Abstract
In this paper, we study the exact controllability and boundary stabilization of the torsional vibrations of a flexible space structure (such as a solar cell array) modeled by a rectangular panel, incorporating the material damping of the structure. The panel is hoisted at one end by a rigid hub and the other end is totally free. For the attachment of this hub on one side of the panel, the hub dynamics leads to a nonstandard boundary condition. To incorporate internal damping of the material, we assume Voigt-type viscoelasticity of the structure. Exact controllability theory is established using the Hilbert uniqueness method by means of a control torque applied only on the rigid hub of the panel. At the same time, uniform exponential energy decay rate is obtained directly for the solution of this problem.
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Gorain, G.C., Bose, S.K. Exact Controllability and Boundary Stabilization of Torsional Vibrations of an Internally Damped Flexible Space Structure. Journal of Optimization Theory and Applications 99, 423–442 (1998). https://doi.org/10.1023/A:1021778428222
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DOI: https://doi.org/10.1023/A:1021778428222