Abstract
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 essential 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.
Partially supported by DFG via project B01 in SFB 1114.
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Acknowledgements
The authors is grateful to Martin Heida and Elias Pipping for stimulating discussions. The research was partially supported by DFG via the project B01 Fault networks and scaling properties of deformation accumulation within the SFB 1114 Scaling Cascades in Complex Systems.
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Mielke, A. (2018). Three Examples Concerning the Interaction of Dry Friction and Oscillations. In: Rocca, E., Stefanelli, U., Truskinovsky, L., Visintin, A. (eds) Trends in Applications of Mathematics to Mechanics. Springer INdAM Series, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-319-75940-1_8
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