Dynamics of nonlinear beam-propeller system with different numbers of blades

The dynamics of elastic systems coupled with rotating bladed-rotors is rich and complex, and the blade number may have an influence on the in-vacuo system dynamics. This paper aims to model its nonlinear dynamics in-vacuo and study the effects of blade number on its dynamics. To this end, a nonlinear model consisting of a nonlinear inextensible beam, a motor assembly and a rotating propeller is developed. This model is linearized, and modal analyses are performed with different blade numbers. It is validated numerically and experimentally that a two-bladed propeller introduces time-varying characteristics, while the system is time-invariant with more than two blades. For the two-bladed case, frequencies in the non-rotating condition split into two frequency loci with increasing rotational speed; while with more than two blades, one frequency in the non-rotating condition increases and the other in the same pair decreases with increasing speed. A structural instability due to frequency lock-in is identified in two-bladed configuration, while not identified with more than two blades. The static deformation using the nonlinear model is calculated and validated against the experiment. In the stable speed range, the frequency response functions calculated using the nonlinear and linearized models do not show notable differences. In the unstable speed range with two-bladed propeller, the nonlinear model is consistent with the experiment in terms of unstable frequencies and bounded steady-state oscillations. The system vibration in the unstable speed range features forward whirling pattern, in which the beam vibration is close to the first bending pattern.