Effect of stochasticity on targeted energy transfer from a linear medium to a strongly nonlinear attachment

Themistoklis P. Sapsis, Alexander F Vakakis, Lawrence Bergman

Research output: Contribution to journalArticle


In this work the problem of targeted energy transfer (TET) from a linear medium to a nonlinear attachment is studied in the presence of stochasticity. Using a Green's function formulation, complexification-averaging technique and diffusion approximation we derive a complex, nonlinear, Ito stochastic differential equation that governs the slow dynamics of the system. Through the numerical solution of the corresponding FokkerPlanckKolmogorov (FPK) equation we study the optimal regime of TET and its robustness to stochasticity for the case of nonlinear interactions of the nonlinear attachment with a single mode of the linear system. The probabilistic analysis reveals that in the presence of stochasticity the optimal TET regime, predicted in the deterministic theory, is not only preserved but also is enhanced due to the interaction of nonlinearity and stochasticity.

Original languageEnglish (US)
Pages (from-to)119-133
Number of pages15
JournalProbabilistic Engineering Mechanics
Issue number2
StatePublished - Apr 1 2011



  • Diffusion approximation
  • Energy harvesting
  • FokkerPlanckKolmogorov equation
  • Random nonlinear vibrations
  • Stochastic targeted energy transfer

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Civil and Structural Engineering
  • Nuclear Energy and Engineering
  • Aerospace Engineering
  • Condensed Matter Physics
  • Ocean Engineering
  • Mechanical Engineering

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