Identification of normal modes of a set of strongly nonlinear springs

The dynamics of connecting elements should be identified to evaluate their effects on the assemblies where they are employed. In general, a linear analysis is sufficient to determine their dynamics. However, in some cases, their responses depend on the amplitude and frequency of the excitation, thus nonlinear analyses must be carried out. Following a modal approach, Nonlinear Normal Modes (NNMs) can be used. The aim of this work is to identify the NNMs of a set of nonlinear connecting elements properly designed to be considered as strongly nonlinear springs. These elements have been manufactured and tested to measure some of their NNMs. The time series of the oscillation on some points is recorded using a laser vibrometer for different amplitude and frequencies of excitation. Then, the Virtual Point Transformation (VPT) is used to reduce the obtained data on the two physical points through which the spring is connected to other subsystems. The procedure is repeated for each NNM and the modal basis of each element is expressed as function of the level of excitation.