Vibro-Impact NES: A Correlation Between Experimental Investigation and Analytical Description

  • Giuseppe PennisiEmail author
  • Cyrille Stéphan
  • Guilhem Michon
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


In this work the dynamics of a Vibro-Impact Nonlinear Energy Sink (VI-NES) is experimentally investigated via a harmonically forced single-degree-of- freedom linear oscillator (LO) to which a VI-NES is attached. Depending on external force amplitude and frequency, either a Strongly Modulated Response (SMR) or a constant amplitude response (CAR) is observed. In both cases an irreversible transfer of energy occurs from the LO towards the VI-NES: process known as passive Targeted Energy Transfer(TET). Furthermore, the problem is analytically studied by using the multiple scales method. For the fast and the slow time scales the Slow Invariant Manifold (SIM) is obtained. The 0-order SIM shows the existence of a stable and an unstable branch of solution, and of an energy threshold (a saddle-node bifurcation) for the solutions to appear. Subsequently the 1-order SIM is calculated to find the fixed points of the problem. When a stable fixed point exists, the system is naturally drawn to it and a CAR is reached. Otherwise a SMR state is established and no stable point is attained. Finally a good agreement between experimental and analytical results is shown.


Nonlinear dynamics Vibro-Impact Vibrations absorber Experimental Analytical 


  1. 1.
    Gendelman, O.V.: Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators. Nonlinear Dyn. 25, 237–253 (2001)CrossRefzbMATHGoogle Scholar
  2. 2.
    Vakakis, A.F., Gendelman, O.V.: Energy pumping in nonlinear mechanical oscillators: part II resonance capture. J. Appl. Mech. Trans. ASME 68, 42–48 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Gendelman, O.V., Vakakis, A.F., Manevitch, L.I., McCloskey, R.: Energy pumping in nonlinear mechanical oscillators I: dynamics of the underlying Hamiltonian system. J. Appl. Mech. Trans. ASME 68, 34–41 (2001)CrossRefzbMATHGoogle Scholar
  4. 4.
    Manevitch, L.I., Gourdon, E., Lamarque, C.H.: Towards the design of an optimal energetic sink in a strongly inhomogeneous two-degree-of-freedom system. ASME J. Appl. Mech. 74, 1078–1086 (2007)CrossRefGoogle Scholar
  5. 5.
    Kerschen, G., Lee, Y.S., Vakakis, A.F., McFarland, D.M., Bergman, L.A.: Irreversible passive energy transfer in coupled oscillators with essential nonlinearity. SIAM J. Appl. Math. 66(2), 648–679 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Starosvetsky, Y., Gendelman, O.: Strongly modulated response in forced 2D of oscillatory system with essential mass and potential asymmetry. Physica D 237(13), 1719–1733 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gourc, E., Michon, G., Seguy, S., Berlioz, A.: Experimental investigation and design optimization of targeted energy transfer under periodic forcing. ASME J. Vib. Acoust. 136(2), 021021 (2013)CrossRefGoogle Scholar
  8. 8.
    Gendelman, O.: Analytic treatment of a system with a vibro-impact nonlinear energy sink. J. Sound Vib. 331, 4599–4608 (2012)CrossRefGoogle Scholar
  9. 9.
    Gendelman, O.V., Alloni, A.: Dynamics of forced system with vibro-impact energy sink. J. Sound Vib. (2015).
  10. 10.
    Gourc, E., Michon, G., Seguy, S., Berlioz, A.: Theoretical and experimental study of an harmonically forced vibro-impact nonlinear energy sink. J. Vib. Acoust. (2014). VIB-14-1008. doi:10.1115/1.4029285Google Scholar

Copyright information

© The Society of Experimental Mechanics, Inc. 2016

Authors and Affiliations

  • Giuseppe Pennisi
    • 1
    Email author
  • Cyrille Stéphan
    • 2
  • Guilhem Michon
    • 3
  1. 1.ONERA, The French Aerospace LabUniversité de ToulouseChâtillonFrance
  2. 2.ONERA, The French Aerospace LabChâtillonFrance
  3. 3.Université de Toulouse, ICAToulouseFrance

Personalised recommendations