Free Vibrations of Embedded Functionally Graded Graphene Platelets Reinforced Porous Nanocomposite Plates with Various Shapes Using P-Ritz Method

In this study, the free vibrations of functionally graded graphene platelet-reinforced porous nanocomposite plates with various shapes such as rectangular, elliptical, and triangular ones embedded on an elastic foundation are analyzed. To mathematically model the considered plate and elastic foundation, the first-order shear deformation plate theory, and Pasternak model are used, respectively. Three types of graphene nanoplatelet distribution patterns and porous dispersion types through the thickness are considered for the nanocomposite plate. To obtain the effective material properties of the considered nanocomposite, a micromechanical model is employed. Then, the energy functional of considered functionally graded graphene platelet-reinforced porous nanocomposite plates are expressed, and the analytical P-Ritz method is used to solve the vibration problem corresponding to different shapes and boundary conditions, the influences of porosity coefficient, the weight fraction of graphene nanoplatelets, elastic foundation coefficients and also the lengths-to-width and -thickness ratios on the natural frequency are analyzed. It is illustrated that the plate with non-uniform and symmetric of first type porosity distribution pattern and the first type graphene nanoplatelets has a higher natural frequency. Also, by increasing the porosity coefficient, the natural frequency of the plate associated with all patterns of graphene nanoplatelets is reduced.