Resonance in dangerous mode and chaotic dynamics of a rotating pre-twisted graphene reinforced composite blade with variable thickness

A rotating pre-twisted graphene reinforced composite panel model is developed to investigate resonance behaviors of the rotating blade under dangerous mode. Three types of blade thickness variations are considered. The influences of rotating speed, variable thickness and pre-twisted angle are considered during the modeling process, which will increase the complexity of the system. With the aid of first-order shear deformation theory and Rayleigh-Ritz procedure, natural frequencies and mode shapes can be acquired. Moreover, Campbell diagram is depicted to determine the dangerous rotating speeds and the corresponding dangerous modes. Based on the dangerous mode, Lagrange’s equation is taken into account to formulate the nonlinear ordinary differential equations. Then, the method of multiple scale is carried out to derive the modulation equations. The frequency–response curves and force-response curves are plotted to reveal nonlinear vibration characteristics, where the emphasis is placed on discussing the influences of several decisive parameters on the response curves of the rotating blade, such as excitation amplitude and damping coefficient. Finally, the chaotic dynamics in the form of bifurcation diagrams, maxLyapunov exponents, phase portraits and time histories are analyzed.