Weierstraß-Institut für Angewandte Analysis und Stochastik Three examples concerning the interaction of dry friction and oscillations Three examples concerning the interaction of dry friction and oscillations

Alexander Mielke, Alexander Mielke
2010 Mathematics Subject Classification. 34C55   unpublished
We discuss recent work concerning the interaction of dry friction, which is a rate independent effect, and temporal oscillations. First, we consider the temporal averaging of highly oscillatory friction coefficients. Here the effective dry friction is obtained as an infimal convolution. Second, we show that simple models with state-dependent friction may induce a Hopf bifurcation, where constant shear rates give rise to periodic behavior where sticking phases alternate with sliding motion. The
more » ... ssential feature here is the dependence of the friction coefficient on the internal state, which has an internal relaxation time. Finally, we present a simple model for rocking toy animal where walking is made possible by a periodic motion of the body that unloads the legs to be moved.
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