# Stabilization of Timoshenko Beam by Means of Pointwise Controls

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

- Volume: 9, page 579-600
- ISSN: 1292-8119

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topXu, Gen-Qi, and Yung, Siu Pang. "Stabilization of Timoshenko Beam by Means of Pointwise Controls." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 579-600. <http://eudml.org/doc/90712>.

@article{Xu2010,

abstract = {
We intend to conduct a fairly complete study on
Timoshenko beams with pointwise feedback controls and seek to obtain information
about the eigenvalues, eigenfunctions, Riesz-Basis-Property,
spectrum-determined-growth-condition, energy decay rate and various stabilities
for the beams. One major difficulty of the present problem is the non-simplicity
of the eigenvalues.
In fact, we shall indicate in this paper situations where the multiplicity of
the eigenvalues is at least two. We build all the above-mentioned results from an effective
asymptotic analysis on both the eigenvalues and the eigenfunctions, and conclude
with the Riesz-Basis-Property and the
spectrum-determined-growth-condition. Finally, these results are used to examine
the stability effects on the system by the location of the pointwise control
relative to the length of the whole beam.
},

author = {Xu, Gen-Qi, Yung, Siu Pang},

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

keywords = {Timoshenko beam; pointwise feedback control; generalized eigenfunction
system; Riesz basis.; generalized eigenfunction system; Riesz basis},

language = {eng},

month = {3},

pages = {579-600},

publisher = {EDP Sciences},

title = {Stabilization of Timoshenko Beam by Means of Pointwise Controls},

url = {http://eudml.org/doc/90712},

volume = {9},

year = {2010},

}

TY - JOUR

AU - Xu, Gen-Qi

AU - Yung, Siu Pang

TI - Stabilization of Timoshenko Beam by Means of Pointwise Controls

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 9

SP - 579

EP - 600

AB -
We intend to conduct a fairly complete study on
Timoshenko beams with pointwise feedback controls and seek to obtain information
about the eigenvalues, eigenfunctions, Riesz-Basis-Property,
spectrum-determined-growth-condition, energy decay rate and various stabilities
for the beams. One major difficulty of the present problem is the non-simplicity
of the eigenvalues.
In fact, we shall indicate in this paper situations where the multiplicity of
the eigenvalues is at least two. We build all the above-mentioned results from an effective
asymptotic analysis on both the eigenvalues and the eigenfunctions, and conclude
with the Riesz-Basis-Property and the
spectrum-determined-growth-condition. Finally, these results are used to examine
the stability effects on the system by the location of the pointwise control
relative to the length of the whole beam.

LA - eng

KW - Timoshenko beam; pointwise feedback control; generalized eigenfunction
system; Riesz basis.; generalized eigenfunction system; Riesz basis

UR - http://eudml.org/doc/90712

ER -

## References

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