Resonance behavior of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets

For the first time, forced resonance vibration of Graphene Nano-Platelets (GNPs) reinforced Functionally Graded Polymer Composite (FG-PC) nanoplates is studied. The effective Young's modulus is determined using the Halpin-Tsai model while the rule of mixture is used to compute the effective Poisson's ratio and mass density. The governing equations, classical and non-classical boundary conditions are obtained through Hamilton's principle for nonlocal strain gradient Kirchhoff plate theory. Employing Navier solution procedure, a closed form solution is introduced for forced resonance vibration of the nanoplate. The influences of the GNPs distribution schemes, nonlocal and strain gradient length scale parameters, weight fraction and the total number of layers of GNPs as well as geometrically parameters are discussed in detail. The results show that the impact of layer's number on the resonance position depends on the reinforcement patterns.