Bifurcation techniques for stiffness identification of an impact oscillator

• Bifurcations of a piecewise linear oscillator are studied in two parameter space, both experimentally, and numerically using the continuation package TC-Hat.
• A method for identification of the properties of the impact phase of the response is presented based on a bifurcation approach.
• Time of contact as a function of stiffness ratio is presented, based on numerical simulation.
• Experimental hysteresis is shown from numerics to be the result of a cusp singularity near grazing.

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 predictions for the impact oscillator are verified by a number of experimental observations.