A numerical study of the dynamics of three-mass system on frictional tracks

Abstract

The study of dynamical systems subjected to friction force is of both fundamental and practical importance. In this work, the numerical investigation of the dynamics of a three-mass system where the middle mass slides on a moving track and the two other masses slide on stationary tracks is presented. Friction between the tracks and masses is considered. It is found that the all-stick state, where all masses stick to the tracks, plays a critical role in the qualitative behaviour of the unforced dynamics where period-adding and subcritical graze-sliding bifurcation are observed. The forced vibration due to a harmonic excitation is quasiperiodic in nature. Chaos emerges from large forcing amplitude via a likely Ruelle–Takens route and an exotic route evolved directly from a periodic orbit.