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Shock and Vibration
Volume 14, Issue 5, Pages 321-337
http://dx.doi.org/10.1155/2007/517852

Passive Control of Flexible Structures by Confinement of Vibrations

M. Ouled Chtiba,1 S. Choura,1 S. El-Borgi,1 and A.H. Nayfeh2

1Applied Mechanics Research Laboratory, Tunisia Polytechnic School, La Marsa, Tunisia
2Department of Engineering Sciences and Mechanics, Virginia Tech, Blacksburg, VA, USA

Received 26 April 2006; Revised 14 August 2007

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a two-step strategy for the design of passive controllers for the simultaneous confinement and suppression of vibrations (SCSV) in mechanical structures. Once the sensitive and insensitive elements of these structures are identified, the first design step synthesizes an active control law, which is referred to as the reference control law (RCL), for the SCSV. We show that the problem of SCSV can be formulated as an LQR-optimal control problem through which the maximum amplitudes, associated with the control input and the displacements of the sensitive and insensitive parts, can be regulated. In the second design step, a transformation technique that yields an equivalent passive controller is used. Such a technique uses the square root of sum of squares method to approximate an equivalent passive controller while maximizing the effects of springs and dampers characterizing passive elements that are added to the original structure. The viability of the proposed control design is illustrated using a three-DOF mechanical system subject to an excitation. It is assumed that all of the masses are sensitive to the excitation, and thus the vibratory energy must be confined in the added passive elements (insensitive parts). We show that the vibration amplitudes associated with the sensitive masses are attenuated at fast rate at the expense of slowing down the convergence of the passive elements to their steady states. It is also demonstrated that a combination of the RCL and the equivalent passive control strategy leads to similar structural performance.