Nonlinear Vibration System Identification via the Hilbert Transform

Hilbert Transform (HT) of vibration signals provides a technique for nonlinear vibration system identification. The application of HT on free response of a vibrating system provides additional information about modal parameters. In this time domain identification technique free response of system is converted by the HT to a new analytic signal. The analytic signal contains a slow varying function called envelope and instantaneous phase. Every specific nonlinearity in the stiffness of the system has its own characteristics represented by a skeleton curve or backbone. If a system has nonlinear damping characteristics, instantaneous damping dependents on the envelope. In this paper, various classical nonlinearity elements both in stiffness and damping have been treated and discussed by HT method.