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Spectral properties of non-homogeneous Timoshenko beam and its rest-to-rest controllability. (English) Zbl 1131.74034

Summary: We consider the controllability of a slowly rotating non-homogeneous beam clamped to a disc. It is assumed that at the beginning the beam remains at the position of rest, and it is supposed to rotate by a given angle and stop. The motion is governed by the system of two differential equations with non-constant coefficients: mass density, flexural rigidity and shear stiffness. To solve the problem of controllability, we study the spectrum of the operator generating the dynamics of the model. Then the problem of controllability is reduced to a moment problem that is, in turn, solved with the use of the asymptotics of the spectrum.

MSC:

74M05 Control, switches and devices (“smart materials”) in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
93C20 Control/observation systems governed by partial differential equations
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