Toward an Optimal Design Procedure of a Nonlinear Vibration Absorber Coupled to a Duffing Oscillator

Viguié, Régis; Kerschen, Gaëtan

Download

Paper published in a book (Scientific congresses and symposiums)

Toward an Optimal Design Procedure of a Nonlinear Vibration Absorber Coupled to a Duffing Oscillator

Viguié, Régis; Kerschen, Gaëtan

2008 • In International Conference on Noise and Vibration Engineering, Leuven, 2008

Permalink
https://hdl.handle.net/2268/18702

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

C53_2008_Leuven_ISMAb.pdf

Author preprint (407.9 kB)

Download

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

tuned mass damper; nonlinear energy sink; frequency-energy plot; targeted energy transfer

Abstract :

[en] In the present study, the focus is set on the development of a design methodology for nonlinear vibration absorbers, termed nonlinear energy sink (NES), to optimize the vibrating level reduction on a Duffing oscillator. The idea lies in the assessment of a duality property between, on the one hand, the tuning procedure of the tuned mass damper (TMD) coupled to a linear oscillator and, on the other hand, the assumed design scheme of NES coupled to a purely nonlinear Duffing oscillator. To this end, the basics on the TMD tuning methodology are recalled and extended to the concept of frequency-energy plot (FEP) [1]. Then, based upon this concept, the development of a NES design procedure is undertaken and the related dynamics analyzed. Finally, it is shown how to design a vibration absorber to deal with a general Duffing oscillator.

Disciplines :

Mechanical engineering
Aerospace & aeronautics engineering

Author, co-author :

Viguié, Régis ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Vibrations et identification des structures

Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Language :

English

Title :

Toward an Optimal Design Procedure of a Nonlinear Vibration Absorber Coupled to a Duffing Oscillator

Publication date :

2008

Event name :

International Conference on Noise and Vibration Engineering

Event place :

Leuven, Belgium

Audience :

International

Main work title :

International Conference on Noise and Vibration Engineering, Leuven, 2008

Available on ORBi :

since 13 August 2009

Statistics

Number of views

129 (4 by ULiège)

