Analysis of discontinuous dynamical behaviors for a 3-DOF friction collision system with dynamic vibration absorber

In this work, the discontinuous dynamic behavior of a 3-DOF (three-degree-of-freedom) friction collision system with dynamic vibration absorber is studied by the flow transformation theory. This paper aims to explore the conversion of movement in the friction collision system with discontinuous and non-smooth properties. The global dynamics of the 3-DOF system are reflected by separately studying the movement of each target. The different motion states and equations are defined by the force of each target and the mode of model connection. The flow barriers at the boundary/edge are defined by the characteristics of the friction model. The domains are divided in the two-dimensional phase space of each object, and the continuous vector field and G-function are defined in each domain. Based on this, the motion switching criteria at the separation boundary/edge are researched. Finally, some classical motion states and periodic phenomena are drawn by MATLAB software to simulate the global movement of the system. The study of the 3-DOF model enriches the theoretical basis for the mechanical devices with dynamic vibration absorbers.