In the recent past the characterization of the response of non-linear vibration systems has been approached using the Hilbert transform in time domain. The objective was to propose a, methodology to identify and classify various types of non-linearity from measured response data. The proposed methodology also concentrates on the Hilbert transform signed processing techniques, which, allows us to compute the signal envelope and the instantaneous frequency. It enables us to estimate systems instantaneous dynamic parameters and also the elastic non-symmetric force characteristics. Using the Hilbert transform in the time domain together with the proposed methodology for system identification, we obtain both the instantaneous modal parameters together with the non-linear force characteristics. Modeling examples of vibrations of non-linear non-symmetric elastic force characteristics are included.
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