Volume 9, March 2003
|Page(s)||579 - 600|
|Published online||15 September 2003|
Stabilization of Timoshenko Beam by Means of Pointwise Controls
Department of Mathematics of
Shanxi University, TaiYuan 030006, P.R. China.; email@example.com.
2 Department of Mathematics of the University of Hong Kong, Hong Kong, P.R. China; firstname.lastname@example.org.
Revised: 15 April 2003
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.
Mathematics Subject Classification: 34K35 / 47A65 / 93B52 / 93C20
Key words: Timoshenko beam / pointwise feedback control / generalized eigenfunction system / Riesz basis.
© EDP Sciences, SMAI, 2003
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.