Experiment-Based Motion Reconstruction and Restitution Coefficient Estimation of a Vibro-Impact System

The objective of this paper is to demonstrate the motion reconstruction and the parameter estimation of a vibro-impact (VI) system from limited experimental information. Based on the measured displacement and acceleration of its linear main system, the rest motion information such as the displacement and velocity of the attached VI energy sink can be calculated rather than difficult direct measurement, and therefore, different response regimes from the strongly modulated response to the classic regime with two impacts per cycle are reconstructed. Consequently, it provides comprehensive experimental data for the validation of analytical and numerical results and for any experimental bifurcation analysis. Moreover, a procedure to estimate the restitution coefficient from periodic impacts is demonstrated. This new experimental approach to estimate the value of the restitution coefficient is simple and this accurate value could play an important role in analytical and numerical study.