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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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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