employed to derive the natural frequencies. The accuracy of the results using the present framework model is examined with those available in previous attempts and an excellent agreement is achieved. A large range of parametric studies was carried out with a view to investigate the effect of several factors including lay-up arrangements, graphene distribution patterns, lamination sequence, plate geometric parameters, plate boundary conditions, and plate mode shapes on the free vibration behavior of functionally graded graphene-reinforced composite (FG-GRC) laminated plates. New suggestions are presented with the aim of providing useful remarks and new design criteria for future and innovative nanocomposite structures.