Frequency-energy plots of steady-state solutions for forced and damped systems, and vibration isolation by nonlinear mode localization

Mehmet Kurt, Melih Eriten, D. Michael McFarland, Lawrence A. Bergman, Alexander F. Vakakis

Research output: Contribution to journalArticlepeer-review


We study the structure of the periodic steady-state solutions of forced and damped strongly nonlinear coupled oscillators in the frequency-energy domain by constructing forced and damped frequency - energy plots (FEPs). Specifically, we analyze the steady periodic responses of a two degree-of-freedom system consisting of a grounded forced linear damped oscillator weakly coupled to a strongly nonlinear attachment under condition of 1:1 resonance. By performing complexification/averaging analysis we develop analytical approximations for strongly nonlinear steady-state responses. As an application, we examine vibration isolation of a harmonically forced linear oscillator by transferring and confining the steady-state vibration energy to the weakly coupled strongly nonlinear attachment, thereby drastically reducing its steady-state response. By comparing the nonlinear steady-state response of the linear oscillator to its corresponding frequency response function in the absence of a nonlinear attachment we demonstrate the efficacy of drastic vibration reduction through steady-state nonlinear targeted energy transfer. Hence, our study has practical implications for the effective passive vibration isolation of forced oscillators.

Original languageEnglish (US)
Pages (from-to)2905-2917
Number of pages13
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number8
StatePublished - Aug 2014


  • Frequency-energy plots
  • Nonlinear steady-state solutions

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics


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