Modal identification of time-varying systems using Hilbert transform and signal decomposition

The present work investigates modal identification of time-varying dynamical systems by exploiting the Hilbert transform. The proposed method, initially based on the Hilbert Vibration Decomposition (HVD) method, first identifies the instantaneous frequencies of the system. Their corresponding components and modal deflection shapes are then extracted from a set of dynamic responses of the system. The proposed method is first presented and then is illustrated on an experimental set-up. The system under investigation is a recurrent experiment in the field of time-varying systems consisting in a beam travelled by a non-negligible mass while excited by a random external force. The results highlight the time dependency of the modal parameters of the system due to the variant position of the mass with time.