Nonlinear free vibration of rotating functionally graded graphene platelets reinforced blades with variable cross-sections

Titanium alloys are widely used for blades due to their favorable combination of high strength, low density and fatigue resistance. Dispersing graphene platelets (GPLs) into titanium alloy in a layer-wise manner to develop novel functionally graded (FG) GPL/titanium alloy blades can achieve further enhanced mechanical performance. This paper first proposes a functionally graded graphene/titanium alloy composite trapezoid plate to investigate the nonlinear free vibration of rotating blades with varying cross-sections. It is assumed that graphene platelets are uniformly dispersed in each layer of titanium alloy, and the weight fraction of GPLs increases from the middle layer to the top layers. The effective Young's modulus, effective Poisson's ratio and mass density are calculated by the modified Halpin-Tsai model and the rule of mixture, respectively. The discretized motion equations of the functionally graded graphene platelets reinforced composite (FG-GPLRC) trapezoid plate are derived by the energy method and Lagrange equations. The Rayleigh-Ritz method and direct iterative process are applied to obtain the linear frequencies and nonlinear frequencies, respectively. A detailed numerical study is carried out to investigate the effects of the material parameters and dimensional parameters on the linear and nonlinear free vibrations of the rotating FG-GPLRC trapezoid plate.