Identification of Non-linear System Parameters via the Instantaneous Freequency: Application of the Hilbert Transform and Wigner-ville Techniques

Vibration signals of non-linear systems can be locally represented by a frequency and a spread about that frequency on the base of the Wigner-Vie Distribution as distribution of energy in time and frequency. They can also be represented via the instantaneous frequency as the first derivative of the instantaneous phase of the analytic signal. Frequency estimations of non-linear systems are time varying functions. The Hilbert transform of the equation of motion will consist of a new additional fast varying part in the spring and damping characteristics. The obtained equation of motion in the signal analytic form combines the fast modulation spring and friction force functions. Time varying natural frequency and damping coefficient have their own envelopes and after using a lowpass filter to filtrate these parameters we can estimate an average friction envelope and an average spring force functions. These average forces are slow varying functions that describe the correct relations between solution and forces. Some modeling examples of non-linear vibration systems with backlash, dry friction and hard spring are included.