Bifurcations in Dynamic Systems with Dry Friction
Dry 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.
Unable to display preview. Download preview PDF.
- Hagedorn, P.: Nichtlineare Schwingungen. Wiesbaden: Akademische Verlagsgesellschaft, 1984Google Scholar
- Leven, R.W.; Koch, B.-P.; Pompe, B.: Chaos in dissipativen Systemem. Berlin: Akademie-Verlag, 1982.Google Scholar
- Miyamoto, M.: Effect of Dry Friction in Link Suspension on Forced Vibration of Two-Axle Car. In: Quarterly Reports Vol. 14 No. 2 (1973), S. 99–103Google Scholar
- Popp, K.; Stelter, P.: Nonlinear Oscillations of Structures Induced by Dry Friction. In: Proceedings of IUTAM Symposium on nonlinear dynamics in engineering systems. Stuttgart, (1989)Google Scholar
- Seydel, R.: BIFPACK—A Program Package for Continuation, Bifurcation and Stability Analysis. Mathematische Institute der Julius-Maximilians-Universitaet Wuerzburg, Version 2. 3 (1988)Google Scholar