Stability of Steady Frictional Slipping

Assistant Professor, Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, N.Y. 14850 The shear resistance of slipping surfaces at fixed normal stress is given by r = r( v,state). Here V = slip velocity, dependence on «state" is equivalent to functional dependence with fading memory on prior V(t), and ar( v,state) /iJV>O. We establish linear stability conditions for steadY'slipstates (V(t), r(t) constant). For single degree-of-freedom elastic or viscoelastic dynamical systems, instability occurs, if at all, by a flutter mode when the spring stiffness (or appropriate viscoelastic generalization) .reduces to a critical value. Similar conclusions are reached for slipping continua with spatially periodic perturbations along their interface, and in this case the existence of propagating frictional creep waves is established at critical conditions. Increases in inertia of the slipping systems are found to be destabilizing, in that they increase the critical stiffness level requiredfor stability.