Considering high harmonics for identification of non-linear systems by Hilbert transform

The objective of this paper is to propose a new method for analysis and identification of non-linear vibration structures by considering the primary and high harmonics of the solution. The method is based on two other Hilbert transform methods:•the methods for extracting the instantaneous and average dynamic structure characteristics,•the Hilbert Vibration Decomposition method that splits non-stationary wideband oscillating signal into separate components.The study focuses on combined non-linearities and on identification of precise dynamic parameters (natural frequencies, damping, static force characteristics) for free and forced vibration.