Effect of normal load variation on the frictional behavior of a simple Coulomb frictional oscillator

Various authors have studied the frictional contact problem for a simple concentrated mass under periodic forcing terms. In this paper, we give some additional closed form results for this problem for both the quasi-static limit and the full dynamic regime. We find in particular the regime where normal load is high enough to obtain a bounded displacement at all frequencies, which is of particular interest for “optimal” damping: in this case, the dynamic solution involves 2 stops of finite time. Contrary to the quasi-static prediction, the effect of normal load variation can decrease the peak displacement amplitude for in-phase loading up to the 80 percent. Moreover, similar to the quasi-static prediction, it can lead to a very large increase (up to more than 200 percent) for quadrature loading. Similar pattern is found for the frictional dissipation per cycle. For in-phase loading, therefore, the vibratory motion is damped more effectively, with additional beneficial effects on joint lifetime.