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Abstract

This study investigates impact vibration by using a bifurcation diagram with one or two varying control parameters. Sticking, periodic, and chaotic motions are explored using the Poincaré mapping and impact mapping techniques. A full range of bifurcation diagrams with varying driving frequencies is obtained, and the statistical index of the standard deviation (Std) is used to calculate the impact series in the bifurcation diagrams. The results indicate strong agreement between impact conditions and their corresponding statistical index values for the Std. Subsequently, the Std values for two control parameters of (w, m), (w, c), (w, k), (w, f), and (w, r) are obtained. The generated three-dimensional plots display a mountain-like area indicating unstable regions and a flat area indicating stable regions. The corresponding contour plots display the boundary of the stable and unstable regions in two-parameter domains. These findings expand our understanding of impact vibration and how it benefits condition monitoring.

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