Summary
The objective of the present work is to reexamine the dynamic phenomenon of sprag-slip instability. To that purpose, a model consisting of an elastic beam sliding over a rigid belt at constant speed is set up and investigated. It turns out that there are parameter combinations for which the system does not posess a static solution corresponding to a steady sliding state, neither stable nor unstable, a phenomenon first discovered by Painlevé considering sliding rigid bodies, sometimes referred to as the Painlevé paradox. The nonexistence of a steady sliding state is a sufficient criterion for the appearance of sprag-slip oscillations, since in the corresponding configurations the fundamental behavior of the system is intrinsically dynamic in nature.
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The authors would like to acknowledge multifold support from the acoustics research division FV/FLP of the Robert Bosch GmbH in Gerlingen, Stuttgart. Also the critical and helpful discussions on the topic with Dr. Nils Wagner, Institut A für Mechanik, Universität Stuttgart, are gratefully acknowledged. Special thanks are also due to the Referees of the AAM whose comments helped to add further substantial aspects to the paper.
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Hoffmann, N., Gaul, L. A sufficient criterion for the onset of sprag-slip oscillations. Archive of Applied Mechanics 73, 650–660 (2004). https://doi.org/10.1007/s00419-003-0315-4
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DOI: https://doi.org/10.1007/s00419-003-0315-4