Post-doctoral research project, 2000-2001 at the TU München

Funding: Dutch Science Foundation STW (STW grant EWO.5531)

This research project has been concerned with the analysis of complex bifurcation phenomena occuring in mechanical systems with impact and friction. A number wooden toys has been chosen as example systems and have been studied in depth. Each of these systems shows a self-excited periodic motion under the influence of impact and friction.

These wooden toy systems are geometrically simple but show the same complex dynamical behaviour occuring in machines with play and friction. The advantage of the aforementioned toys is that they show a very rich dynamical behviour and that can very well be modelled using a rigid multibody approach with a few degrees of freedom (3 or 4 DOF's). It has been shown that a change in the order of two consecutive impacts leads to a non-classical bifurcation bifurcation not known from the standard bifurcation theory for smooth dynamical systems. Furthermore, if a contact closes, then the dimension of the system is temporarily reduced. This reduction in dimension can be used to set up a low-dimensional event map which captures the dynamics of the system in a discrete way. The non-smoothness of the systems therefore not only complicates the dynamic behaviour but also facilitates the analysis. A one-dimensional event map was constructed for the Woodpecker Toy. The non-classical bifurcations, typical for non-smooth systems with impact, can very well be studied using this event mapping technique. See also the webpage on the Nonlinear Dynamics of Wooden Toys.

Analysis of the Woodpecker Toy

Publications:

Leine, R.I., Van Campen, D.H and Glocker, Ch., "Nonlinear dynamics and modelling of various wooden toys with impact and friction", Journal of Vibration and Control, Vol. 9, pp. 25-78, 2003 PDF (2753kb)

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