Dynamic response and stability of a rotating asymmetric shaft mounted on a flexible base

This paper presents the dynamic response and stability of an asymmetric rotating shaft supported by a flexible base near the major critical speed and the secondary critical speed. In this system, the base is movable only in a direction transversal to the shaft. In the theoretical analysis, taking into account the effects of damping, the unstable vibrations near the major critical speed are mainly considered, and also the behavior of the forced oscillations near the major and secondary critical speeds is investigated. From the theoretical analysis, the unstable region is found to be divided into at most six subregions which depend on the mass of the base, the stiffness of the base, and the asymmetry of the shaft. In addition, the resonance curves near unstable subregions are calculated. It is found that there exist two shapes of resonance curves. In experiments, five types of response curves, which contained n unstable subregion (n = 1, 2, ..., 5) near the major critical speed, were obtained by changing the mass of the base. It was ascertained that the theoretical results for the behavior near the major critical speed agreed quantitatively with the experimental results.