Abstract
The stability of two mathematical models of a viscoelastic rotor—a 2-parameter solid model and a 3-parameter solid model—is investigated by means of a complex Routh—Hurwitz analysis. While the 2-parameter model possesses a certain well-known stability limit for the angular velocity, it is shown that the 3-parameter model has two stable regions for the angular velocity, separated by an unstable one, if the coefficient of external damping is less than a special value d * e . For external damping coefficients greater than d * e the rotor is stable for all angular velocities. It is interesting that the stabilizing value d * e does not depend on the coefficient of internal damping. Moreover, the general result for the 3-parameter model is shown to include the following special cases: small external and internal damping coefficients (Muller, 1981), and very large internal damping coefficient (Hendricks, 1986).
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