Analytical approximations for stick-slip vibration amplitudes

Jon Juel Thomsen, A. Fidlin

Research output: Contribution to journalJournal articleResearchpeer-review


The classical "mass-on-moving-belt" model for describing friction-induced vibrations is considered, with a friction law describing friction forces that first decreases and then increases smoothly with relative interface speed. Approximate analytical expressions are derived for the conditions, the amplitudes, and the base frequencies of friction-induced stick¿slip and pure-slip oscillations. For stick¿slip oscillations, this is accomplished by using perturbation analysis for the finite time interval of the stick phase, which is linked to the subsequent slip phase through conditions of continuity and periodicity. The results are illustrated and tested by time-series, phase plots and amplitude response diagrams, which compare very favorably with results obtained by numerical simulation of the equation of motion, as long as the difference in static and kinetic friction is not too large.
Original languageEnglish
JournalInternational Journal of Non-linear Mechanics
Issue number3
Pages (from-to)389-403
Publication statusPublished - 2003

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