Investigating the bi-stable behavior of a lumped system with frictional contact

In non-conservative systems with frictional contact interfaces, the complex eigenvalue analysis is widely used to detect the instabilities of the system and it is generally performed on a linearized model around the equilibrium position. The change of contact status, due to the apparent negative damping, modifies the system dynamics and in certain condition it can induce instabilities. For instance, an equilibrium position that is stable in uniform sliding conditions can become a limit cycle when a portion of the contact interface passes from sliding to sticking condition, due to the action of an external perturbation force. In this paper this bi-stable behavior, that is typical of mechanical system with subcritical Hopf bifurcations, is investigated by a lumped parameter model with frictional contact. The effect of the friction on the system eigenvalues is analyzed not only for the uniform sliding condition but also for the other possible contact states, finding the ranges of the friction coefficient value that could lead to a bi-stable behavior.