Non-Linear Dynamics of Simple Elastic Systems Undergoing Friction-Ruled Stick–Slip Motions

The stick–slip phenomenon is a jerking motion that can occur while two objects slide over each other with friction. There are several situations in which this phenomenon can be observed: between the slabs of the friction dampers used to mitigate vibrations in buildings, as well as between the components of the base isolation systems used for seismic protection. The systems of this kind are usually designed to work in a smooth and flawless manner, but under particular conditions undesired jerking motions may develop, yielding complex dynamic behavior even when only a few degrees of freedom are involved. A simplified approach to the problems of this kind leads to the mechanical model of a rigid block connected elastically to a rigid support and at the same time with friction to a second rigid support, both the supports having a prescribed motion. Despite the apparent simplicity of this model, it is very useful for studying important features of the non-linear dynamics of many physical systems. In this work, after a suitable formulation of the problem, the equations of motion are solved analytically in the sticking and sliding phases, and the influence of the main parameters of the system on its dynamics and limit cycles is investigated and discussed.