Grazing–sliding bifurcation in a dry-friction oscillator on a moving belt under periodic excitation

In this paper, we consider the grazing–sliding bifurcations in a dry-friction oscillator on a moving belt under periodic excitation. The system is a nonlinear piecewise smooth system defined in two zones whose analytical expressions of the solutions are not available. Thus, we obtain conditions of the existence of grazing–sliding orbits numerically by the shooting method. Then, we compute the lower and higher order approximations of the stroboscopic Poincaré map, respectively, near the grazing–sliding bifurcation point by the method of local zero-time discontinuity mapping. The results of computing the bifurcation diagrams obtained by the lower and higher order maps, respectively, are compared with those from direct simulations of the original system. We find that there are big differences between the lower order map and the original system, while the higher order map can effectively reduce such disagreements. By using the higher order map and numerical simulations, we find that the system undergoes very complicated dynamical behaviors near the grazing–sliding bifurcation point, such as period-adding cascades and chaos.