Post-doctoral research project, 2001

Funding: Dutch Science Foundation STW (STW grant EWO.5647)

This project is concerned with the analysis of vibratory behaviour induced by a frictional catastrophe, e.g. the hopping motion of a finger which is pushed over a rough table. The periodic motion and bifurcations of the Frictional Impact Oscillator is studied, which consists of an object with normal and tangential degrees of freedom that comes in contact with a rigid surface. The Frictional Impact Oscillator contains the basic mechanism for a hopping phenomenon observed in many practical applications. It is shown that the hopping or bouncing motion in this type of systems is closely related to the Painlevé paradox. A dynamical system exhibiting the Painlevé paradox has nonuniqueness and nonexistence of solutions in certain sliding modes. Furthermore, it is demonstrated that this type of systems can exhibit the Painlevé paradox for physically realistic values of the friction coefficient.

The frictional impact oscillator with time-history

Publications:

Leine, R.I., Brogliato, B., Nijmeijer, H., "Periodic motion and bifurcations induced by the Painlevé paradox", European Journal of Mechanics A/Solids, Vol 21, No 5, pp. 869-896, 2002. PDF(389kb)

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09/12/11 | Remco Leine | ZfM | ETH