On the dynamic response of a system with dry friction

The response of a single degree of freedom system with dry friction is considered. Den Hartog [1] gave an exact solution for the symmetric steady state motions of such a system in 1930. In this paper these results are extended to include a static coefficient of friction different from the dynamic one. More importantly, the asymptotic stability of the steady state motions and some transient behaviors are also determined. It is shown that for positive viscous damping the non-sticking steady state solutions of the same period as the forcing are nearly always asymptotically stable, but that for negative viscous damping, which may arise from aerodynamic forces [2], such motions can become unstable. By using bifurcation theory it is shown that new behaviors, such as aperiodic motions containing two distinct frequency components, can result from such dynamic instabilities. It is also shown that the symmetric motions with two stops per period can be unstable and that pairs of unsymmetric motions are born at the bifurcation points.