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

Nonlinear Dyn DOI 10.1007/s11071-017-3779-4 ORIGINAL PAPER

A. Papangelo, M. Ciavarella, N. Hoffmann

http://rdcu.be/wd3D

The dynamical behavior of a single-degree-of-freedom system that experiences friction-inducedvibrations is studied with particular interest on the pos-sibility of the so-called hard effect of a subcritical Hopfbifurcation, using a velocity weakening–strengtheningfriction law. The bifurcation diagram of the system isnumerically evaluated using as bifurcation parameterthe velocity of the belt. Analytical results are providedusing standard linear stability analysis and nonlinearstabilityanalysistolargeperturbations.Theformerper-mits to identify the lowest belt velocity(vlw)at whichthe full sliding solution is stable, the latter allows toestimate a priori the highest belt velocity at which largeamplitude stick–slip vibrations exist. Together the twoboundaries[vlw,vup]define the range where two equi-librium solutions coexist, i.e., a stable full sliding solu-tion and a stable stick–slip limit cycle. The model isused to fit recent experimental observations.