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Note on the Stability of a Slowly Rotating Timoshenko Beam with Damping

Published online by Cambridge University Press:  09 September 2015

J. Woźniak  and
M. Firkowski
J. Woźniak*
Affiliation:
Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
M. Firkowski
Affiliation:
Department of Mathematics and Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
*
*Corresponding author. Email: wozniak@univ.szczecin.pl (J. Woźniak), firkowski@wmf.univ.szczecin.pl (M. Firkowski)
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Abstract

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.

Keywords

35L1035B3574K10Timoshenko beamstabilitytransfer function
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 6 , December 2015 , pp. 736 - 753
Copyright
Copyright © Global-Science Press 2015 

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