11. Mapping from Parametric Characteristics to the GFRFs and Output Spectrum

A mapping function from the parametric characteristics to the GFRFs is established. The nth-order GFRF can directly be written into a more straightforward and meaningful form in terms of the first order GFRF and model parameters based on the parametric characteristic, which explicitly unveils the linear and nonlinear factors included in the GFRFs and can be regarded as an n-degreepolynomial function of the first order GFRF. These results demonstrate some new properties of the GFRFs, which can reveal clearly the relationship between the nth-order GFRF and its parametric characteristic, and also the relationship between the higher order GFRF and the first order GFRF. These provide a novel and useful insight into the frequency domain analysis and design of nonlinear systems based on the GFRFs.