Free Vibrations of Functionally Graded Graphene-Reinforced Composite Blades with Varying Cross-Sections

In this paper, free vibrations of functionally graded (FG) graphene-reinforced composite blades with varying cross-sections are investigated. Considering the cantilever boundary conditions, the dynamic model of a rotating blade is simplified as a varying cross-sections plate with pre-installed angle and pre-twisted angle. As a reinforcement, the graphene platelets (GPLs) are distributed either uniformly or gradiently on the plate along its thickness direction. The effective Young’s modulus is formulated by the modified Halpin–Tsai model. The rule of mixture is applied to calculate the effective Poisson’s ratio and mass density. The equations of motion are established by using the first-order shear deformation theory and von Karman geometric nonlinear theory. Based on the Rayleigh–Ritz method, the natural frequencies of the rotating FG blade reinforced with the GPLs are obtained. The accuracy of the present method is verified by comparing the obtained results with those of the finite element method and published literature. A comprehensive parametric study is conducted, with a particular focus on the effects of distribution pattern, weight fraction, and geometries size of the GPLs together with dimensional parameters of varying cross-sections blade on the dynamics of the FG blades reinforced with the GPLs.