This paper deals with the transient vibration of asymmetric rotor systems during acceleration passing through several critical speeds at which synchronous or super-harmonic resonance occurs. The dynamic equations of the rotor-bearing system are formulated by the finite element model and the resulting dynamic equations are time-varying due to the effects of acceleration and asymmetry. In the formulation, a Timoshenko beam element is employed to simulate the rotating shaft and Eulerian angles are used to describe the orientations of the shaft element and disk. The numerical integration scheme for transient analysis is generated from the finite element model. Numerical examples are presented to illustrate (1) the effects of acceleration on peak amplitude and speed at which the peak occurs as the system passes through critical speeds, (2) the optimal acceleration process, which can be obtained by minimizing the peak response and the period of acceleration, (3) the speed regions where the transient instability exists.

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