Period doubling bifurcation analysis and isolated sub-harmonic resonances in an oscillator with asymmetric clearances

In this paper, a frequency-domain characterization of the period doubling bifurcation is proposed. This allows an efficient detection and localization of such points along frequency response curves computed through continuation and the harmonic balance method. A simple strategy for branch switching to sub-harmonic regimes is presented as well. Furthermore, these bifurcations are tracked in a two-dimensional parameter space, and extremum points with respect to the tracking parameter are characterized and linked to sub-harmonic isola formation. As a test case for these methods, a forced Duffing oscillator with asymmetric clearances is studied numerically. The results, which include the prediction of period doubling cascades and sub-harmonic isolas, are then compared to experimental results, yielding an excellent agreement.