The paper deals with the stability of a rotor subject to hysteretic forces and externally damped only through the shaft supports. Bearings with negligible cross-coupling are assumed, but asymmetry of support stiffness and damping is considered. The mechanism of internal friction is not defined specifically in the analysis; viscous Coulomb and standard linear hysteretic forces are considered as specific examples derived from a common general solution. It is concluded that stability limits may vary considerably with different hysteresis mechanisms and that irrespective of this, optima in bearing damping can be specified.

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