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
Gourdon, E., Lamarque, C.H.: Energy pumping with various nonlinear structures: Numerical evidences. Nonlinear Dyn. 40, 281–307 (2005)
Gourdon, E., Lamarque, C.H.: Energy pumping for a larger span of energy. J. Sound Vib. 285, 711–720 (2005)
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)
Vakakis, A.F., Gendelman, O.: Energy pumping in nonlinear mechanical oscillators: Part II-Resonance capture. J. Appl. Mech. 68, 42–48 (2001)
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)
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)
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)
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
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)
Gendelman, O.: Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators. Nonlinear Dyn. 25, 237–253 (2001)
Vakakis, A.F.: Inducing passive nonlinear energy sinks in linear vibrating systems. J. Vib. Acoust. 123(3), 324–332 (2001)
Vakakis, A.F.: Designing a linear structure with a local nonlinear attachment for enhanced energy pumping. Meccanica 38, 677–686 (2003)
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)
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)
Musienko, A.I., Lamarque, C.H., Manevitch, L.I.: Design of mechanical energy pumping devices. J. Vib. Control 12, 355–371 (2006)
Dantas, M.J., Balthazar, J.M.: On energy transfer between linear and non-linear oscillators. J. Sound Vib. 315(4–5), 1047–1070 (2008)
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)
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)
Rosenberg, R.M.: The normal modes of nonlinear n-degree-of-freedom systems. J. Appl. Mech. 29, 7–14 (1962)
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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