Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening-strengthening friction law: analytical results and comparison with experiments

The dynamical behavior of a single-degree-of-freedom system that experiences friction-induced vibrations is studied with particular interest on the possibility of the so-called hard effect of a subcritical Hopf bifurcation, using a velocity weakening-strengthening friction law. The bifurcation diagram of the system is numerically evaluated using as bifurcation parameter the velocity of the belt. Analytical results are provided using standard linear stability analysis and nonlinear stability analysis to large perturbations. The former permits to identify the lowest belt velocity (vlw) at which the full sliding solution is stable, the latter allows to estimate a priori the highest belt velocity at which large amplitude stick-slip vibrations exist. Together the two boundaries [ vlw, vup] define the range where two equilibrium solutions coexist, i.e., a stable full sliding solution and a stable stick-slip limit cycle. The model is used to fit recent experimental observations.