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TECHNICAL PAPERS

Experimental Application of Feedback Control to Localize Vibration

[+] Author and Article Information
F. J. Shelley, W. W. Clark

Vibration and Control Laboratory, Mechanical Engineering Department, University of Pittsburgh, Pittsburgh, PA 15232

J. Vib. Acoust 122(2), 143-150 (Jan 01, 1996) (8 pages) doi:10.1115/1.568451 History: Received January 01, 1996
Copyright © 2000 by ASME
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References

Bendiksen,  O. O., 1987, “Mode Localization Phenomena in Large Space Structures,” AIAA J., 25, No. 3, pp. 1241–1248.
Bollich, R. K. G., Hobdy, M. A., and Rabins, M. J., 1992, “Multi-Pendulum Rig: Proof of Mode Localization and Laboratory Demonstration Tool,” Proceedings of the American Control Conference, pp. 460–467.
Pierre,  C., and Cha,  P. D., 1989, “Strong Mode Localization in Nearly Periodic Disordered Structures,” AIAA J., 27, No. 2, pp. 227–241.
Valero,  N. A., and Bendiksen,  O. O., 1986, “Vibration Characteristics of Mistuned Shrouded Blade Assemblies,” ASME J. Eng. Gas Turbines Power, 108, pp. 293–299.
Hodges,  C. H., 1982, “Confinement of Vibration by Structural Irregularity,” J. Sound Vib., 82, No. 3, pp. 411–424.
Song, B.-K., and Jayasuriya, S., 1993, “Active Vibration Control Using Eigenvector Assignment for Mode Localization,” Proceedings of the American Control Conference, pp. 1020–1024.
Shelley, F. J., and Clark, W. W., 1994, “Closed-Loop Mode Localization for Vibration Control in Flexible Structures,” Proceedings of the American Control Conference, pp. 1826–1830.

Figures

Grahic Jump Location
Effect of eigenvector scaling on system mode shapes, with the (a) typical set of uncontrolled eigenvectors (b) scaling terms di used to reshape the eigenvectors (c) scaled (controlled) system eigenvectors
Grahic Jump Location
Controlled system gains and description matrices for (a) setup 1, localization of pendulums 2 and 3 (b) setup 2, localization of pendulum 3. Note that for either setup, only two coupling elements in each system (shown in gray) are affected by the localization process because the matrices are tridiagonal. Also note sparsely populated gain matrices and corresponding actuator placement.
Grahic Jump Location
Three-pendulum test rig used in active control mode localization experiments
Grahic Jump Location
Steady state experimental and simulation displacements for pendulum model. Results are for setup 1, with localization on pendulums 1 and 2. Note the reduction in amplitudes of pendulum 1 as the localization factor d increases.
Grahic Jump Location
Steady state experimental and simulation displacements for pendulum model. Results are for setup 2, with localization on pendulum 3. Note the reduction in amplitudes of pendulums 1 and 2 as the localization factor d increases.
Grahic Jump Location
Transient response of a 3-pendulum rig, setup 2. Controller isolates pendulums 1 and 2, with d=1 (no localization), and d=3 (one third the uncontrolled displacement). Note the changes in the response amplitude for pendulums 1 and 2 as d increases.
Grahic Jump Location
Transient response of a 3-pendulum rig, setup 1. Controller isolates pendulum 1 with d=1 (no localization), and d=3 (one third the uncontrolled displacement). Note the difference in the amplitude response for pendulum 1 as d increases.

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