LAUSR

Abstract This paper focuses on the free vibration of circular and annular three-dimensional graphene foam (3D-GrF) plates under various boundary conditions. The Chebyshev-Ritz method is developed to solve the present problem. Different types of foam distribution are considered and the effective elastic modulus and mass density vary along the thickness or radial directions of the plates. The Kirchhoff plate theory is employed to derive the energy equations of the 3D-GrF plates. The numerical results show that the developed method has good accuracy and stability for analyzing free vibration problem of circular and annular 3D-GrF plates. It is also found that the increase in foam coefficient leads to the decrease in natural frequencies of 3D-GrF plates. Among different types of foam distribution, the 3D-GrF-I results in the highest natural frequency while the 3D-GrF-II corresponds to the lowest natural frequency of circular and annular 3D-GrF plates for most cases, depending on the specific boundary condition and foam coefficient. Moreover, the foam coefficient, the boundary condition, and the foam distribution interact with each other and have coupled effect on free vibration characteristics of 3D-GrF plates.