
doi: 10.1051/cocv:2003028
handle: 10722/156149
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.
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
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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