Nonlinear free vibration of functionally graded fiber-reinforced composite hexagon honeycomb sandwich cylindrical shells

•A novel class of honeycomb sandwich cylindrical shell reinforced by the FG-FRCs is conducted.•An analytical model is proposed that considers geometric nonlinearity of von Kármán.•Nonlinear free vibration of the FG-FRC-HHS cylindrical shells is investigated by adopting the multiple scales method.•Influence of HHC and types of FG-FRC on nonlinear vibration behavior is discussed. In the present study, the nonlinear free vibration of functionally graded fiber-reinforced composite hexagon honeycomb sandwich cylindrical shells is investigated with consideration of the large-amplitude effect. First, an analytical model of such shell structures is proposed, which considers the functionally graded fiber-reinforced composite skins and a hexagon honeycomb core with their respective effective material properties being evaluated through the micromechanical model of Halpin-Tsai and the mixture law, as well as the modified Gibson's formula. Meanwhile, based on the first-order shear deformation theory and von Kármán geometrical nonlinear relations, the nonlinear partial differential governing equations are deduced via Hamilton’s principle, which is further discretized into several ordinary differential equations by the Galerkin approach. Subsequently, the static condensation technique is adopted to decrease the degrees of freedom, and the frequency-amplitude relationships are obtained by the multiple scale expansion method. Following the validation of the developed model via comparing the predicted results to literature ones, a detailed parameter study of critical geometric and material parameters on the nonlinear vibration characteristics of the structure is conducted, with some important conclusions being provided to weaken the nonlinear hardening-spring behavior of the structure.