Detachment Waves in Frictional Contact II: Analysis and Simulations of a Three-Mass System

This work continues the study of a mathematical model for the motion of a mass–spring–damper system with friction. There, a two-mass model was constructed, its solvability established, the steady states investigated, and numerical simulations presented. The main interest here is in the modeling, analysis of the steady states, and simulation of a three-mass system—in particular, in the propagation of detachment or slip waves, which happen when the system transits from a stick state to a slip motion. The introduction of friction changes the problem into systems of three differential set-valued inclusions, which are mathematically and computationally very challenging. The analysis of the steady states shows the regions of stick, where there is enough frictional resistance that prevents motion. The proposed numerical methods are implemented, and the simulations show some representative types of system behavior, especially the cases of detachment waves. Some of the numerical simulations specifically support the theoretical analysis of slip initiation, reachability, and energy balance.