Friction induced stick-slip chaos of a class of non-smooth oscillator

Nonlinear systems affected by non-smooth factors are widely used in mathematical modeling and the description of dynamic behaviors, where the selection of system parameters plays a crucial role in solving practical problems. Whereas the theoretical analysis of the effects of system parameters on global bifurcations and chaotic motions has been thoroughly established in smooth systems, the parametric influence on chaotic thresholds in non-smooth systems remains unresolved. In this paper, a class of single-degree-of-freedom nonlinear dry friction systems with nonlinear damping, subjected to periodic excitation, is considered. Through in-depth analysis of the Melnikov function, it is discovered that the ratio of linear to nonlinear damping alters the morphology of the chaos threshold in non-smooth systems. Under specific conditions, this ratio takes 12/35 as the critical value that transforms the dominant factor of the system's chaos threshold. Simultaneously, analytical chaos thresholds corresponding to three distinct damping ratios are derived. Based on these thresholds, further demonstrate the bell-shaped variation of the threshold with external excitation frequency and its monotonic dependence on conveyor belt speed and friction force. Finally, combining the theoretical analysis with numerical simulations, the effect of these parameter sets on the homoclinic orbits and chaos thresholds are verified. The research demonstrates that the dynamic behavior of the system is highly sensitive to parameter variations, with both theoretical and numerical results being consistent. This provides strong theoretical support for further optimizing the dynamic performance of nonlinear conveyor belt systems and improving their stability and reliability.