Three-Dimensional Static and Free Vibrational Analysis of Graphene Reinforced Composite Circular/Annular Plate Using Differential Quadrature Method

Abstract

Free vibrational and bending behavior of functionally graded graphene platelet reinforced composite (FG-GPLRC) circular and annular plate with various boundary conditions is studied using the differential quadrature method (DQM). The weight fraction differs gradually across the thickness direction. Effective elasticity modulus of the nanocomposite has been estimated by the modified Halpin–Tsai model. Using equations of motion in the framework of the elasticity theory and constitutive relation, the state-space first-order differential equation along the thickness direction is derived. A semi-analytical solution is carried out based on the application of DQM along the radial direction and the state-space technique across the thickness of the plate. The present approach is validated by comparing the numerical results with those reported in the literature. Effect of graphene platelets (GPLs) weight fraction, different GPL distribution patterns, thickness-to-radius and outer-to-inner radius ratios and edge boundary conditions on the static and vibrational behavior of GPLs reinforced composite circular/annular plates are examined. The results implied that GPLs can improve the composite strength against different loading and GPLs could have an extraordinary reinforcing influence on the static and vibrational behavior of the circular/annular plates.