Electronic circuit equivalent of a mechanical impacting system

Abstract

Mechanical impacting systems exhibit a large array of interesting dynamical behaviors including a large amplitude chaotic oscillation close to the grazing condition. This phenomenon has been explained by means of square-root singularity and the occurrence of dangerous border collision bifurcation. However, experimental investigation in the area is constrained by the fact that the parameters of such a mechanical system cannot be changed easily. Here, we propose an electronic circuit that can act as an analog of an impacting mechanical system. We show that the phenomena earlier reported through numerical simulation (like narrow-band chaos, finger-shaped attractor, etc.) occur in this system also. We have experimentally obtained the evolution of the chaotic attractor at grazing as the stiffness ratio is varied—which is not possible in mechanical experiments. We experimentally confirm the theoretical prediction that the occurrence of narrow-band chaos can be avoided for some parameter settings.