The onset of friction-induced vibration and spragging

The minimal dynamic models are used to investigate the influences of geometric coupling on frictionally-excited system. At a certain set of system parameters, spragging can occur where the steady-sliding is indeterminate. It is found that the sprag condition becomes the boundary of the regime for the non-existence of the equilibrium in the parametric space. Equilibrium instability induced by the negative friction-velocity slope and mode-coupling is determined for the regime in which the steady-sliding is defined. Its ensuing nonlinear response is shown to reach the stick-slip limit cycle.