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TECHNICAL PAPERS

Active Mode Localization in Distributed Parameter Systems with Consideration of Limited Actuator Placement, Part 1: Theory

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

Vibration and Control Laboratory, Mechanical Engineering Department, University of Pittsburgh, Pittsburgh, PA 15261

J. Vib. Acoust 122(2), 160-164 (Jul 01, 1995) (5 pages) doi:10.1115/1.568453 History: Received July 01, 1995
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.
Pierre,  C., and Murthy,  D. V., 1992, “Aeroelastic Modal Characteristics of Mistuned Blade Assemblies: Mode Localization and Loss of Eigenstructure,” AIAA J., 30, No. 10, pp. 2483–2496.
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 ACC, pp. 1020–1024.
Yigit,  A., and Choura,  S., 1995, “Vibration Confinement in Flexible Structures via Alternation of Mode Shapes by Using Feedback,” J. Sound Vib., 179, No. 4, pp. 552–568.
Shelley,  F. J., and Clark,  W. W., 1996, “Eigenvector Shaping for Mode Localization in Vibrating Systems,” AIAA J. Guid. Control. Dyn., 19, No. 6, pp. 1342–1348.
Shelley,  F. J., and Clark,  W. W., 1994, “Experimental Verification of Closed-Loop Mode Localization in Vibrating Structures,” Active Control Vib. Noise, ASME DE-75, pp. 99–104.
Moore,  B. C., 1976, “On the Flexibility Offered by State Feedback in Multivariable Systems Beyond Closed Loop Eigenvalue Assignment,” IEEE Trans. Autom. Control, AC-21, pp. 689–692.
Cunningham, T. B., 1980, “Eigenspace Selection Procedures for Closed Loop Response Shaping with Modal Control,” Proceedings of the ACC, pp. 178–186.
Andry, A. N., Shapiro, E. Y., and Sobel, K. M., 1986, “Modal Control and Vibrations,” Frequency Domain and State Space Methods for Linear Systems, C. I. Byrnes and A. Lindquist, eds., Elsevier Science Publishers Co., New York, pp. 185–199.
DeCarlo, R. A., 1989, Linear Systems, Prentice Hall, Englewood Cliffs, NJ, pp. 297–307.
Shelley, F. J., 1995, “Active Mode Localization for Vibration Control in Flexible Structures,” Ph.D. Dissertation, University of Pittsburgh.

Figures

Grahic Jump Location
Effect of scaling matrix [D] on typical eigenvector. Portions of eigenvector scaled by d are considered to be in the localized region of the structure.
Grahic Jump Location
(a) Effect of eigenvector scaling on system description terms. (Stiffness component submatrix shown as typical.) Note that as the number of diagonals in the system description increases, the number of terms affected by scaling also increases. (b) Spring-mass system with tri-diagonal description, as given in Fig. 2(a).
Grahic Jump Location
Probability distribution function
Grahic Jump Location
Eigenvectors for a ten-element simply supported beam model, with (a) uncontrolled system and (b) direct eigenvector scaling (ten sensors and actuators required)
Grahic Jump Location
Eigenvectors for a ten-element simply supported beam model using singular value decomposition, with a varying number of sensor and actuator pairs m

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