# Stabilization of Timoshenko beam by means of pointwise controls

ESAIM: Control, Optimisation and Calculus of Variations (2003)

- 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 (2003): 579-600. <http://eudml.org/doc/245066>.

@article{Xu2003,

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},

language = {eng},

pages = {579-600},

publisher = {EDP-Sciences},

title = {Stabilization of Timoshenko beam by means of pointwise controls},

url = {http://eudml.org/doc/245066},

volume = {9},

year = {2003},

}

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

PY - 2003

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

UR - http://eudml.org/doc/245066

ER -

## References

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