HARMONIC ANALYSIS OF NON-LINEAR STRUCTURES BY MEANS OF GENERALISED FREQUENCY RESPONSE FUNCTIONS COUPLED WITH NARX MODELS

The harmonic analysis of non-linear structures can be equivalently carried out with many different approaches, such as generalised frequency response functions (GFRF) or, more commonly, direct integration methods, Integration techniques provide only approximate results, since the integration procedure is usually carried out for few iteration steps. On the other hand, computational questions and accuracy problems may also arise with GFRFs for different reasons: for example, jump phenomena cannot be detected by means of GFRFs. In practice, for all these reasons, particular care is required in the usage and interpretation of these tools. In this paper, a comparison of the two methodologies is drawn by means of a simple example, and the advantages and drawbacks of GFRF-based harmonic analysis methodology are discussed in extent. In particular, it is shown how GFRFs can be effectively used to derive parametric approaches for harmonic analysis, which represents a substantial advantage over direct integration methods and allows for the development of modular algorithms. In fact, a simple and modular procedure which couples these tools with NARX/NARMAX modelling is proposed. The methodology is tested on a laboratory-scale model of a dam buttress.