Non-linear system vibration analysis using Hilbert transform--I. Free vibration analysis method 'Freevib'

Abstract This study concentrates on techniques for non-linear system investigation, which enable us to identify instantaneous modal parameters (natural frequencies, damping characteristics and their dependencies on a vibration amplitude and frequency) in the process of free vibration analysis and through various kinds of excitation of the dynamic system. Modal parameters identification is based on input and output signal measurements from the dynamic system and on signal processing, including the Hilbert transform. Part I presents the free vibration analysis of the system including the identification technique for the main characteristics of the non-linear oscillatory systems. For non-linear effects representation, a sdof system with a hard spring has been considered.