A numerical study of a dry friction oscillator with parametric and external excitations

In this paper, the dynamic behavior of a block-on-belt system subjected to simultaneous parametric and external excitations is studied, in which the parametric excitation arises from the variable stiffness of a spring in the system while the external excitation consists of a harmonic force. In addition, the system is damped by dry friction that follows the classical Coulomb's law. The focus of the paper is on analyzing the influence of the parametric excitation on the qualitative features of system dynamics, under various frequency ratios between the external and parametric excitations. Numerical simulations are carried out, whose results are visualized by means of bifurcation diagrams, Poincaré sections and Lyapunov exponents. The results show that the system possesses rich dynamics characterized by periodic, quasi-periodic and chaotic attractors. Furthermore, it is found that the parametric excitation amplitude and the frequency ratio between the excitations have a significant impact on the dynamical behavior of the system.