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Stick-slip vibrations are self-sustained oscillations induced by dry friction. They occur in engineering systems as well as in our everyday life, e.g. the sound of bowed instruments results from stick—slip vibrations of the strings. Two discrete and two continuous models of stick-slip systems have been investigated in this paper, which exhibit rich bifurcational and chaotic behaviour. Results from numerical simulations and experimental observations could be obtained. In the latter case, chaos has to be distinguished from noise in the measurements. This requires special analysis methods like the reconstruction of a pseudo-state space from a time series and the calculation of the so-called correlation integral.

The chattering of machine tools, the squealing noise generated by tram wheels in narrow curves and the noise of band saws are examples of physical processes in which elastic structures exhibit self-sustained stick-slip vibrations. The nonlinear contact forces are often due to dry friction. Periodic, multiperiodic, and chaotic motions can occur, depending on the parameters.Because the governing equations of motion are non-integrable, solutions can only be determined by numerical integration methods. The numerical investigations of continuous structures requires the modal approach to reduce the number of degrees of freedom.As an example, a beam system has been investigated numerically and experimentally in this paper. The nonlinear motion of a point of the continuous structure has been measured by a specially developed laser vibrometer.The friction characteristic has been measured directly and identified from a measured time series by means of a modal state observer. The correlation dimension, which represents a lower bound of the fractal dimension, has been calculated using the correlation integral method from a measured time series of the beam system.

Summary 343Dry friction is a main factor of self-sustained oscillations in dynamic systems. The mathematical modelling of dry friction forces result in strong nonlinear equations of motion. The bifurcation behaviour of a deterministic system has been investigated by the bifurcation theory. The stability of stationary solutions has been analyzed by the eigenvalues of the Jacobian. Period doublings and Hopf-bifurcations as well as turning points could be determined with the program package BIFPACK. Phase plane plots of periodic and chaotic motions have been shown for a better understanding of the bifurcation diagrams. Both, unstable branches and stable coexisting solutions have been calculated. Several jumping effects, which are typical for nonlinear systems, have been found.

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