Free vibration analysis of functionally graded plates reinforced with graphene oxide powder

In this research, free vibration analysis of nanocomposite plate reinforced with graphene oxide powder (GOPR) is carried out using an exact analytical approach. So, for the first time the results of the new reinforcement models according to various functionally graded (FG) distributions across the thickness, namely U, X, V and O. The main objective here is to discover the most effective GOP distribution model to improve the vibration behavior of the structure. Moreover, the laws governing the effective material properties of the nanocomposite plate were derived using the Halpin-Tsai micromechanical model. The equations of the studied problem are based on the theory of first order shear deformation. They were developed using Hamilton's principle and solved by an exact analytical approach for a simply supported GOPR nanocomposite plate. Detailed parametric studies are carried out to show the influence of different variables on the natural frequency of nanocomposite plates. The findings of this work reveal that the frequency responses of nanocomposite plates significantly depend on the distribution pattern of GOP.