Irreversible passive energy transfer in coupled oscillators with essential nonlinearity

Gaetan Kerschen, Young Sup Lee, Alexander F. Vakakis, D. Michael Mcfarland, Lawrence A. Bergman

Research output: Contribution to journalArticlepeer-review


We study numerically and analytically the dynamics of passive energy transfer from a damped linear oscillator to an essentially nonlinear end attachment. This transfer is caused by either fundamental or subharmonic resonance capture, and in some cases is initiated by nonlinear beat phenomena. It is shown that, due to the essential nonlinearity, the end attachment is capable of passively absorbing broadband energy at both high and low frequencies, acting, in essence, as a passive broadband boundary controller. Complicated transitions in the damped dynamics can be interpreted based on the topological structure and bifurcations of the periodic solutions of the underlying undamped system. Moreover, complex resonance capture cascades are numerically encountered when we increase the number of degrees of freedom of the system. The ungrounded essentially nonlinear end attachment discussed in this work can find application in numerous practical settings, including vibration and shock isolation of structures, seismic isolation, flutter suppression, and packaging.

Original languageEnglish (US)
Pages (from-to)648-679
Number of pages32
JournalSIAM Journal on Applied Mathematics
Issue number2
StatePublished - 2006


  • Energy pumping
  • Essential nonlinearity
  • Nonlinear energy sinks
  • Passive energy transfer
  • Resonance capture

ASJC Scopus subject areas

  • Applied Mathematics


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