Sub-Harmonic Response Analysis of Nonlinear Dynamic Behaviors Induced by Piecewise-Type Nonlinearities in a Torsional Vibratory System.

Piecewise-type nonlinearities, such as clutch dampers in a torsional system, induce complex nonlinear dynamic behaviors that resemble super- and sub-harmonic responses. This study focuses on investigating the sub-harmonic responses induced by piecewise-type nonlinearities in the middle of various dynamic behaviors in a torsional vibratory system. To examine the dynamic characteristics in a sub-harmonic regime, the harmonic balance method (HBM) was implemented. Its results were compared with the numerical simulation (NS). To reveal the sub-harmonic responses, the input conditions of the HBM were modified with a small number of input values. In addition, bifurcation diagrams were numerically determined and projected onto stable and unstable solutions of the HBM to examine the effective dynamic behaviors within the unstable regimes. The results of the HBM with the modified input conditions reveal the sub-harmonic effects well, and the comparisons of bifurcation diagrams under unstable conditions lead to an understanding of the complex dynamic behaviors. Overall, this study suggests the first analytical technique to determine the sub-harmonic responses with the HBM, and second investigates the complex dynamic behaviors in a practical vibratory system by considering the bifurcations in the unstable regimes. [ABSTRACT FROM AUTHOR]