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This paper continues the authors previous investigations of stability of the slowly rotating Timoshenko beam whose movement is controlled by the angular acceleration of the disk of the driving motor into which the beam is rigidly clamped. We consider the problem of optimal value of damping coefficient of a particular type of viscoelastic damping operator. To determine location of spectrum of an appropriate operator we use a transfer function method.

This paper continues the senior author’s previous investigation of the slowly rotating Timoshenko beam in a horizontal plane whose movement is controlled by the angular acceleration of the disk of the driving motor into which the beam is rigidly clamped. It was shown before that this system preserves the total energy. We consider the problem of stability of the system after introducing a particular type of damping. We show that the energy of only part of the system vanishes. We illustrate obtained solution with the critical case of the infinite value of the damping coefficient.