An Investigation into the Characteristics of Nonlinear Frequency Response Functions, Part 1: Understanding the Higher Dimensional Frequency Spaces

The characteristics of generalised frequency response functions (GFRF's) of nonlinear systems in higher dimensional space are investigated using a combination of graphical and symbolic decomposition techniques. It is shown how a systematic analysis can be achieved for a wide class of nonlinear systems in the frequency domain using the proposed methods. The paper is divided into two parts. In Part 1, the concepts of input and output frequency subdomains are introduced to give insight into the relationship between one dimensional and multi-dimensional frequency spaces. The visualisation of both magnitude and phase-responses of third order generalised frequency response functions is presented for the first time. In Part 2 symbolic expansion techniques are introduced and new methods are developed to analyse the properties of generalised frequency response functions of nonlinear systems described by the NARMAX class of models. Case studies are included in Part 2 to illustrate the application of new methods.