Free vibration analysis of functionally graded composite rectangular plates reinforced with graphene nanoplatelets (GPLs) using full layerwise finite element method

The current investigation is the first endeavor to apply the full layerwise finite element method (FEM) in free vibration analysis of functionally graded (FG) composite plates reinforced with graphene nanoplatelets (GPLs). Unlike the equivalent single-layer (ESL) theories, the layerwise FEM focuses on all three-dimensional (3D) effects. Therefore, it can compute interlaminar stresses and other local effects with the same accuracy as 3D FEM, requiring a lower computational cost. The GPLs weight fraction is presumed invariable in each layer but varies through the plate thickness in a layerwise model. The modified Halpin-Tsai model is employed to acquire the effective Young's modulus. The rule of mixtures is applied to specify the effective Poisson's ratio and mass density. First, the current method is validated by comparing the numerical results with those stated in the available works. Next, a thorough numerical study is performed to examine how various factors involving the pattern of distribution, weight fraction, geometry, and size of GPLs, together with the thickness-to-span ratio and boundary conditions of the plate, affect its free vibration behaviors. Numerical results demonstrate that employing a small percentage of GPL as reinforcement considerably grows the natural frequencies of the pure epoxy. Also, distributing more square-shaped GPLs, involving a smaller amount of graphene layers, and vicinity to the upper and lower surfaces make it the most efficient method to enhance the free vibration behaviors of the plate.