Nonlinear internal resonances of rotating twisted multilayer functionally graded graphene nanoplatelet-reinforced composite blades

The nonlinear responses of primary resonance characteristics for the composite rotating blade are investigated in the presence of 1:2 internal resonance, where two primary resonance cases are considered, namely, the first mode and second mode being excited. The composite properties can be deduced via modified Halpin-Tsai micromechanics model and the rule of mixture. Lagrange formulation is employed in conjunction with Ritz procedure for the determination of the ordinary differential equations (ODEs). Then, modulation equations associated with two resonance relationships are obtained via the method of multiple scales for purpose of seeking steady state responses. Comparisons are conducted to demonstrate the accuracy of the proposed method. Bifurcations and chaotic dynamics are conducted in the form of double-parameter maps. Frequency response curves and force response curves are presented when one mode is excited. The influence of various parameters such as excitation amplitude and detuning parameter on nonlinear responses is assessed. The investigation illustrates the existence of softening, hardening and softening-hardening nonlinear resonance behaviors identified by jumping and the corresponding multiple value phenomena.