Bursting oscillations in dry friction system under external excitation

In this paper, a system containing switching manifolds is constructed based on a non-linear conveyor belt model by introducing a periodic external excitation term. When the frequency of the external excitation is much smaller than the intrinsic frequency of the system, a series of bursting phenomena can be observed. Using the Filippov convex method, bifurcation mechanisms on the non-smooth boundary are discussed. Particularly, the explicit expression of the sliding region is obtained. Based on that, different bursting dynamics, especially the switching patterns dominated by sliding phenomena, are revealed by considering two cases of stiffness and excitation amplitude. It is shown that there exist different types of equilibrium points, leading to multiple modes of bifurcation, as stiffness changes. However, there always exist a pair of subcritical Hopf bifurcation points, which lie on the unstable equilibrium curve. Varying the excitation amplitude, different types of bursting oscillation modes may occur. In addition, both the transition of the type of equilibrium and the intrinsic structure of the system have effects on the local structure of the trajectory.