Threshold of Multiple Stick-Slip Chaos for an Archetypal Self-Excited SD Oscillator Driven by Moving Belt Friction

Abstract

In this paper, we investigate the multiple stick-slip chaotic motion of an archetypal self-excited smooth and discontinuous (SD) oscillator driven by moving belt friction, which is constructed with the SD oscillator and the classical moving belt. The friction force between the mass and the belt is modeled as a Coulomb friction for this system. The energy introduction or dissipation during the slip and stick modes in the system is analyzed. The analytical expressions of homoclinic orbits of the unperturbed SD oscillator are derived by using a special coordinate transformation without any pronominal truncation to retain the natural characteristics, which allows us to utilize the Melnikov’s method to obtain the chaotic thresholds of the self-excited SD oscillator in the presence of the damping and external excitation. Numerical simulations are carried out to demonstrate the multiple stick-slip dynamics of the system, which show the efficiency of the prediction for stick-slip chaos of the perturbed self-excited system. The results presented herein this paper demonstrate the complicated dynamics of stick-slip periodic solutions, multiple stick-slip chaotic solutions and also coexistence of multiple solutions for the perturbed self-excited SD oscillator.