Nonlinear characteristics identification of an impact oscillator with a one-sided elastic constraint

Impacting systems are widely used in many engineering applications, such as self-propelled robots, energy harvesting and percussive drilling, which exhibit rich and complex nonlinear phenomena. Among these applications, predicting nonlinearities and estimating system parameters are of great interest of nonlinear dynamics research community. Backbone curve is an analytical tool that captures the frequency-amplitude dependence of nonlinear systems. In this paper, we estimate the impacting stiffness of a single-degree-of-freedom non-smooth dynamical system qualitatively by using the backbone curve. It was found that an increase of the impacting stiffness may lead to lowering the backbone curve. An adaptive differential evolution algorithm with the Metropolis criterion is proposed to identify the parameters of the impacting system quantitatively using experimental data, which are consistent with our theoretical predictions. Finally, the identified parameters are verified, and the limitations of the backbone curve are drawn. The nonlinear characteristics identification method studied in this paper could be extended to other vibro-impact systems and is potentially applicable to structural health monitoring and robotic sensing.