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Shock and Vibration
Volume 16, Issue 2, Pages 213-228

Control of 2D Flexible Structures by Confinement of Vibrations and Regulation of Their Energy Flow

Fakhreddine Landolsi,1 Slim Choura,2 and Ali H. Nayfeh3

1Robotics and Intelligent Systems Laboratory, Department of Mechanical Engineering and Materials Science, Rice University, Houston, TX 77005-1892, USA
2Applied Mechanics and Systems Research Laboratory, Tunisia Polytechnic School, B.P. 743, La Marsa 2078, Tunisia
3Department of Engineering Science and Mechanics, MC 0219, Virginia Tech, Blacksburg, VA 24061, USA

Received 21 June 2007; Revised 7 December 2007

Copyright © 2009 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.


In this paper, we investigate the control of 2D flexible structures by vibration confinement and the regulation of their energy flow along prespecified spatial paths. A discretized-model-based feedback strategy, aiming at confining and suppressing simultaneously the vibration, is proposed. It is assumed that the structure consists of parts that are sensitive to vibrations. The control design introduces a new pseudo-modal matrix derived from the computed eigenvectors of the discretized model. Simulations are presented to show the efficacy of the proposed control law. A parametric study is carried out to examine the effects of the different control parameters on the simultaneous confinement and suppression of vibrations. In addition, we conducted a set of simulations to investigate the flow control of vibrational energy during the confinement-suppression process. We found that the energy flow can be regulated via a set of control parameters for different confinement configurations.