Synchronisation Analysis of a De-Tuned Three-Bladed Rotor

The aim of the paper is to study a synchronisation phenomenon as observed in a rotating structure consisting of three composite beams and a hub. The beams are made of eighteen carbon-epoxy prepreg material layers stacked in a specific sequence. In the performed analysis it is assumed one of the beams is de-tuned due to small misalignment of its reinforcing fibers orientation with regard to the two remaining nominal design blades. The non-classical effects like transverse shear, material anisotropy, non-uniform torsion and cross-section warping are taken into account in the mathematical model of the blades. The partial differential equations of motion of the structure are derived by the Hamilton principle; next the reduction to the ordinary differential ones is done by the Galerkin method. Finally, the equations are solved numerically and the resonance curves for the hub and the individual beams are plotted. In the performed studies two possible variants of the rotor excitation are considered: (a) driving torque expressed by a harmonic function or (b) torque given by a chaotic oscillator formula. The analysis of the synchronisation phenomenon of the hub and the blades motion is based on the study of the resonance curves and time histories in the prepared graphs. The analysis of the structure driven by chaotic oscillator revealed the existence of the strange chaotic attractor for every beam of the rotor; in the particular, nominal beams are fully synchronised, but the de-tuned one is synchronised with a small difference in amplitude.