# Controllability of a slowly rotating Timoshenko beam

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- 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 (2010): 333-360. <http://eudml.org/doc/197303>.

@article{Gugat2010,

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; rotating Timoshenko beam; moment problem; fractional order equations},

language = {eng},

month = {3},

pages = {333-360},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/197303},

volume = {6},

year = {2010},

}

TY - JOUR

AU - Gugat, Martin

TI - Controllability of a slowly rotating Timoshenko beam

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

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; rotating Timoshenko beam; moment problem; fractional order equations

UR - http://eudml.org/doc/197303

ER -

## References

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- M. Gugat, A Newton method for the computation of time-optimal boundary controls of one-dimensional vibrating systems. J. Comput. Appl. Math.114 (2000) 103-119.
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- W. Krabs, On moment theory and contollability of one-dimensional vibrating systems and heating processes. Springer-Verlag, Heidelberg, Lecture Notes in Control and Informat. Sci.173 (1992).
- W. Krabs, Controllability of a rotating beam. Springer-Verlag, Lecture Notes in Control and Inform. Sci.185 (1993) 447-458.
- W. Krabs and G.M. Sklyar, On the controllability of a slowly rotating Timoshenko beam. J. Anal. Appl.18 (1999) 437-448.
- M.A. Moreles, A classical approach to uniform null controllability of elastic beams. SIAM J. Control Optim.36 (1998) 1073-1085.
- D.L. Russel, Nonharmonic Fourier series in the control theory of distributed parameter systems. J. Math. Anal. Appl.18 (1967) 542-560.
- M.A. Shubov, Spectral operators generated by Timoshenko beam model. Systems Control Lett.38 (1999).
- 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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