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