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.