Simple Identification of Nonlinear Modal Parameters Using Wavelet Transform

Estimation of the modal parameters of mechanical systems or structures is usually achieved by applying the well-known Frequency Response Function (FRF) method to experimental data obtained from free vibration after a shock excitation of the system or forced vibration using a variety of excitation signals. This method is however limited only to linear systems. The problem becomes more complex when nonlinear systems have to be identified. If the nonlinear system is ‘well-behaved’, i.e. if it shows periodic response to a periodic excitation, ‘skeleton’ identification using Hilbert Transform techniques may be used to estimate the modal parameters, in function of the amplitude and frequency of excitation. However, Hilbert transform has some limitations. This technique introduces more errors when high damping is present in the system. An improvement is offered by introducing Wavelet analysis to replace the Hilbert transform. This paper deals with the application of the aforementioned nonlinear identification techniques to an experimental mechanical system with backlash.