Stabilization of Timoshenko Beam by Means of Pointwise Controls
Open Access
- 1 August 2003
- journal article
- research article
- Published by EDP Sciences in ESAIM: Control, Optimisation and Calculus of Variations
- Vol. 9, 579-600
- https://doi.org/10.1051/cocv:2003028
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.This publication has 15 references indexed in Scilit:
- The Riesz basis property of discrete operators and application to a Euler-Bernoulli beam equation with boundary linear feedback controlIMA Journal of Mathematical Control and Information, 2001
- On the Stabilization of a Flexible Beam with a Tip MassSIAM Journal on Control and Optimization, 1998
- Feedback stabilization of a Timoshenko beam with an end massInternational Journal of Control, 1998
- Exponential Stability of Coupled Beams with Dissipative Joints: A Frequency Domain ApproachSIAM Journal on Control and Optimization, 1995
- Boundary control of a Timoshenko beam attached to a rigid body: planar motionInternational Journal of Control, 1991
- Semigroup model and stability of the structurally damped Timoshenko beam with boundary inputsInternational Journal of Control, 1991
- Stabilization of Beams by Pointwise Feedback ControlSIAM Journal on Control and Optimization, 1990
- Analysis, Designs, and Behavior of Dissipative Joints for Coupled BeamsSIAM Journal on Applied Mathematics, 1989
- Boundary Control of the Timoshenko BeamSIAM Journal on Control and Optimization, 1987
- Modeling, Stabilization and Control of Serially Connected BeamsSIAM Journal on Control and Optimization, 1987