In the paper there is proposed an algorithm of an efficient semi-active control of steady-state periodic lateral vibrations of the overhung rotor-shaft system. This algorithm has been developed using fundamentals of the Optimal Control Theory. In the considered system the control is realized by means of the linear dampers with the magneto-rheological fluid built in the bearing housing. The computational example demonstrates possibilities of the applied approach resulting in an additional reduction of out-of-resonance and near-resonance harmonic oscillation amplitudes in comparison with an analogous passive control.
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