We investigate the dynamics of finite degree-of-freedom, planar mechanical systems with multiple sliding, unilateral frictional point contacts. A complete classification of systems with 2 sliding contacts is given. The contact-mode-based approach of rigid body mechanics is combined with linear stability analysis using a compliant contact model to determine the feasibility and the stability of every possible contact mode in each class. Special forms of non-stationary contact dynamics including “impact without collision” and “reverse chattering” are also investigated. Many types of solution inconsistency and indeterminacy are identified and new phenomena related to Painlevé’s non-existence and non-uniqueness paradoxes are discovered. Among other results, we show that the non-existence paradox is not fully resolvable by considering impulsive contact forces. These findings contribute to a growing body of evidence that rigid body mechanics cannot be developed into a complete and self-consistent theory in the presence of contacts and friction.
CITATION STYLE
Várkonyi, P. L. (2017). Dynamics of mechanical systems with two sliding contacts: new facets of Painlevé’s paradox. Archive of Applied Mechanics, 87(5), 785–799. https://doi.org/10.1007/s00419-016-1165-1
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