The dynamic vibration absorbers have been applied to attenuate the critical or unbalanced vibration but may create the fluid-induced vibration instability in the rotor/seal system. The major purpose of this study is devoted to the effects of the dynamic vibration absorber on the nonlinear dynamic behavior and stability of the fluid-induced vibration in the rotor/seal system. The dynamic vibration absorber is attached on the shaft in the perpendicular directions. The model of the rotor/seal-dynamic vibration absorber system is established as the modified Jeffcott rotor system, and Muszynska nonlinear seal force is applied. The numerical method is used for the dynamic behavior analysis. The effects of the natural frequency and damping ratio of the dynamic vibration absorber on the dynamic behavior are discussed. The stability of the rotor/seal-dynamic vibration absorber system is judged by the eigenvalue theory. The variations of the instability threshold with the parameters of the dynamic vibration absorber are obtained. The results show that the instability threshold and instability vibration frequency are changed by the dynamic vibration absorber. The parameters of the dynamic vibration absorber must be selected carefully to avoid reducing the instability threshold and causing the instability vibration to occur in advance when the dynamic vibration absorber is applied to attenuate the critical or unbalanced vibration of the rotor/seal system.

The dynamic vibration absorbers have been applied to attenuate the rotor unbalance and torsional vibrations. The major purpose of this paper is to research the elimination of the fluid-induced vibration in the rotor/seal system using the absorber. The simplified rotor model with the absorber is established, and the Muszynska fluid force model is employed for the nonlinear seal force. The numerical method is used for the solutions of the nonlinear differential equations. The nonlinear responses of the rotor/seal system without and with the absorber are obtained, and then the rotating speed ranges by which the fluid-induced instability can be eliminated completely and partially are presented, respectively. The absorber parameters ranges by which the instability vibration can be eliminated completely and partially are obtained. The results show that the natural frequency vibration due to the fluid-induced instability in the rotor/seal system can be eliminated efficiently using the absorber. The appropriate natural frequency and damping ratio of the absorber can extend the complete elimination region of the instability vibration and postpone the occurrence of the instability vibration.

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：Sommerfeld effect is a nonlinear jumping phenomenon caused by the failure of a non-ideal motor to provide enough power near the critical speed of the system to enable the system to pass through the resonance region smoothly. Sommerfeld effect and unbalanced response of an induction motor driven single disk rotor system with eccentric mass are studied. The dynamic model of induction motor is introduced into the rotor system, and the induction motor rotor dynamic model is established. It is found that Sommerfeld effect will occur in the induction motor -rotor system based on fully considering the interaction between induction motor and rotor system. The influences of the eccentric mass on Sommerfeld effect and unbalanced response are analyzed. The results show that when the mass ratio of eccentric mass to total rotor mass η is about less than 0.026, namely η<0.026, since the motor can provide enough power to ensure the rotor system smoothly pass the critical speed, Sommerfeld effect will not occur in the induction motorrotor system. When 0.026<η<0.083, since the max electromagnetic torque provided by the motor is less than the output torque required for the rotor system to smoothly pass the critical speed, Sommerfeld effect will occur. When η>0.083, with the supply frequency increasing, the induction motor will not provide enough power to make the rotor system pass through the critical speed, and the rotor system's speed will always be lower than the critical speed. The research can provide reference for the power design and selection of rotor system.