Boundary control of the Timoshenko beam. (English) Zbl 0632.93057

The paper investigates uniform stabilization of the Timoshenko beam with boundary control. The main result of the first part, established by means of the energy method combined with \(C_ 0\)-semigroup theory, is that the natural energy of the beam decays exponentially fast.
A numerical study on the spectrum is carried out in the second part of the paper, the Chebyshev - tau method being used in order to discretize the spatial variation of the eigenfunctions. Results of these numerical experiments are also presented.
Reviewer: O.Pastravanu


93D15 Stabilization of systems by feedback
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
93C20 Control/observation systems governed by partial differential equations
47D03 Groups and semigroups of linear operators
35B37 PDE in connection with control problems (MSC2000)
35L15 Initial value problems for second-order hyperbolic equations
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
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