Damping the Transverse Vibrations of a Rapidly Rotating Disc

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Abstract
The rotation of a thin elastic disk around its axis is considered. It is assumed that the disk is rigidly fixed in the center and performs small transverse vibrations described in the framework of the membrane model. To suppress vibrations, the flexible disk is subjected to external mechanical stress. The vibration damping process is estimated by a quadratic energy criterion and is optimized using the modern theory of optimal control. Optimality conditions are derived that are used to suppress elastic vibrations in a finite time interval, and a developed iterative algorithm for damping vibrations is presented, illustrated by the example of the analytical determination of a stabilizing effect.

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