Dynamics of a strongly nonlinear vibration absorber coupled to a harmonically excited two-degree-of-freedom system

Journal of Sound and Vibration

Volumn 312, Issue 1-2, 2008, Pages 234-256

  Starosvetsky, Y ^a   Gendelman, O V ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); HARMONIC ANALYSIS; LINEAR SYSTEMS; NONLINEAR CONTROL SYSTEMS; PROBLEM SOLVING; TUNING;

EXCITED MODES; LINEAR SUBSYSTEMS; NONLINEAR VIBRATION ABSORBERS;

VIBRATION CONTROL;

EID: 39149087065     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2007.10.035     Document Type: Article

References (32)

1. H. Frahm, Device for damping vibrations of bodies, US Patent 989,958, 1911.
2. Den Hartog J.P. Mechanical Vibrations. fourth ed. (1956), McGraw-Hill Book Company, New York
3. Ormondroyd J., and Den Hartog J.P. The theory of the dynamic vibration absorber. Transactions of the American Society of Mechanical Engineers 50 (1928) A9-A22
4. Hadi M.N.S., and Arfiadi Y. Optimum design of absorber for MD structures. Journal of Structural Engineering 124 (1998) 1272-1280
5. Singh M.P., and Moreschi L.M. Optimal placement of dampers for passive response control. Earthquake Engineering and Structural Dynamics 31 (2002) 955-976
6. Mehmet Bulent Ozer, and Royston T.J. Extending Den Hartog's vibration absorbertechnique to multi-degree-of-freedom systems. Journal of Vibration and Acoustics 127 4 (2004) 341-350
7. Roberson R.E. Synthesis of a nonlinear dynamic vibration absorber. Journal of the Franklin Institute 254 (1952) 205-220
8. Shaw J., Shaw S.W., and Haddow A.G. On the response of the nonlinear vibration absorber. International Journal of Non-Linear Mechanics 24 (1989) 281-293
9. Rice H.J., and McCraith J.R. Practical non-linear vibration absorber design. Journal of Sound and Vibration 116 3 (1987) 545-559
10. Jordanov I.N., and Cheshankov I.B. Optimal design of linear and nonlinear dynamic vibration absorbers. Journal of Sound and Vibration 123 (1988) 157-170
11. Natsiavas S. Steady state oscillations and stability of non-linear dynamic vibration absorbers. Journal of Sound and Vibration 156 2 (1992) 227-245
12. Gendelman O.V. Transition of energy to nonlinear localized mode in highly asymmetric system of nonlinear oscillators. Nonlinear Dynamics 25 (2001) 237-253
13. Gendelman O.V., Vakakis A.F., Manevitch L.I., and McCloskey R. Energy pumping in nonlinear mechanical oscillators I: dynamics of the underlying Hamiltonian system. Journal of Applied Mechanics 68 1 (2001) 34-41
14. Vakakis A.F., and Gendelman O.V. Energy pumping in nonlinear mechanical oscillators II: resonance capture. Journal of Applied Mechanics 68 1 (2001) 42-48
15. Vakakis A.F. Inducing passive nonlinear energy sinks in linear vibrating systems. Journal of Vibration and Acoustics 123 3 (2001) 324-332
16. Vakakis A.F., Manevitch L.I., Gendelman O., and Bergman L. Dynamics of linear discrete systems connected to local essentially nonlinear attachments. Journal of Sound and Vibration 264 (2003) 559-577
17. Gendelman O.V. Bifurcations of nonlinear normal modes of linear oscillator with strongly nonlinear damped attachment. Nonlinear Dynamics 37 2 (2004) 115-128
18. Shaw S.W., and Pierre C. Normal modes for nonlinear vibratory systems. Journal of Sound and Vibration 164 (1993) 85-124
19. Vakakis A.F., Manevitch L.I., Mikhlin Yu.V., Pilipchuk V.N., and Zevin A. Normal Modes and Localization in Nonlinear Systems (1996), Wiley Interscience, New York
20. Jang X., McFarland M., Bergman L.A., and Vakakis A.F. Steady state passive nonlinearenergy pumping in coupled oscillators: theoretical and experimental results. Nonlinear Dynamics 33 (2003) 7-102
21. Gendelman O.V., Gourdon E., and Lamarque C.H. Quasiperiodic energy pumping in coupled oscillators under periodic forcing. Journal of Sound and Vibration 294 (2006) 651-662
22. Gendelman O.V., and Starosvetsky Y. Quasiperiodic response regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing. Journal of Applied Mechanics 74 (2006) 325-331
23. O.V. Gendeman, Y. Starosvetsky, M. Feldman, Attractors of harmonically forced linear oscillator with attached nonlinear energy sink I: description of response regimes, online first, Nonlinear Dynamics (2007), doi:10.1023/A:1012967003477.
24. Y. Starosvetsky, O.V. Gendelman, Attractors of harmonically forced linear oscillator with attached nonlinear energy sink II: optimization of a Nonlinear vibration absorber, online first, Nonlinear Dynamics (2007), doi:10.1007/s11071-006-9168-z.
25. Arnold V.I., Afrajmovich V.S., Il'yashenko Y.S., and Shil'nikov L.P. Dynamical Systems V. Encyclopedia of Mathematical Sciences (1994), Springer, Berlin
26. Guckenheimer J., Wechselberger M., and Young L.-S. Chaotic attractors of relaxation oscillators. Nonlinearity 19 (2006) 701-720
27. Guckenheimer J., Hoffman K., and Weckesser W. Bifurcations of relaxation oscillations near folded saddles. International Journal of Bifurcations and Chaos 15 11 (2005) 3411-3421
28. Gourdon E., Alexander N.A., Taylor C.A., Lamarque C.H., and Pernot S. Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: theoretical and experimental results. Journal of Sound and Vibration 300 (2007) 522-551
29. Y. Starosvetsky, O.V. Gendelman, Strongly modulated response in forced 2DOF oscillatory system with essential mass and potential asymmetry, Physica D (2007), submitted for publication.
30. Y. Starosvetsky, O.V. Gendelman, Extensive study of periodic regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing-account of detuning, Proceedings of ASME DETC-2007, paper DETC2007-34222, 2007.
31. Lee Y., Kerschen G., McFarland D., Hill W., Nichkawde C., Strganac T., Bergman L., and Vakakis A. Suppressing aeroelastic instability using broadband passive targeted energy transfers, part 2: experiments. AIAA Journal 45 (2007) 2391-2400
32. Cochelin B., Herzog P., and Mattei P.-O. Experimental evidence of energy pumping in acoustics. Comptes Rendus Mechanique 334 (2006) 639-644