Free and Forced Vibration of Beams Reinforced by 3D Graphene Foam
Feng Liu Yang, Yan Qing Wang
Abstract
In this paper, free and forced vibrations of nanocomposite beams reinforced by 3D graphene foam (3D-GrF) are studied. Different distributions of 3D-GrF in the beam thickness direction are considered. In accordance with the rule of mixture, the effective Young’s modulus, Poisson’s ratio and mass density of the 3D-GrF reinforced beams are predicted. Based on the Timoshenko beam theory, the governing equation of the 3D-GrF reinforced beam is derived by using the Lagrange equation. The natural frequencies and dynamic responses of the 3D-GrF reinforced beam are solved by the Ritz method and the Newmark-[Formula: see text] method, respectively. Results show that the foam coefficient, the 3D-GrF distribution, the slenderness ratio and the 3D-GrF mass fraction play important roles on free and forced vibration characteristics of the 3D-GrF reinforced beams.