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Targeted energy transfer in mechanical systems by means of non-smooth nonlinear energy sink

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Abstract

Targeted energy transfer (TET) in a compound nonlinear 2 degrees-of-freedom system during free and forced excitations is studied analytically and numerically. The nonlinearity of the system is represented intentionally by a non-smooth piece-wise linear function for the sake of practical investigations. Further stability analysis of the system is demonstrated and commented upon and the behavior of the system during relaxation and its strongly modulated response is studied and pinpointed.

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References

  1. Vakakis A.F.: Inducing passive nonlinear energy sinks in vibrating systems. ASME J. Vib. Acoust. 123, 324–332 (2001)

    Article  Google Scholar 

  2. Gendelman O.V., Manevitch L.I., Vakakis A.F., M’Closkey R.: Energy pumping in nonlinear mechanical oscillators I: dynamics of the underlying Hamiltonian systems. ASME J. Appl. Mech. 68, 34–41 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Vakakis A.F., Gendelman O.V.: Energy pumping in nonlinear mechanical oscillators II: resonance capture. ASME J. Appl. Mech. 68, 42–48 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gendelman O.V.: Bifurcations of nonlinear normal modes of linear oscillator with strongly nonlinear damped attachment. Nonlinear Dyn. 37, 115–128 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gendelman O.V., Lamarque C.-H.: Dynamics of linear oscillator coupled to strongly nonlinear attachment with multiple states of equilibrium. Chaos, Solitons Fractals 24, 501–509 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gendelman O.V., Gourdon E., Lamarque C.-H.: Quasiperiodic energy pumping in coupled oscillators under periodic forcing. J. Sound Vib. 294, 651–662 (2006)

    Article  Google Scholar 

  7. Manevitch L.I., Gourdon E., Lamarque C.-H.: Parameters optimization for energy pumping in strongly nonhomogeneous 2 DoF system. Chaos Solitons Fractals 31, 900–911 (2007)

    Article  Google Scholar 

  8. Manevitch L.I., Musienko A.I., Lamarque C.-H.: New analytical approach to energy pumping problem in strongly non homogeneous 2 DoF systems. Meccanica 42, 77–83 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. 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. Trans. ASME 2007(74), 1078–1086 (2007)

    Google Scholar 

  10. Vakakis, A.F., Gendelman, O.V., Bergman, L.A., McFarland, D.M., Kerschen, G., Lee, Y.S.: Nonlinear Trageted Energy Transfer in Mechanical and Structural Systems I, 375. Springer, Berlin (2009)

  11. Vakakis, A.F., Gendelman, O.V., Bergman, L.A., McFarland, D.M., Kerschen, G., Lee, Y.S.: Nonlinear Trageted Energy Transfer in Mechanical and Structural Systems II, 655. Springer, Berlin (2009)

  12. Starosvetsky Y., Gendelman O.V.: Vibration absorption in systems with nonlinear energy sink: nonlinear damping. J. Sound Vib. 324, 916–939 (2009)

    Article  Google Scholar 

  13. Starosvetsky Y., Gendelman O.V.: Interaction of nonlinear energy sink with a two degrees of freedom linear system: internal resonance. J. Sound Vib. 329, 1836–1852 (2010)

    Article  Google Scholar 

  14. Gendelman O.V., Sapsis T., Vakakis A.F., Bergman L.A.: Enhanced passive targeted energy transfer in strongly nonlinear mechanical oscillators. J. Sound Vib., Rapid Communication 330, 1–8 (2011)

    Article  Google Scholar 

  15. McFarland D.M., Bergman L., Vakakis A.F.: Experimental study of non-linear energy pumping occurring at a single fast frequency. Int. J. Non-Linear Mech. 40, 891–899 (2005)

    Article  MATH  Google Scholar 

  16. McFarland D.M., Kerschen G., Kowtko J.J., Lee Y.S., Bergman L.A., Vakakis A.F.: Experimental investigation of targeted energy transfers in strongly and nonlinearly coupled oscillators. J. Acoust. Soc. Am. 118, 791–799 (2005)

