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Bifurcation techniques for stiffness identification of an impact oscillator

Abstract:

In this paper, a change in stability (bifurcation) of a harmonically excited impact oscillator interacting with an elastic constraint is used to determine the stiffness of constraint. For this purpose, detailed one- and two-parameter bifurcation analyzes of the impacting system are carried out by means of experiments and numerical methods. This study reveals the presence of codimension-one bifurcations of limit cycles, such as grazing, period-doubling and fold bifurcations, as well as a cusp singularity and hysteretic effects. Particularly, the two-parameter continuation of the obtained codimension-one bifurcations (including both period-doubling and fold bifurcations) indicates a strong correlation between the stiffness of the impacted constraint and the frequency at which a certain bifurcation appear. The undertaken approach may prove to be useful for condition monitoring of dynamical systems by identifying mechanical properties through bifurcation analysis. The theoretical pbkp_redictions for the impact oscillator are verified by a number of experimental observations.