The bending stiffness of a shaft in a two pole generator and so on is regarded as a random variable, thus the amplitude and the stability of a rotor system are statistically analyzed to seek the influence of the error of the bending stiffness on the system, That is, the variance of amplitude of the rotor and the mode function due to the error are obtained. The probability of unstable vibration of the rotor system is predicted and compared with the results of the simulation of Monte Carlo method. The variation of the amplitude of the rotor appears remarkable near the critical speed of the symmetrical rotor and a half of that speed. The probability of unstable vibration is in good agreement with results of the simulation, so the statistical analysis serves as a reference in designing or producing a rotary machine.
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