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Numerical and experimental methods in free and forced vibrations of the rotating structure consisting of the rigid hub and three flexible beams are considered. Firstly, the system of four mutually coupled dimensionless differential governing equations is presented and then forced response of the system as well as synchronization phenomenon are investigated. Next, the finite elements method is used to design the rotating structure and analyse complex dynamic response. During the numerical calculations symmetric, as well as de-tuned rotor are analyzed. Finally, results obtained from ordinary differential equations and numerical simulations are compared with experimental tests.

Abstract. The aim of the paper is to analyze the synchronization phenomenon of a rotating structure composed of three beams attached to a rigid hub. It is assumed in the calculations that one beam is 10% thicker comparing to the remaining ones. Furthermore, two possible variants of excitation are considered: (a) torque given by harmonic function or (b) torque produced by a chaotic oscillator. Next, the equations have been solved numerically and the resonance curves and time series have been analyzed in terms of synchronized motion of the hub and blades of the rotor. The influence of hub's mass moment of inertia have been checked as well. For the system with chaotic Duffing oscillator Poincaré maps have been obtained.

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