DAMPING THE TRANSVERSE VIBRATIONS OF A RAPIDLY ROTATING DISC

— 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 str...

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Bibliographic Details
Published inMechanics of solids Vol. 57; no. 1; pp. 57 - 64
Main Authors Banichuk, N. V., Ivanova, S. Yu, Afanas’ev, V. S.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.02.2022
Springer Nature B.V
Subjects
Classical Mechanics
Iterative algorithms
Iterative methods
Optimal control
Optimization
Physics
Physics and Astronomy
Rotating disks
Transverse oscillation
Vibration damping
rotating flexible disk
damping optimization
vibration damping
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Summary:— 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.
ISSN:0025-6544
1934-7936
DOI:10.3103/S0025654422010010