Secondary Resonances of Asymmetric Gyroscopic Spinning Composite Box Beams

A comprehensive theoretical investigation on the occurrence of secondary resonances in parametrically excited unbalanced spinning composite beams under the stretching effects is conducted numerically and analytically. Based on an optimal stacking sequence and Rayleigh’s beam theory, the governing equations of the system are derived using extended Hamilton’s principle. The system’s partial differential equations are then discretized using the Galerkin method. Numerical (Runge–Kutta technique) and analytical (multiple scales method) approaches are exploited to solve the reduced-order equations, and their results are compared and verified accordingly. Comparison and convergence investigations are performed to guarantee the validity of the outcomes. Stability and bifurcation analyses are accomplished, and resonance effects are thoroughly studied utilizing frequency-response diagrams, phase portraits, Poincaré maps and time-history responses. It is observed that among the various types of secondary resonance, only a combination resonance can be observed in the system dynamics. The outputs reveal that, in this resonance, the gyroscopic coupling results in the steady-state time response consisting of three main frequencies. By examining the effects of damping, eccentricity, and beam length, it is exhibited that this resonance does not occur in the system’s dynamics for any combination of these parameters. Therefore, these parameters can be adjusted in the design of asymmetric beams to prevent this type of resonance.