Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: Theoretical and experimental results

Journal of Sound and Vibration

Volumn 300, Issue 3-5, 2007, Pages 522-551

  Gourdon, E ^a   Alexander, N A ^a   Taylor, C A ^a   Lamarque, C H ^b   Pernot, S ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EARTHQUAKES; EXCITONS; NONLINEAR SYSTEMS; SHOCK ABSORBERS; TRANSIENTS; VIBRATION CONTROL;

ENERGY PUMPING; EXTERNAL EXCITATION; NONLINEAR COUPLING; NONLINEAR ENERGY SINK (NES);

ENERGY TRANSFER;

EID: 33845885140     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2006.06.074     Document Type: Article

References (26)

1. Vakakis A.F., Kounadis A.N., and Raftoyiannis I.G. Use of nonlinear localization for isolating structures from earthquake-induced motions. Earthquake Engineering and Structural Dynamics 28 (1999) 21-36
2. Vakakis A.F., Manevitch L.I., Gendelman O., and Bergman L. Dynamics of linear discrete systems connected to local, essentially non-linear attachments. Journal of Sound and Vibration 264 (2003) 559-577
3. Gendelman O.V. Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators. Nonlinear Dynamics 25 (2001) 237-253
4. Gendelman O., Manevitch L.I., Vakakis A.F., and Closkey R.M. Energy pumping in nonlinear mechanical oscillators: Part I-dynamics of the underlying Hamiltonian systems. Journal of Applied Mechanics 68 (2001) 34-41
5. Vakakis A.F., and Gendelman O. Energy pumping in nonlinear mechanical oscillators: Part II-resonance capture. Journal of Applied Mechanics 68 (2001) 42-48
6. O. Gendelman, L.I. Manevitch, A.F. Vakakis, L. Bergman, A degenerate bifurcation structure in the dynamics of coupled oscillators with essential stiffness nonlinearities, Nonlinear Dynamics (2003).
7. Gourdon E., and Lamarque C.H. Energy pumping with various nonlinear structures: numerical evidences. Nonlinear Dynamics 40 (2005) 281-307
8. McFarland D., Bergman L., and Vakakis A. Experimental study of non-linear energy pumping occurring at a single fast frequency. International Journal of Non-Linear Mechanics 40 (2005) 891-899
9. Hagedorn P. Non-linear Oscillations (1988), Clarendon Press, Oxford
10. G.S. Agnes, Performance of Nonlinear Mechanical, Resonant-Shunted Piezoelectric, and Electronic Vibration Absorbers for Multi-Degree-of-Freedom Structures, PhD Thesis, Virginia Polytechnic Institute and State University, 1997.
11. Arnold F.R. Steady-state behavior of systems provided with nonlinear dynamic vibration absorbers. Journal of Applied Mechanics 22 (1955) 487-492
12. Hunt J.B., and Nissen J.C. The broadband dynamic vibration absorber. Journal of Sound and Vibration 83 (1982) 573-578
13. Gendelman O.V., Gorlov D.V., Manevitch L.I., and Moussienko A.I. Dynamics of coupled linear and essentially nonlinear oscillators with substantially different masses. Journal of Sound and Vibration 286 1-2 (2005) 1-19
14. Arias A. A measure of earthquake intensity. Seismic Design for Nuclear Power Plants (1970), MIT Press, Cambridge, MA 438-483
15. Den Hartog J.P. Mechanical Vibration (1947), McGraw-Hill, New York
16. Jang X., McFarland D.M., Bergman L.A., and Vakakis A.F. Steady state passive nonlinear energy pumping in coupled oscillators: theoretical and experimental results. Nonlinear Dynamics 33 (2003) 87-102
17. O.V. Gendelman, E. Gourdon, C.H. Lamarque, Quasiperiodic energy pumping in coupled oscillators under periodic forcing, Journal of Sound and Vibration, 249 (2006) 651-662.
18. Gendelman O.V. Bifurcations of nonlinear normal modes of linear oscillator with strongly nonlinear damped attachment. Nonlinear Dynamics 37 2 (2004) 115-128
19. Manevitch L.I. Complex representation of dynamics of coupled nonlinear oscillators. Mathematical Models of Nonlinear Excitations Transfer, Dynamics, and Control in Condensed Systems and Other Media (1999), Kluwer Academic Press, Plenum Publishers, New York 269-300
20. Nayfeh Ali.H. Perturbation Methods (February 1973), Wiley, New York
21. Jackson E.A. Perspectives of Nonlinear Dynamics vol. 1 (1994), Cambridge University Press, Cambridge
22. S. Pernot, Méthodes Ondelettes pour l'étude des Vibrations et de la Stabilité des Systèmes Dynamiques, Thesis in Civil Engineering, Institut National des Sciences Appliquées, Lyon, France, Isal no.0071:441p, 2000.
23. Gourdon E., and Lamarque C.H. Energy pumping for a larger span of energy. Journal of Sound and Vibration 285 3 (2005) 711-720
24. Mallat S. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence 11 (1989) 674-693
25. I. Daubechies, Orthogonal bases of compactly supported wavelets, Communication on Pure and Applied Mathematics XLV (1998) 909-996.
26. Vakakis A.F. Inducing passive nonlinear energy sinks in vibrating systems. ASME Transactions, Journal of Vibration and Acoustics 123 3 (2001) 324-332