Flow switchability of motions in a horizontal impact pair with dry friction

Abstract Using the flow switchability theory of the discontinuous dynamical systems, the present paper is to develop mechanical complexity in a periodic-excited horizontal impact pair with dry friction. The impact pair studied models the motions of a single bolted connection which is vibrated in the plane perpendicular to the bolt axis. According to motion character, the phase space can be partitioned into several domains and boundaries, in which a continuous dynamical system is defined in each domain, and it possesses dynamical properties different from its adjacent subsystem, the boundaries have different properties and can fall into two kinds – displacement boundaries and velocity boundaries. In this paper, using G–functions defined on separation boundaries to study flow switching on corresponding boundaries, the analytical switching conditions on each boundary are developed: the sufficient and necessary conditions of occurrence and disappearance of sliding-stick motion and side-stick motion are obtained, the sufficient and necessary conditions of grazing motion appearing on velocity boundaries are also obtained, and the analytical conditions of appearance for grazing motion on displacement boundaries are preliminarily discussed. Thus it can be seen that dynamical behaviors of the horizontal impact pair with or without dry friction are essentially different, in particular flow switchability on displacement boundaries depend on whether the conditions of passable flows on velocity boundaries are satisfied. The numerical simulations are given to demonstrate the analytical results of two stick motions and grazing motions in such pair. More details of the motions for the object reaching the intersection point of displacement boundary and velocity boundary need to be considered further in the future.

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