Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: Approximate analytical solution

This paper investigates nonlinear free vibration of three-dimensional graphene foam skeleton reinforced rectangular plates. The three-dimensional graphene foam skeleton can distribute in different patterns along the thickness direction of the plate. According to the mixing rule, the effective Poisson's ratio, mass density and elastic modulus of three-dimensional graphene foam reinforced (3D-GFR) plates are described. In the framework of the von Kármán nonlinear plate theory, Hamilton's principle is utilized to derive equations of motion. Then, analytical nonlinear frequencies of 3D-GFR plates are solved by using the Galerkin method and the harmonic balance method. Results show that 3D-GFR plates exhibit hardening nonlinearity. The effect of porosity coefficient on nonlinear vibration depends on the foam skeleton distribution. In addition, the nonlinear frequencies of 3D-GFR plates increase as the skeleton weight fraction rises.