Abstract: A flexible Jeffcott rotor supported at the ends by identical squeeze film dampers is investigated to study the non stationary vibration due to rubbing with casings during passing through the critical speed.The rotational speed of the rotor is supposed increasing at a constant angular acceleration.The contact force theory is used to calculate the impacting forces and friction forces.The numerical ealculation reveals the effects of the rotational acceleration on the occurrence of diverging backward whirl,so as to determine whether the rotor can pass through the critical speed or not.The influence of some system parameters on the critical acceleration is also discussed.