International Applied Mechanics

, Volume 41, Issue 2, pp 203–209 | Cite as

Damping of Free Elastic Vibrations in Linear Systems

  • K. V. Avramov
  • Yu. V. Mikhlin


The possibility of using a Mises truss as an absorber of free elastic vibrations in a linear elastic system is examined. The nonlinear normal mode method is used to analyze nonlinear vibrations. A local nonlinear normal mode is shown to be favorable for vibration damping


linear elastic system free elastic vibrations Mises truss nonlinear normal mode method vibration damping 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. V. Frolov (ed.), Vibrations in Engineering [in Russian], Mashinostroenie, Moscow (1995).Google Scholar
  2. 2.
    J. P. Den-Hartog, Mechanical Vibrations, McGraw-Hill, New York (1956).Google Scholar
  3. 3.
    L. I. Manevich, Yu. V. Mikhlin, and V. N. Pilipchuk, The Normal Mode Method for Essentially Nonlinear Systems [in Russian], Nauka, Moscow (1989).Google Scholar
  4. 4.
    A. H. Nayfeh, Perturbation Methods, Wiley, New York (1973).Google Scholar
  5. 5.
    L. I. Shteinvol’f, Dynamic Design of Machines and Mechanisms [in Russian], Mashgiz, Moscow (1961).Google Scholar
  6. 6.
    K. V. Avramov, “Bifurcations at combination resonance and quasiperiodic vibration of flexible beams, ” Int. Appl. Mech., 39, No.8, 976–982 (2003).CrossRefGoogle Scholar
  7. 7.
    K. V. Avramov and Yu. V. Mikhlin, “Forced oscillations of system, containing a snap-through truss, close to its equilibrium position,” Nonlin. Dynam., 35, 361–379 (2004).CrossRefGoogle Scholar
  8. 8.
    R. S. Haxton and A. D. S. Barr, “The autoparametric vibration absorber,” J. Eng. Ind., 94, 119–225 (1982).Google Scholar
  9. 9.
    A. A. Martynyuk and N. V. Nikitina, “A note on bifurcations of motions in the Lorentz system,” Int. Appl. Mech., 39, No.2, 224–231 (2003).CrossRefGoogle Scholar
  10. 10.
    A. A. Martynyuk and V. I. Slyn’ko, “Choosing the parameters of a mechanical system with interval stability,” Int. Appl. Mech., 39, No.9, 1089–1092 (2003).CrossRefMathSciNetGoogle Scholar
  11. 11.
    S. Natsiavas, “Steady state oscillations and stability of non-linear dynamic vibration absorber.” J. Sound Vibr., 156(22), 227–245 (1992).CrossRefGoogle Scholar
  12. 12.
    S. W. Shaw and S. Wiggins, “Chaotic motions of a torsional vibration absorber,” Trans. ASME, J. Appl. Mech., 55, 952–958 (1988).Google Scholar
  13. 13.
    A. F. Vakakis, L. I. Manevitch, Yu. V. Mikhlin, V. N. Pilipchuk, and A. A. Zevin, Normal Modes and Localization in Nonlinear Systems, Wiley Interscience, New York (1996).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • K. V. Avramov
    • 1
  • Yu. V. Mikhlin
    • 1
  1. 1.National Technical University (Kharkov Polytechnic Institute)KharkovUkraine

Personalised recommendations