The European Physical Journal Special Topics

, Volume 228, Issue 9, pp 1823–1837 | Cite as

Steady state performance of a nonlinear vibration absorber on vibration reduction of a harmonically forced oscillator

  • B. YuEmail author
  • A. C. J. Luo
Regular Article Topical issue
Part of the following topical collections:
  1. Periodic Motions and Chaos in Nonlinear Dynamical Systems


In this paper, the periodic steady-state responses of a nonlinear vibration absorber are investigated using the general harmonically balanced method. The periodic steady-state responses are presented via the frequency-amplitude curves. The bifurcation and stability are investigated through the eigenvalue analysis of a developed dynamical system of coefficients of the finite Fourier series. Numerical simulations of stable symmetric and asymmetric periodic steady-state responses are completed. The harmonic amplitude spectrums show harmonic effects on steady-state periodic motions, and the corresponding accuracy of approximate analytical solutions can be prescribed specifically.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E.I. Rivin, Precis. Eng. 17, 41 (1995)CrossRefGoogle Scholar
  2. 2.
    D.B. Debra, CIRP Ann. Manuf. Technol 41, 711 (1992)CrossRefGoogle Scholar
  3. 3.
    W.G. Flannelly. Dynamic anti-resonant vibration isolator, U.S. Patent No. 3,322,379. 1967Google Scholar
  4. 4.
    A.D. Rita, J.H. McGarvey, R. Jones, J. Am. Helicopter Soc. 23, 22 (1978)CrossRefGoogle Scholar
  5. 5.
    V.A. Ivovich, M.K. Savovish, Proc. Inst. Civil Eng. Struct. Buildings 146, 391 (2001)CrossRefGoogle Scholar
  6. 6.
    B. Ravindra, A.K. Mallik, J. Sound Vib. 170, 325 (1994)ADSCrossRefGoogle Scholar
  7. 7.
    D.L. Platus, Proc. SPIE 1619, 44 (1992)ADSCrossRefGoogle Scholar
  8. 8.
    W.G. Molyneux, Aircr. Eng. Aerosp. Technol. 30, 160 (1958)CrossRefGoogle Scholar
  9. 9.
    J.P. Den Hartog, Trans. ASME Adv. Pap. 9, 107 (1931)Google Scholar
  10. 10.
    J.E. Ruzicka, T.F. Derby, Influence of Damping in Vibration Isolation (The Shock and Vibration Information Center, Washington, DC, 1971)Google Scholar
  11. 11.
    L. Jiang, D. Stredulinsky, J. Szabo, M.W. Chernuka, Can. Acoust. Acousti. Can. 30, 70 (2002)Google Scholar
  12. 12.
    G. Warburton, Earthquake Eng. Struct. Dyn. 10, 381 (1982)CrossRefGoogle Scholar
  13. 13.
    T. Asani, O. Nishihara, A.M. Baz, ASME J. Vibr. Acoust. 124, 67 (2002)Google Scholar
  14. 14.
    A.C.J. Luo, Continuous Dynamical Systems (Higher Education Press/L&H Scientific Publishing, Beijing/ Glen Carbon, 2012)Google Scholar
  15. 15.
    A.C.J. Luo, J.Z. Huang, Int. J. Bifurc. Chaos 22, 29 (2012)CrossRefGoogle Scholar
  16. 16.
    A.C.J. Luo, B. Yu, J. Vib. Control 21, 907 (2013)Google Scholar
  17. 17.
    A.C.J. Luo, A.B. Laken, Int. J. Dyn. Control 1, 99 (2013)CrossRefGoogle Scholar
  18. 18.
    A.C.J. Luo, B. Yu, Int. J. Bifurc. Chaos 25, 40 (2015)Google Scholar
  19. 19.
    B. Yu, A.C.J. Luo, Int. J. Dyn. Control 5, 436 (2015)CrossRefGoogle Scholar
  20. 20.
    B. Yu, A.C.J. Luo, ASME Proceedings Dynamics, Vibration, and Control. Paper No. IMECE2017-71032, (2017)Google Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringUniversity of Wisconsin-PlattevillePlattevilleUSA
  2. 2.Department of Mechanical and Industrial EngineeringSouthern Illinois University EdwardsvilleEdwardsvilleUSA

Personalised recommendations