Study the Bifurcations of a 2DoF Mechanical Impacting System

TL;DR

This paper investigates bifurcations and chaotic behavior in a two-degree-of-freedom impacting mechanical system, extending prior one-degree systems analysis, and confirms findings through numerical simulations and electronic circuit experiments.

Contribution

It demonstrates that phenomena like narrowband chaos and border collision bifurcations occur in two-degree-of-freedom systems and provides numerical and experimental validation.

Findings

Narrowband chaos can be predicted under specific parameters.

Chaos can be avoided by adjusting system parameters.

Experimental electronic circuit confirms numerical predictions.

Abstract

Impacting mechanical systems with suitable parameter settings exhibit a large amplitude chaotic oscillation close to the grazing with the impacting surface. The cause behind this uncertainty is the square root singularity and the occurrence of dangerous border collision bifurcation. In the case of one degree of freedom mechanical systems, it has already been shown that this phenomenon occurs under certain conditions. This paper proposes the same uncertainty of a two-degree freedom mechanical impacting system under specific requirements. This paper shows that the phenomena earlier reported in the case of one degree of freedom mechanical systems (like narrow band chaos, finger-shaped attractor, etc.) also occur in the two degrees of freedom mechanical impacting system. We have numerically predicted the narrowband chaos ensues under specific parameter settings. We have also shown that the narrowband chaos can be avoided under some parameter settings. At last, we demonstrate the numerical predictions experimentally by constructing an equivalent electronic circuit of the mechanical rig.