Nonlinear dynamics for a class of 2-DOF systems with viscoelastic limit devices on a curved track

This paper presents the nonlinear dynamics of a complex 2-DOF (two degree-of-freedom) system including nonlinear stiffness and damping elements, friction as well as impact, and the purpose of study is to give an original and deep investigation on the discontinuous dynamical behaviors for such a 2-DOF system through strict mathematical consideration. Firstly, the physical model of the system consisting of a ball and an object with curved track and viscoelastic limit devices is established by Coulomb friction and non-linear spring-damping model. And the eight motion states associated with free, sliding or stick motions are defined for the oscillator. Secondly, based on the non-smoothness/discontinuity resulted from impact/friction, the phase space is divided into different domains and boundaries in absolute and relative coordinates, respectively. Thirdly, some necessary and sufficient conditions for oscillator's motion switching at separation boundaries are given by G-functions of the flow switchability theory in discontinuous dynamical systems. Finally, in order to better understand the switching criteria and the complexity of oscillator's motion, some illustrative examples for several typical motions in system are studied by numerical simulation. The nonlinear spring-damping model is widely used as a shock absorber in machinery, aerospace, construction and other fields, which can accurately reflect the energy loss during impact process.