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Stabilization of Timoshenko Beam by Means of Pointwise Controls

Stabilization of Timoshenko beam by means of pointwise controls
Authors: Xu, GQ; Yung, SP;

Stabilization of Timoshenko Beam by Means of Pointwise Controls

Abstract

Summary: 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.

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Keywords

Control problems for functional-differential equations, Structure theory of linear operators, Control/observation systems governed by partial differential equations, Control, switches and devices (``smart materials'') in solid mechanics, Riesz Basis, Feedback control, Pointwise Feedback Control, Timoshenko beam, Riesz basis, 515, Generalized Eigenfunction System, Rods (beams, columns, shafts, arches, rings, etc.), Timoshenko Beam, pointwise feedback control, generalized eigenfunction system

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
46
Top 10%
Top 10%
Average
bronze