Modelling and experimental validation of 1-degree-of-freedom impacting oscillator

Abstract

In this article, a mechanical 1-degree-of-freedom oscillator with harmonic forcing and impacts was analysed both numerically and experimentally. A special attention was paid to the mathematical modelling and realistic numerical simulations of a real system. The developed experimental rig consists of a cart mounted on a guide, connected with springs to the support, and equipped with one-sided stiff limiter of motion. The cart was excited by an unbalanced disc mounted on the shaft of a stepper motor. Modelling was focused on the mathematical description of the impact process, where soft obstacle with Hertzian stiffness was assumed and different forms of non-linear damping were tested, including original modifications of the already used models. Model parameters are identified based on two experimental solutions corresponding to free vibrations – with and without impacts. Then, the model was validated by means of experimental and numerical analysis of bifurcation dynamics of the forced system.