Nonlinear vibrations of rotating pretwisted TC4 composite blades reinforced by graphene under transverse two-parameter aerodynamic loads and tip gap airflow

Titanium-6 aluminum-4 vanadium (TC4), a titanium alloy, exhibits the excellent mechanical properties. The primary resonance and nonlinear vibrations are investigated for a functionally graded Graphene Platelet-Reinforced TC4 (GPR-TC4) rotating pre-twisted composite blade under the combined transverse two-parameter excitation and axial excitation by using O, U, and X distribution patterns to the composite blades reinforced by the graphene. The GPR-TC4 rotating pre-twisted composite blade is modeled as a functionally graded graphene platelet-reinforced rotating pre-twisted composite cantilever plate. A new approach is proposed for addressing the transverse aerodynamic loads through the trigonometric series expansion. The steady-state rotational speed is considered with the minor periodic disturbances. The classical plate theory is used to derive the nonlinear governing equation of motion by using von Kármán geometric relations, Lagrange equations, and mode functions satisfying the boundary conditions. Two-degree-of-freedom nonlinear ordinary differential equations are obtained to govern the nonlinear vibrations of the GPR-TC4 rotating pre-twisted composite cantilever plate under the multi-parameter excitations. Runge-Kutta method is utilized to analyze the primary resonance and nonlinear dynamics of the GPR-TC4 rotating pre-twisted composite cantilever plate. The results include the amplitude-frequency response curves, waveforms, Poincaré maps, 2D and 3D bifurcation diagrams, maximum Lyapunov exponent, and phase portraits. This study provides a comprehensive analysis of the nonlinear dynamic responses of the GPR-TC4 rotating pre-twisted composite cantilever plate under varying excitation parameters.