FORCED VIBRATIONS OF A CONTINUOUS ROTOR WITH STRONG GEOMETRICAL NONLINEARITY

摘要

When both ends of an elastic continuous rotor are supported simply by double-row self-aligning ball bearings, the geometrical nonlinearity appears due to the stiffening effect in elongation of the rotor if the movement of the bearings in the longitudinal direction is restricted. As the rotor becomes more slender, the geometrical nonlinearity becomes stronger. In this paper, we study unique nonlinear phenomena due to the strong nonlinear spring characteristics and an initial axial force in the vicinity of the major critical speed ω_c and twice ω_c. When the rotor is supported horizontally, the difference in support stiffness and the asymmetrical nonlinearity appear as a result of the rotor of the equilibrium position. By the influences of the internal resonance and the initial axial force, the nonlinear resonance phenomena become very complex. For example, a peak of resonance curves split into two peaks, these two peaks leave each other and then become a hard and a soft spring types, respectively, and almost periodic motions and chaotic vibrations appear. We clarified these phenomena theoretically and experimentally.