Study the bifurcations of a 2DoF mechanical impacting system

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 that the narrowband chaos ensues under specific parameter settings. We have also shown that 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.