Number of downloads

210 (1 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

Bibliography

Y. S. Lee, G. Kerschen, A. F. Vakakis, P. N. Panagopoulos, L. A. Bergman, and D. M. McFarland, "Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment," Physica D, vol. 204, pp. 41-69, 2005.
H. Frahm, A Device for Damping Vibrations of Bodies. US Patent 989958, 1911.
J. P. Den Hartog, Mechanical Vibrations. Dover Books on Engineering, 4th ed., 1985.
O. V. Gendelman, "Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators," Nonlinear dynamics, vol. 25, pp. 237-253, 2001.
O. V. Gendelman, L. I. Manevitch, A. F. Vakakis, and R. McCloskey, "Energy pumping in nonlinear mechanical oscillators: Part i - dynamics of the underlying hamiltonian systems," Journal of Applied Mechanics, vol. 68, pp. 34-41, January 2001.
A. F. Vakakis and O. V. Gendelman, "Energy pumping in nonlinear mechanical oscillators: Part ii-resonance capture," Journal of Sound and Vibration, vol. 68, pp. 42-48, January 2001.
A. F. Vakakis, "Inducing passive nonlinear energy sinks in vibrating systems," Journal of Vibration and Acoustics, vol. 123, pp. 324-332, 2001.
G. Kerschen, A. F. Vakakis, Y. S. Lee, D. M. McFarland, J. J. Kowtko, and L. A. Bergman, "Energy transfers in a system of two coupled oscillators with essential nonlinearity: 1:1 resonance manifold and transient bridging orbits," Nonlinear Dynamics, vol. 42, pp. 289-303, 2005.
D. M. McFarland, L. A. Bergman, and A. F. Vakakis, "Experimental study of nonlinear energy pumping occurring at a single fast frequency," International Journal of Non-Linear Mechanics, vol. 40, pp. 891-899, 2005.
G. Kerschen, D. M. McFarland, J. J. Kowtko, Y. S. Lee, L. A. Bergman, and A. F. Vakakis, "Experimental demonstration of transient resonance capture in a system of two coupled oscillators with essential stiffness nonlinearity," Journal of Sound and Vibration, vol. 299, pp. 822-838, February 2007.
O. V. Gendelman, D. V. Gorlov, L. I. Manevitch, and A. I. Musienko, "Dynamics of coupled linear and essentially nonlinear oscillators with substantially different masses," Journal of Sound an Vibration, vol. 286, pp. 1-19, 2005.
G. Kerschen, Y. S. Lee, A. F. Vakakis, D. M. McFarland, and L. A. Bergman, "Irreversible passive energy transfer in coupled oscillators with essential nonlinearity," SIAM Journal of Applied Mathematics, vol. 66, pp. 648-679, January 2006.
E. Gourdon and C. H. Lamarque, "Nonlinear energy sinks with uncertain parameters," Journal of Computational and Nonlinear Dynamics, vol. 1, pp. 187-195, 2006.
B. Cochelin, P. Herzog, and P. O. Mattei, "Experimental evidence of energy pumping in acoustics," Compte Rendus de Mécanique, vol. 334, pp. 639-644, 2006.
Y. S. Lee, G. Kerschen, D. M. McFarland, W. J. Hill, C. Nichkawde, T.W. Strganac, L. A. Bergman, and A. F. Vakakis, "Suppression of aeroelastic instability by means of broadband passive targeted energy transfers, part i: Theory," AIAA Journal, vol. 45, 2007.
R. Viguié, G. Kerschen, J.-C. Golinval, D. M. McFarland, L. A. Bergman, and N. van de Wouw, "Using passive nonlinear targeted energy transfer to stabilize drill-string system," Mechanical Systems and Signal Processing, 2007.
R. Viguié, M. Peeters, G. Kerschen, and J.-C. Golinval, "Energy transfer and dissipation in a duffing oscillator coupled to a nonlinear attachment," Journal of Computational and Nonlinear Dynamics (In Review), 2008.
L. I. Manevitch, E. Gourdon, and C. H. Lamarque, "Parameters optimization for energy pumping in strongly nonhomogeneous 2 dof system," Chaos, Solitons and Fractals, vol. 31, pp. 900-911, February 2007.
Y. Starosvetsky and O. V. Gendelman, "Attractors of harmonically forced linear oscillator with attached nonlinear energy sink ii: Optimization of a nonlinear vibration absorber," Nonlinear Dynamics, vol. 51, pp. 47-57, January 2007.
T. Asami. Nishihara, and A. M. Baz, "Analytical solutions to hinf and h2 optimization of dynamic vibration absorbers attached to damped linear systems," Journal of Vibration and Acoustics, Transactions of the ASME, vol. 124, pp. 284-295, April 2002.
O. Nishihara and T. Asami, "Closed-form solutions to the exact optimizations of dynamic vibration absorbers (minimizations of the maximum amplitude magnification factors)," Journal of Vibration and Acoustics, Transactions of the ASME, vol. 124, pp. 576-582, October 2002.
T. Asami and O. Nishihara, "Closed-form exact solution to hinf optimization of dynamic vibration absorbers. application to different transfer functions and damping systems," Journal of Vibration and Acoustics, Transactions of the ASME, vol. 125, pp. 381-411, July 2003.
Y. Fujino and M. Abe, "Design formulas for tuned mass damper based on a pertubation technique," John Wiley & Sons. LTD., Earthquake Engineering and Structural Dynamics, vol. 22, pp. 833-854, 1993.
M. B. Ozer and T. J. Royston, "Extending den hartog's vibrations absorber technique to multi-degreeof- freedom systems," Journal of Vibration and Acoustics, Transactions of the ASME, vol. 127, pp. 341-350, August 2005.
G. Kerschen, M. Peeters, and J.-C. Golinval, "Nonlinear normal modes, part 1: A useful framework for the structural dynamiscist," MSSP (in review), 2007.
M. Peeters, R. Viguié, G. Sérandour, G. Kerschen, and J.-C. Golinval, "Nonlinear normal modes, part 2: Toward a practical computation using numerical continuation techniques," MSSP (in press), 2008.
A. Vakakis, O. Gendelman, L. Bergman, D. McFarland, G. Kerschen, and Y. Lee, Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems. Dordrecht: Springer, 2008, in press.
L. I. Manevitch, "Complex representation of dynamics of coupled oscillators," Mathematical Models of Nonlinear Excitations, Transfer Dynamics and Control in condensed Systems, Kluwer Academic/ Plenum Publishers, pp. 269-300, 1999.
A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations. New-York: Wiley-Interscience, 1995.