Theoretical and Experimental Analysis of Coupled Flexural-Torsional Vibrations of Rotating Beams

In this paper, the flexural-torsional vibrations of a segmented cantilever beam are considered both theoretically and experimentally under steady-state base rotation. While operating in this steady-state, a piezoelectric actuator is used to excite the beam at various test frequencies. Further, through preliminary investigations, it is demonstrated that accelerometer measurements are not suitable for such a testing apparatus, as these sensors add complex unmodeled dynamics and change the natural frequencies of vibration. The resulting unmodeled dynamics appear to be caused by a large initial deflection due to the added sensor mass, contradicting the conventional assumption that the beam is initially undeformed. This initial bending results in a Coriolis acceleration, and consequently produces a substantial deviation from the anticipated tip response. To further investigate the effect of base rotation on flexural vibrations, experiments were performed in the absence of piezoelectric excitation, both with and without the tip mass. For these conditions, the theory uniformly predicts no flexural or torsional vibrations, while the experimental results demonstrate significant vibrations in both cases. These discrepancies illuminate the presence of significant unmodeled dynamics that are neglected in the conventional mathematical modeling, potentially invalidating the classical simplifications when considering rotating beams.