The paper considers the problem of suppressing the free vibration, induced by nonzero initial conditions, in a flexible system governed by the wave equation. First an exact response of the system, with general linear boundary conditions, is derived in terms of propagating waves that are reflected from the boundaries. The solution is explicit and with clear physical interpretation. The general expressions for the response are then used to investigate the behavior of the system under control with the absolute vibration suppression controller, which was originally designed for tracking control. It is shown that the vibration suppression properties of this controller apply also to nonzero initial conditions. In cases where the load end is free or contains only damping, the vibration stops completely in finite time and if it contains only inertia and damping it decays exponentially without vibration.
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e-mail: lsirota@technion.ac.il
e-mail: yoramh@technion.ac.il
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June 2010
Research Papers
Free Response and Absolute Vibration Suppression of Second-Order Flexible Structures—The Traveling Wave Approach
Lea Sirota,
Lea Sirota
Faculty of Mechanical Engineering,
e-mail: lsirota@technion.ac.il
Technion-Israel Institute of Technology
, Haifa 32000, Israel
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Yoram Halevi
Yoram Halevi
Faculty of Mechanical Engineering,
e-mail: yoramh@technion.ac.il
Technion-Israel Institute of Technology
, Haifa 32000, Israel
Search for other works by this author on:
Lea Sirota
Faculty of Mechanical Engineering,
Technion-Israel Institute of Technology
, Haifa 32000, Israele-mail: lsirota@technion.ac.il
Yoram Halevi
Faculty of Mechanical Engineering,
Technion-Israel Institute of Technology
, Haifa 32000, Israele-mail: yoramh@technion.ac.il
J. Vib. Acoust. Jun 2010, 132(3): 031008 (10 pages)
Published Online: April 23, 2010
Article history
Received:
November 30, 2008
Revised:
September 13, 2009
Online:
April 23, 2010
Published:
April 23, 2010
Citation
Sirota, L., and Halevi, Y. (April 23, 2010). "Free Response and Absolute Vibration Suppression of Second-Order Flexible Structures—The Traveling Wave Approach." ASME. J. Vib. Acoust. June 2010; 132(3): 031008. https://doi.org/10.1115/1.4000771
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