Energy Estimate of Boundary Controlled Vibrating Hybrid Structure Subject to Uncertain Forces
Publication: Journal of Aerospace Engineering
Volume 16, Issue 3
Abstract
We study here a model hybrid system consisting of a flexible rectangular space structure such as a solar cell array, hoisted at one end by a movable rigid hub, set to vibration from certain initial conditions, but subject to uncertain disturbing forces distributed along its length. Assuming that the control of vibrations is sought by a damper at the hub end proportional to a general nonlinear function of the velocity of the point, we obtain an energy estimate of vibrations over a time interval in terms of initial energy of the system and the time integral of the norm of the disturbance over the length of the panel. From this, estimates of tolerance level of the disturbances are obtained. Both torsional and flexural modes of vibration are considered.
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References
Bose, S. K.(2001). “On initial conditions for boundary stabilized hybrid Euler–Bernoulli beam.” Proc., Indian Acad. Sci. (Math. Sci.), 111, 365–370.
Chen, G.(1979). “Energy decay estimates and exact boundary-value controllability for the wave equation in a bounded domain.” J. Math. Pures Appl., 58, 249–273.
Chen, G.(1981). “A note on the boundary stabilization of the wave equation.” SIAM J. Control Optim., 19, 106–113.
Chen, G., Delfour, M. C., Krall, A. M., and Payre, G.(1987). “Modeling, stabilization, and control of serially connected beams.” SIAM J. Control Optim., 25, 526–546.
Chen, G., and Zhou, J.(1990). “The wave propagation method for the analysis of boundary stabilization in vibrating structures.” SIAM J. on Appl. Math., 50, 1254–1283.
Gorain, G. C., and Bose, S. K.(1998a). “Exact controllability and boundary stabilization of torsional vibrations of an internally damped flexible space structure.” J. Optim. Theory Appl., 99, 423–442.
Gorain, G. C., and Bose, S. K.(1998b). “Exact controllability of a linear Euler-Bernoulli panel.” J. Sound and Vibr., 217, 637–652.
Gorain, G. C., and Bose, S. K.(1999). “Boundary stabilization of a hybrid Euler-Bernoulli beam.” Proc., Indian Acad. Sci. (Math. Sci.), 109, 411–416.
Komornik, V.(1991). “Rapid boundary stabilization of wave equations.” SIAM J. Control Optim., 29, 197–208.
Krall, A. M.(1989). “Asymptotic stability of the Euler-Bernoulli beam with boundary control.” J. Math. Anal. Appl., 137, 288–295.
Lagnese, J.(1983). “Decay of solutions of wave equations in a bounded region with boundary dissipation.” J. Diff. Eqns., 50, 163–182.
Lagnese, J.(1988). “Note on boundary stabilization of wave equations.” SIAM J. Control Optim., 26, 1250–1256.
Lions, J. L.(1988). “Exact controllability, stabilization, and perturbations for distributed systems.” SIAM Rev., 30, 1–68.
Littman, W., and Markus, L.(1988). “Stabilization of a hybrid system of elasticity by feedback boundary damping.” Ann. Math. Pura Appl., 152, 281–330.
Morgül, Ö.(1992). “Dynamic boundary control of a Euler-Bernoulli beam.” IEEE Trans. Autom. Control, 37, 639–642.
Rao, B.(1995). “Uniform stabilization of a hybrid system of elasticity.” SIAM J. Control Optim., 33, 440–454.
Shisha, O. (1967). Inequalities, Academic, New York.
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Copyright © 2003 American Society of Civil Engineers.
History
Received: Jan 2, 2002
Accepted: Feb 13, 2002
Published online: Jun 13, 2003
Published in print: Jul 2003
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