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.

Keywords: Timoshenko beam, pointwise feedback control, generalized eigenfunction system, Riesz basis

@article{COCV_2003__9__579_0, author = {Xu, Gen-Qi and Yung, Siu Pang}, title = {Stabilization of {Timoshenko} beam by means of pointwise controls}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {579--600}, publisher = {EDP-Sciences}, volume = {9}, year = {2003}, doi = {10.1051/cocv:2003028}, zbl = {1068.93024}, mrnumber = {1998716}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2003028/} }

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 SP - 579 EP - 600 VL - 9 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2003028/ DO - 10.1051/cocv:2003028 LA - en ID - COCV_2003__9__579_0 ER -

%0 Journal Article %A Xu, Gen-Qi %A Yung, Siu Pang %T Stabilization of Timoshenko beam by means of pointwise controls %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 579-600 %V 9 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2003028/ %R 10.1051/cocv:2003028 %G en %F COCV_2003__9__579_0

Xu, Gen-Qi; Yung, Siu Pang. Stabilization of Timoshenko beam by means of pointwise controls. ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 579-600. doi : 10.1051/cocv:2003028. http://www.numdam.org/articles/10.1051/cocv:2003028/

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