Nonstationary vibrations of a rotating shaft with nonlinear spring characteristics during acceleration through critical speeds

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Recently, there exist many rotating machineries which are operated above the major critical speeds. It is necessary for such a rotating shaft to pass resonance points under the rated speed with a small deflection safely at the start or end of its operation. In this paper, nonstationary vibration characteristics of a rotating shaft with nonlinear spring characteristics are investigated concerning the following critical speeds: a major critical speed, the critical speeds of subharmonic oscillations of orders 1/2 and 1/3, and a critical speed of a summed-and-differential harmonic oscillation. The rotating speed is changed with a constant acceleration. Especially, the influences of the angular acceleration λ, the initial angular positionΨ[0] of a rotor unbalance, the initial rotating speedω[s] and the initial disturbance on the maximum amplitude are investigated.

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