Near-elastic vibro-impact analysis by discontinuous transformations and averaging

Jon Juel Thomsen, Alexander Fidlin

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We show how near-elastic vibro-impact problems, linear or nonlinear in-between impacts, can be conveniently analyzed by a discontinuity-reducing transformation of variables combined with an extended averaging procedure. A general technique for this is presented, and illustrated by calculating transient or stationary motions for different harmonic oscillators with stops or clearances, and self-excited friction oscillators with stops or clearances First- and second-order analytical predictions are derived, and shown to agree to estimated accuracy with results of numerical simulation.
Original languageEnglish
JournalJournal of Sound and Vibration
Issue number1-2
Pages (from-to)386-407
Publication statusPublished - 2008


  • non-linear
  • vibrations
  • vibro-impact


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