Sliding bifurcations of a self-excited SD oscillator with nonlinear damping

This paper investigates the sliding bifurcations of a self-excited smooth and discontinuous (SD) oscillator with a nonlinear damper driven by moving belt friction. A generalized Filippov framework is applied to derive an explicit relationship between the coefficient of the nonlinear term and the maximum static friction coefficient. The conditions for the existence of various sliding bifurcations, including crossing-sliding, grazing-sliding, switching-sliding, and adding-sliding bifurcations, are established. The theoretical analysis is validated through numerical simulations, which confirm the presence of sliding bifurcations and highlight their impact on the system dynamics. To further examine the nonlinear system response, a numerical study via continuation methods is conducted. Bifurcation diagrams are generated to track the evolution of system behavior as key parameters vary. The results reveal complex dynamical transitions, including the onset of sliding bifurcations and their influence on the stability of periodic orbits. The findings demonstrate that nonlinear damping plays a crucial role in shaping the bifurcation structure and sliding behavior of the oscillator. This study provides a refined theoretical framework for analyzing sliding bifurcations in non-smooth dynamical systems and offers insights into the control and design of friction-driven oscillators with nonlinear damping.