Stability boundaries of a spinning rotor with parametrically excited gyroscopic system

Some published papers used Bolotinʹs 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 Bolotinʹs 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 Bolotinʹs method and Floquetʹs method respectively to indicate the differences. The causation of these differences is attributed to the differences in the assumptions of Bolotinʹs and Floquetʹs methods as that the assumption of Floquet multipliers in Bolotinʹs method cannot be satisfied for the gyroscopic system. In this paper it has been shown that the Bolotinʹs method will result with the enlargement of the instability region for the gyroscopic system, which may contradict the results based upon the Floquetʹs method.