Nonlinear vibrations of rotating pretwisted composite blade reinforced by functionally graded graphene platelets under combined aerodynamic load and airflow in tip clearance

The primary resonance and nonlinear vibrations of the functionally graded graphene platelet (FGGP)-reinforced rotating pretwisted composite blade under combined the external and multiple parametric excitations are investigated with three different distribution patterns. The FGGP-reinforced rotating pretwisted composite blade is simplified to the rotating pretwisted composite cantilever plate reinforced by the functionally graded graphene platelet. It is novel to simplify the leakage of the airflow in the tip clearance to the non-uniform axial excitation. The rotating speed of the steady state adding a small periodic perturbation is considered. The aerodynamic load subjecting to the surface of the plate is simulated as the transverse excitation. Utilizing the first-order shear deformation theory, von Karman nonlinear geometric relationship, Lagrange equation and mode functions satisfying the boundary conditions, three-degree-of-freedom nonlinear ordinary differential equations of motion are derived for the FGGP-reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations. The primary resonance and nonlinear dynamic behaviors of the FGGP-reinforced rotating pretwisted composite cantilever plate are analyzed by Runge–Kutta method. The amplitude–frequency response curves, force–frequency response curves, bifurcation diagrams, maximum Lyapunov exponent, phase portraits, waveforms and Poincare map are obtained to investigate the nonlinear dynamic responses of the FGGP-reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations.