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On energy transfer between vibrating systems under linear and nonlinear interactions

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Abstract

The present study deals with energy transfer in a dissipative mechanical system. Numerical results are given by considering two different potentials and periodical excitation. Specifically, we show energy transfer from linear oscillator to another one, depending on initial conditions. Also, energy transfer from linear to nonlinear (energy pumping), as well as from nonlinear to linear, oscillator is analyzed, under linear and nonlinear interactions.

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References

  1. Gourdon, E., Lamarque, C.H.: Energy pumping with various nonlinear structures: Numerical evidences. Nonlinear Dyn. 40, 281–307 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Gourdon, E., Lamarque, C.H.: Energy pumping for a larger span of energy. J. Sound Vib. 285, 711–720 (2005)

    Article  Google Scholar 

  3. Gendelman, O., Manevitch, L.I., Vakakis, A.F., Closkey, R.M.: Energy pumping in nonlinear mechanical oscillators: Part I—Dynamics of the underlying Hamiltonian systems. J. Appl. Mech. 68, 34–41 (2001)

    Article  MATH  Google Scholar 

  4. Vakakis, A.F., Gendelman, O.: Energy pumping in nonlinear mechanical oscillators: Part II-Resonance capture. J. Appl. Mech. 68, 42–48 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gourdon, E., Lamarque, C.H., Pernot, S.: Contribution to efficiency of irreversible passive energy pumping with a strong nonlinear attachment. Nonlinear Dyn. 50(4), 793–808 (2007)

    Article  Google Scholar 

  6. 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 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. 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  Google Scholar 

  8. Felix, J.L.P., Balthazar, J.M., Dantas, M.J.H.: On energy pumping, synchronization and beat phenomenon in a non-ideal structure coupled to an essentially nonlinear oscillator. Nonlinear Dyn. (2008) doi: 10.1007/s11071-008-9374-y

    Google Scholar 

  9. Tsakirtzisa, S., Kerschenb, G., Panagopoulosa, P.N., Vakakis, A.F.: Multi-frequency nonlinear energy transfer from linear oscillators to MDOF essentially nonlinear attachments. J. Sound Vib. 285, 483–490 (2005)

    Article  Google Scholar 

  10. Gendelman, O.: Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators. Nonlinear Dyn. 25, 237–253 (2001)

    Article  MATH  Google Scholar 

  11. Vakakis, A.F.: Inducing passive nonlinear energy sinks in linear vibrating systems. J. Vib. Acoust. 123(3), 324–332 (2001)

    Article  Google Scholar 

  12. Vakakis, A.F.: Designing a linear structure with a local nonlinear attachment for enhanced energy pumping. Meccanica 38, 677–686 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  13. Vakakis, A.F., Manevitch, L.I., Gendelman, O., Bergman, L.: Dynamics of linear discrete systems connected to local essentially nonlinear attachments. J. Sound Vib. 264, 559–577 (2003)

    Article  Google Scholar 

  14. Jiang, X., McFarland, D.M., Bergman, L.A., Vakakis, A.F.: Steady state passive nonlinear energy pumping in coupled oscillators: theoretical and experimental results. Nonlinear Dyn. 33, 87–102 (2003)

    Article  MATH  Google Scholar 

  15. Musienko, A.I., Lamarque, C.H., Manevitch, L.I.: Design of mechanical energy pumping devices. J. Vib. Control 12, 355–371 (2006)

    Article  Google Scholar 

  16. Dantas, M.J., Balthazar, J.M.: On energy transfer between linear and non-linear oscillators. J. Sound Vib. 315(4–5), 1047–1070 (2008)

    Article  Google Scholar 

  17. Dantas, M.J., Balthazar, J.M.: Energy transfer between linear oscillators under non-linear interactions. In: VII Encontro Regional de Matemática Aplicada e Computacional, ERMAC, Uberlândia (2007)

  18. Dantas, M.J., Balthazar, J.M.: On theoretical results on energy transfer on linear and nonlinear mechanical oscillators. In: EUROMECH Colloquium 483, Geometrically Non-linear Vibrations of Structures, Porto, Portugal (2007)

  19. Rosenberg, R.M.: The normal modes of nonlinear n-degree-of-freedom systems. J. Appl. Mech. 29, 7–14 (1962)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Instituto de Geociências e Ciências Exatas, Departamento de Estatística, Matemática Aplicada e Computação, UNESP, 13500-230, Rio Claro, SP, Brazil

    S. N. J. Costa & J. M. Balthazar

  2. Departamento de Mecânica Espacial e Controle, INPE, São José dos Campos, SP, Brazil

    C. H. G. Hassmann

  3. Faculdade de Matemática, UFU, 38400-902, Uberlândia, MG, Brazil

    M. J. H. Dantas

Authors
  1. S. N. J. Costa
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  2. C. H. G. Hassmann
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  3. J. M. Balthazar
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  4. M. J. H. Dantas
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Correspondence to S. N. J. Costa.

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Costa, S.N.J., Hassmann, C.H.G., Balthazar, J.M. et al. On energy transfer between vibrating systems under linear and nonlinear interactions. Nonlinear Dyn 57, 57–67 (2009). https://doi.org/10.1007/s11071-008-9419-2

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  • DOI: https://doi.org/10.1007/s11071-008-9419-2

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