Attractivity of equilibrium sets of systems with dry friction

摘要

The dynamics of mechanical systems with dry friction elements, modelled by set-valued force laws, can be described by differential inclusions. An equilibrium set of such a differential inclusion corresponds to a stationary mode for which the friction elements are sticking. The attractivity properties of the equilibrium set are of major importance for the overall dynamic behaviour of this type of systems. Conditions for the attractivity of the equilibrium set of MDOF mechanical systems with multiple friction elements are presented. These results are obtained by application of a generalisation of LaSalle's principle for differential inclusions of Filippov-type. Besides passive systems, also systems with negative viscous damping are considered. For such systems, only local attractivity of the equilibrium set can be assured under certain conditions. Moreover, an estimate for the region of attraction is given for these cases. The effectiveness of the results is illustrated by means of both 1DOF and MDOF examples.