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A method suggested in the past to suppress the vibrations of flexible rotor systems passing through critical speeds is reconsidered. An appropriate switching of the system stiffness (by using shape memory alloys, for instance) is utilized. To model the nonstationary system behavior more realistically, the rotor is driven by a limited power supply. A special feature is the inclusion of unequal bending stiffnesses of the shaft. The stationary and transient behavior of the motor and system characteristic and the deformation amplitudes and phase angles, are examined. Attention is focussed on the strategy for switching the stiffness to yield small resonance deflections.