# Controllability of a slowly rotating Timoshenko beam

ESAIM: Control, Optimisation and Calculus of Variations (2001)

- Volume: 6, page 333-360
- ISSN: 1292-8119

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topGugat, Martin. "Controllability of a slowly rotating Timoshenko beam." ESAIM: Control, Optimisation and Calculus of Variations 6 (2001): 333-360. <http://eudml.org/doc/90597>.

@article{Gugat2001,

abstract = {Consider a Timoshenko beam that is clamped to an axis perpendicular to the axis of the beam. We study the problem to move the beam from a given initial state to a position of rest, where the movement is controlled by the angular acceleration of the axis to which the beam is clamped. We show that this problem of controllability is solvable if the time of rotation is long enough and a certain parameter that describes the material of the beam is a rational number that has an even numerator and an odd denominator or vice versa.},

author = {Gugat, Martin},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {rotating Timoshenko beam; exact controllability; eigenvalues; moment problem; spectral properties; fractional order equations},

language = {eng},

pages = {333-360},

publisher = {EDP-Sciences},

title = {Controllability of a slowly rotating Timoshenko beam},

url = {http://eudml.org/doc/90597},

volume = {6},

year = {2001},

}

TY - JOUR

AU - Gugat, Martin

TI - Controllability of a slowly rotating Timoshenko beam

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2001

PB - EDP-Sciences

VL - 6

SP - 333

EP - 360

AB - Consider a Timoshenko beam that is clamped to an axis perpendicular to the axis of the beam. We study the problem to move the beam from a given initial state to a position of rest, where the movement is controlled by the angular acceleration of the axis to which the beam is clamped. We show that this problem of controllability is solvable if the time of rotation is long enough and a certain parameter that describes the material of the beam is a rational number that has an even numerator and an odd denominator or vice versa.

LA - eng

KW - rotating Timoshenko beam; exact controllability; eigenvalues; moment problem; spectral properties; fractional order equations

UR - http://eudml.org/doc/90597

ER -

## References

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- [8] W. Krabs and G.M. Sklyar, On the controllability of a slowly rotating Timoshenko beam. J. Anal. Appl. 18 (1999) 437-448. Zbl0959.93005MR1701363
- [9] M.A. Moreles, A classical approach to uniform null controllability of elastic beams. SIAM J. Control Optim. 36 (1998) 1073-1085. Zbl0915.93005MR1613913
- [10] D.L. Russel, Nonharmonic Fourier series in the control theory of distributed parameter systems. J. Math. Anal. Appl. 18 (1967) 542-560. Zbl0158.10201MR211044
- [11] M.A. Shubov, Spectral operators generated by Timoshenko beam model. Systems Control Lett. 38 (1999). Zbl0985.93012MR1754907
- [12] S.P. Timoshenko, On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Philos. Mag. (1921) xli.

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