Modelling and identification of the hysteretic dynamics of inerters

This paper deals with an experimental study on the modeling and identification of the hysterical behavior of inerters. Unlike existing methods that can only consider a constant inertance to capture a static model of the device, we develop three different dynamic models for a ball-screw type inerter. To eliminate the effects of the measurement noise, an empirical mode decomposition (EMD) method is proposed. Then, three dynamic models—the Dahl, LuGre and Bouc–Wen model—are used in order to model the friction behavior of the device. Using the least-square optimization method, the parameters of the models are estimated. The results of the tuned models are compared together within different frequencies. The good agreement between predicted and measured data shows that LuGre and Bouc–Wen models can be effective for modelling the hysteretic behavior of friction inside the inerter mechanism. It is also shown that the Bouc–Wen model has better correlation with the experimental results in all test frequencies and amplitudes.