Stability boundaries of a spinning rotor with parametrically excited gyroscopic system

Some published papers used Bolotin's method for stability boundaries of spinning rotor with parametrically excited gyroscopic system. However, the original work of the method does not indicate that the method can be used to determine the stability of gyroscopic system. This paper intends to highlight the differences in the results using Bolotin's method. As counter examples, dynamic stability of a special case of the parametrically excited gyroscopic system, a simple gyroscopic rotor under parametric excitation and a rotating Timoshenko shaft subjected to periodic axial forces varying with time are analyzed and discussed by using Bolotin's method and Floquet's method respectively to indicate the differences. The causation of these differences is attributed to the differences in the assumptions of Bolotin's and Floquet's methods as that the assumption of Floquet multipliers in Bolotin's method cannot be satisfied for the gyroscopic system. In this paper it has been shown that the Bolotin's method will result with the enlargement of the instability region for the gyroscopic system, which may contradict the results based upon the Floquet's method.