    Article  Google Scholar 

  17. Kerschen G., Kowtko J.J., McFarland D.M., Bergman L.A., Vakakis A.F.: Theoretical and experimental study of multimodal targeted energy transfer in a system of coupled oscillators. Nonlinear Dyn. 47, 285–309 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kerschen G., Kowtko J.J., McFarland D.M., Lee Y.S., Bergman L.A., Vakakis A.F.: Experimental demonstration of transient resonance capture in a system of two coupled oscillators with essential stiffness nonlinearity. J. Sound Vib. 299, 822–838 (2007)

    Article  Google Scholar 

  19. Gourdon E., Alexander N.A., Taylor C.A., Lamarque C.-H., Pernot S.: Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: theoretical and experimental results. J. Sound Vib. 300, 522–551 (2007)

    Article  Google Scholar 

  20. Gourdon E., Lamarque C.-H., Pernot S.: Contribution to efficiency of irreversible passive energy pumping with a strong nonlinear attachment. Nonlinear Dyn. 50, 793–808 (2007)

    Article  MATH  Google Scholar 

  21. Lee Y.S., Kerschen G., McFarland D.M., Hill W.J., Nichkawde C., Strganac T.W., Bergman L.A., Vakakis A.F.: Suppressing aeroelastic instability using broadband passive targeted energy transfers, part 2: experiments. AIAA J. 45, 2391–2400 (2007)

    Article  Google Scholar 

  22. Lee, Y.S., Vakakis, A.F., Bergman, L.A., McFarland, D.M., Kerschen, G., Nucera, F., Tsakirtzis, S., Panagopoulos, P.N.: Passive non-linear targeted energy transfer and its applications to vibration absorption: a review. In: Proceedings of the institution of mechanical engineers, Part K. J. Multi-body Dyn. 222, 77–134 (2008)

  23. Lee Y.S., Vakakis A.F., McFarland D.M., Bergman L.A.: Non-linear system identification of the dynamics of aeroelastic instability suppression based on targeted energy transfers. Aeronaut. J. 114, 61–82 (2010)

    Google Scholar 

  24. Nucera F., Vakakis A.F., McFarland D.M., Bergman L.A., Kerschen G.: Targeted energy transfers in vibro-impact oscillators for seismic mitigation. Nonlinear Dyn. 50, 651–677 (2007)

    Article  MATH  Google Scholar 

  25. Lee Y.S., Nucera F., Vakakis A.F., McFarland D.M., Bergman L.A.: Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments. Phys. D 238, 1868–1896 (2009)

    Article  MATH  Google Scholar 

  26. Gendelman O.V.: Targeted energy transfer in systems with non-polynomial nonlinearity. J. Sound Vib. 315, 732–745 (2008)

    Article  Google Scholar 

  27. Manevitch L.I.: The description of localized normal modes in a chain of nonlinear coupled oscillators using complex variables. Nonlinear Dyn. 25, 95–109 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  28. Nayfeh A.H., Mook D.T.: Nonlinear Oscillations, 720. Wiley, New York (1979)

    Google Scholar 

  29. Gendelman O.V., Starosvetsky Y.: Quasi-periodic response regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing. J. Appl. Mech. 74, 325–331 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  30. Starosvetsky Y., Gendelman O.V.: Strongly modulated response in forced 2DOF oscillatory system with essential mass and potential asymmetry. Phys. D 237, 1719–1733 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Université de Lyon, École Nationale des Travaux Publics de l’État, DGCB, FRE CNRS 3237, 3 rue Maurice Audin, 69518, Vaulx-en-Velin Cedex, France

    Claude-Henri Lamarque, Alireza Ture Savadkoohi & Emilie Etcheverria

  2. Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, 32000, Technion City, Haifa, Israel

    Oleg V. Gendelman

Authors
  1. Claude-Henri Lamarque
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  2. Oleg V. Gendelman
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  3. Alireza Ture Savadkoohi
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  4. Emilie Etcheverria
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Correspondence to Alireza Ture Savadkoohi.

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Lamarque, CH., Gendelman, O.V., Ture Savadkoohi, A. et al. Targeted energy transfer in mechanical systems by means of non-smooth nonlinear energy sink. Acta Mech 221, 175–200 (2011). https://doi.org/10.1007/s00707-011-0492-0

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  • DOI: https://doi.org/10.1007/s00707-011-0492-0

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