Bending, buckling and vibration of shear deformable beams made of three-dimensional graphene foam material

This paper studies bending, buckling and vibration of three-dimensional graphene foam (3D-GrF) beams in the framework of the sinusoidal shear deformation theory. Graphene foams can distribute along the thickness of beams in different patterns. The material properties of three-dimensional graphene foams are described by the scaling laws of open-cell foams. Based on Hamilton’s principle, the governing equations together with boundary conditions are derived. Then, Navier’s method and Rayleigh–Ritz method are used to calculate natural frequencies, critical buckling loads and center deflections of the 3D-GrF beams. Results show that the graphene foam distribution, the foam coefficient and the slenderness ratio have significant effect on buckling, bending and vibration behaviors of 3D-GrF beams. In addition, the present results are verified by the comparison with published ones in the literature.