An analytical approach for vibration analysis of 3D graphene foam reinforced composite panels

This study focuses on deriving an analytical approach to understand the free vibrational behavior of three dimensional (3D) graphene foam-reinforced polymer matrix composites (GrF-PMC) cylindrical shells. The composite incorporates porous graphene foams characterized by their 3D scaffold structures, aimed at enhancing the overall rigidity of the material. Furthermore, the 3D graphene foams can be positioned either uniformly or variably across the shell's thickness. The composite's effective Young's modulus, mass per unit volume, and Poisson's ratio are calculated using a mixture rule. Applying first-order shear deformation shell theory, Donnell's assumptions, and Hamilton's principle, the governing equations are derived and tackled through the state-space method. Numerical solutions are provided for various boundary constraints. The accuracy and reliability of this approach are confirmed by benchmarking against existing literature. Additionally, the work explores how the type of 3D-GrF framework, its weight proportion, foam coefficient, and geometric parameters such as thickness-to-radius and length-to-radius ratios, along with boundary conditions, impact the natural frequencies of the cylindrical panel. The findings reveal that both the configuration of the 3D-GrF network and its relative weight significantly affect the vibrational characteristics of the GrF-PMC structures.