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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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References

[1]Curtain, R. and Morris, K., Transfer functions of distributed parameter systems: A tutorial, Automatica, 45 (2009), pp. 1101–1116.CrossRefGoogle Scholar
[2]Curtain, R. F. and Zwart, H. J., An Introduction to Infinite-Dimensional Linear Systems Theory, Springer, 1995.CrossRefGoogle Scholar
[3]Krabs, W. and Sklyar, G. M., On the controllability of a slowly rotating Timoshenko beam, Z. Anal. Anw., 18(2) (1999), pp. 437–448.CrossRefGoogle Scholar
[4]Krabs, W. and Sklyar, G. M., On Controllability of Linear Vibrations, Nova Science Publishers Inc. 2002, Huntington, NY.Google Scholar
[5]Krabs, W. and Sklyar, G. M., On the stabilizability of a slowly rotating Timoshenko beam, Z. Anal. Anw., 19(1) (2000), pp. 131–145.CrossRefGoogle Scholar
[6]Krabs, W., Sklyar, G. M. and Woźniak, J., On the set of reachable states in the problem of controllability of rotating Timoshenko beams, Z. Anal. Anw., 22(1) (2003), pp. 215–228.CrossRefGoogle Scholar
[7]Valverde, J. and Garcia Vallejo, D., Stability analysis of a substructured model of the rotating beam, Nonlinear Dyn., 55 (2009), pp. 355–372.CrossRefGoogle Scholar
[8]Lesaffre, N., Sinou, J.-J. and Thouverez, F., Stability analysis of rotating beams rubbing on an elastic circular structure, J. Sound Vib., 299(4-5) (2007), pp. 1005–1032.Google Scholar
[9]Sabuncu, M. and Evran, K., Dynamic stability of a rotating asymmetric cross-section Timo-shenko beam subjected to an axial periodic force, Finite Elem. Anal. Des., 41 (2005), pp. 1011–1026.Google Scholar
[10]Rao, S. S. and Gupta, R. S., Finite element vibration analysis of rotating Timoshenko beams, J. Sound Vib., 242(1) (2001), pp. 103–124.Google Scholar
[11]Balakrishnan, A. V., Introduction to Optimization Theory in a Hilbert Space, Berlin, New York, Springer-Verlag, 1971.Google Scholar
[12]Nijmeijer, H. and Van Der Schaft, A. J., Nonlinear Dynamical Control Systems, Springer-Verlag, New York Inc., 1990.Google Scholar