The frequency response of dynamic friction: Enhanced rate-and-state models

Alessandro Cabboi, Thibaut A F Putelat, Jim Woodhouse

Research output: Contribution to journalArticle (Academic Journal)peer-review

22 Citations (Scopus)
263 Downloads (Pure)


The prediction and control of friction-induced vibration requires a sufficiently accurate constitutive law for dynamic friction at the sliding interface: for linearised stability analysis, this requirement takes the form of a frictional frequency response function. Systematic measurements of this frictional frequency response function are presented for small samples of nylon and polycarbonate sliding against a glass disc. Previous efforts to explain such measurements from a theoretical model have failed, but an enhanced rate-and-state model is presented which is shown to match the measurements remarkably well. The tested parameter space covers a range of normal forces (10–50 N), of sliding speeds (1–10 mm/s) and frequencies (100–2000 Hz). The key new ingredient in the model is the inclusion of contact stiffness to take into account elastic deformations near the interface. A systematic methodology is presented to discriminate among possible variants of the model, and then to identify the model parameter values.
Original languageEnglish
Pages (from-to)210-236
Number of pages27
JournalJournal of the Mechanics and Physics of Solids
Early online date1 Apr 2016
Publication statusPublished - Jul 2016


  • vibration
  • dynamic friction
  • mechanical testing
  • rate-and-state
  • contact stiffness


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