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

Kim, Jong Uhn; Renardy, Yuriko

SIAM J. Control Optimization 25, 1417-1429 (1987).

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

MSC:

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

Keywords:

uniform stabilization; Timoshenko beam; boundary control; energy method; \(C_ 0\)-semigroup theory; Chebyshev - tau method