## Detachment waves in frictional contact: analysis and simulations of a two-mass system

### Volume 127 / 2024

#### Abstract

This work continues the study of a mathematical model for motion with friction of a system of two mass-spring-dampers, started in Shillor and Kuttler(2023). It describes another step in our mathematical study of the way *detachment or slip waves* are generated and propagate, when the system transits from a stick state to slip motion. The introduction of friction sets the problems as a coupled system of differential set-valued inclusions, which are mathematically interesting, but rather complex. We present the theory, i.e., the model and its analysis, and study of the steady states. These states form two continua or one continuum, which is characteristic of systems with friction. Then, we describe an algorithm for the system and present numerical simulations of detachment waves in such a ‘simple’ system, which exemplify the theory and some of the possible system behaviors.