Measuring Dynamic Nonlinearities using the Frequency Response and the Hilbert Transform Method

Identification and quantification of dynamic nonlinearities is a long standing issue of the engineering community. During the past years, advances have been made in the theoretical understanding of nonlinear phenomena also thanks to an increased computation power. However, because of the (yet) small understanding of and the mathematical tools required for, too often nonlinear dynamics remains a topic of mostly of academic interest. The two methods discussed in this paper aim at providing a tool for engineers to extract, at least at a first approximation, information on dynamic nonlinear behaviour from data measured from standard experimental methods. Both are single-degree-of-freedom (SDOF) methods: one is based on the properties of the system’s Frequency Response Function (FRF) to a sine-step excitation and is referred to as CONCERTO; the other is the established FORCEVIB method, which is based on the properties the Hilbert Transform in the time domain. The two methods will be applied to numerical simulations and the results discussed and compared.