Free vibration analysis of FG porous spherical cap reinforced by graphene platelet resting on Winkler foundation

In this study, free vibration analysis of FG porous spherical cap reinforced by graphene platelets resting on Winkler-type elastic foundation has been surveyed for the first time. Three different types of porosity patterns are considered for the spherical cap whose two types of porosity patterns in the metal matrix are symmetric and the other one is uniform. Besides, five GPL patterns are assumed for dispersing of GPLs in the metal matrix. Tsai-Halpin and extended rule of the mixture are used to determine the Young modulus and mass density of the shell, respectively. Employing 3D FEM elasticity in conjunction with Hamilton's Principle, the governing motion equations of the structure are obtained and solved. The impact of various parameters including porosity coefficient, various porosity distributions in conjunction with different GPL patterns, the weight fraction of graphene Nano fillers, polar angles and stiffness coefficient of elastic foundation on natural frequencies of FG porous spherical cap reinforced by GPLs have been reported for the first time.