The purpose of this work is to investigate the control of the oscillations and the suppression of vibrations in damped and coupled oscillators. In this sense, we look into the potential of using a nonlinear energy sink in combination with an optimal linear control for nonlinear system to suppress structure vibrations under an impact load. As a result, we obtain that the nonlinear energy pumping (a one-way passive and almost irreversible energy flow from a linear main system to a nonlinear attachment that acts as a nonlinear energy sink) can be enhanced with the help of appropriate active control. The numerical results show the effectiveness of the approach presented here.
Issue Section:
Research Papers
1.
Gendelman
, O.
, Manevitch
, L. I.
, Vakakis
, A. F.
, and Closkey
, R. M.
, 2001, “Energy Pumping in Nonlinear Mechanical Oscillators: Part I—Dynamics of the Underlying Hamiltonian Systems
,” ASME J. Appl. Mech.
0021-8936, 68
, pp. 34
–41
.2.
Gendelman
, O.
, 2001, “Transition of Energy to a Nonlinear Localized Mode in a Highly Asymmetric System of Two Oscillators
,” Nonlinear Dyn.
0924-090X, 25
, pp. 237
–253
.3.
Vakakis
, A. F.
, and Gendelman
, O.
, 2001, “Energy Pumping in Nonlinear Mechanical Oscillators: Part II—Resonance Capture
,” ASME J. Appl. Mech.
0021-8936, 68
, pp. 42
–48
.4.
Manevitch
, L. I.
, Gendelman
, O.
, Musienko
, A. I.
, Vakakis
, A. F.
, and Bergman
, L.
, 2003, “Dynamic Interaction of a Semi-Infinite Linear Chain of Coupled Oscillators With a Strongly Nonlinear End Attachment
,” Physica D
0167-2789, 178
, pp. 1
–18
.5.
Gourdon
, E.
, and Lamarque
, C. H.
, 2005, “Energy Pumping for a Larger Span of Energy
,” J. Sound Vib.
0022-460X, 285
, pp. 711
–720
.6.
Kerschen
, G.
, Lee
, Y. S.
, Vakakis
, A. F.
, McFarland
, D. M.
, and Bergman
, L. A.
, 2006, “Irreversible Passive Energy Transfer in Coupled Oscillators With Essential Nonlinearity
,” SIAM J. Appl. Math.
0036-1399, 66
(2
), pp. 648
–679
.7.
Gendelman
, O. V.
, Gorlov
, D. V.
, Manevitch
, L. I.
, and Musienko
, A. I.
, 2005, “Dynamics of Coupled Linear and Essentially Nonlinear Oscillators With Substantially Different Masses
,” J. Sound Vib.
0022-460X, 286
, pp. 1
–19
.8.
Musienko
, A. I.
, Lamarque
, C. H.
, and Manevitch
, L. I.
, 2006, “Design of Mechanical Energy Pumping Devices
,” J. Vib. Control
1077-5463, 12
(4
), pp. 355
–371
.9.
Gourdon
, E.
, and Lamarque
, C. H.
, 2005, “Energy Pumping With Various Nonlinear Structures: Numerical Evidences
,” Nonlinear Dyn.
0924-090X, 40
, pp. 281
–307
.10.
Costa
, S. N. J.
, Hassmann
, C. H. G.
, Balthazar
, J. M.
, and Dantas
, M. J. H.
, 2008, “On Energy Transfer Between Vibrating Systems Under Linear and Nonlinear Interactions
,” Nonlinear Dyn.
0924-090X, in press.11.
Costa
, S. N. J.
, and Balthazar
, J. M.
, 2008, “Suppression of Vibrations in Strongly Nonhomogeneous 2D of Systems
,” Nonlinear Dyn.
0924-090X, accepted.12.
Dantas
, M. J. H.
, and Balthazar
, J. M.
, 2008, “On Energy Transfer Between Linear and Nonlinear Oscillators
,” J. Sound Vib.
0022-460X, 315
(4–5
), pp. 1047
–1070
.13.
Rafikov
, M.
, and Balthazar
, J. M.
, 2005, “Optimal Linear and Nonlinear Control Design for Chaotic Systems
,” Proceedings of IDETC’05—ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Long Beach, CA, Sept. 24–28, CD ROM, Paper No. DETC2005-84998.14.
Rafikov
, M.
, and Balthazar
, J. M.
, 2008, “On Control and Synchronization in Chaotic and Hyperchaotic Systems Via Linear Feedback Control
,” Commun. Nonlinear Sci. Numer. Simul.
1007-5704, 13
, pp. 1246
–1255
.Copyright © 2009
by American Society of Mechanical Engineers
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