This book is a systematic summary of some new advances in the area of nonlinear analysis and design in the frequency domain, focusing on the application oriented theory and methods based on the GFRF concept, which is mainly done by the author in the past 8 years.

1 Introduction.- 2 The Generalized Frequency Response Functions and Output Spectrum of Nonlinear Systems.- 3 Output Frequency Characteristics of Nonlinear Systems.- 4 Parametric Characteristic Analysis (PCA).- 5 The Parametric Characteristics of the GRFRs and the Parametric Characteristics Based Analysis.- 6 The Parametric Characteristics of Nonlinear Output Spectrum and Applications.- 7 The Parametric Characteristics Based Output Spectrum Analysis.- 8 Determination of Nonlinear Output Spectrum Based on its Parametric Characteristics --- Some Theoretical Issues.- 9 Nonlinear Characteristic Output Spectrum for Nonlinear Analysis and Design.- 10 Using Nonlinearity for Output Vibration Suppression: An Application Study.- 11 Mapping from Parametric Characteristics to the GFRFs and Output Spectrum.- 12 Nonlinear Influence in the Frequency Domain: Alternating Series.- 13 Magnitude Bound Characteristics of Nonlinear Frequency Response Functions.- 14 Parametric Convergence Bounds of Volterra-Type Nonlinear Systems.- 15 Summary and Overview.- References.2 The Generalized Frequency Response Functions and Output Spectrum of Nonlinear Systems.- 3 Output Frequency Characteristics of Nonlinear Systems.- 4 Parametric Characteristic Analysis (PCA).- 5 The Parametric Characteristics of the GRFRs and the Parametric Characteristics Based Analysis.- 6 The Parametric Characteristics of Nonlinear Output Spectrum and Applications.- 7 The Parametric Characteristics Based Output Spectrum Analysis.- 8 Determination of Nonlinear Output Spectrum Based on its Parametric Characteristics --- Some Theoretical Issues.- 9 Nonlinear Characteristic Output Spectrum for Nonlinear Analysis and Design.- 10 Using Nonlinearity for Output Vibration Suppression: An Application Study.- 11 Mapping from ParametricCharacteristics to the GFRFs and Output Spectrum.- 12 Nonlinear Influence in the Frequency Domain: Alternating Series.- 13 Magnitude Bound Characteristics of Nonlinear Frequency Response Functions.- 14 Parametric Convergence Bounds of Volterra-Type Nonlinear Systems.- 15 Summary and Overview.- References.

This book is a systematic summary of some new advances in the area of nonlinear analysis and design in the frequency domain, focusing on the application oriented theory and methods based on the GFRF concept, which is mainly done by the author in the past 8 years. The main results are formulated uniformly with a parametric characteristic approach, which provides a convenient and novel insight into nonlinear influence on system output response in terms of characteristic parameters and thus facilitate nonlinear analysis and design in the frequency domain.  The book starts with a brief introduction to the background of nonlinear analysis in the frequency domain, followed by recursive algorithms for computation of GFRFs for different parametric models, and nonlinear output frequency properties. Thereafter the parametric characteristic analysis method is introduced, which leads to the new understanding and formulation of the GFRFs, and nonlinear characteristic output spectrum (nCOS) and the nCOS based analysis and design method. Based on the parametric characteristic approach, nonlinear influence in the frequency domain can be investigated with a novel insight, i.e., alternating series, which is followed by some application results in vibration control. Magnitude bounds of frequency response functions of nonlinear systems can also be studied with a parametric characteristic approach, which result in novel parametric convergence criteria for any given parametric nonlinear model whose input-output relationship allows a convergent Volterra series expansion. This book targets those readers who are working in the areas related to nonlinear analysis and design, nonlinear signal processing, nonlinear system identification, nonlinear vibration control, and so on. It particularly serves as a good reference for those who are studying frequency domain methods for nonlinear systems.

A state-of-the-art summary of most important and recent advances in the area of frequency domain methods for nonlinear analysis developed in the past 20 years, and there is no other similar book A systematic frequency domain method for nonlinear analysis and design based on Volterra series expansion, which is of both theoretical and application significance to all those researchers related to nonlinear systems A very novel insight into nonlinear dynamics in the frequency domain, which is very different from all the other existing commonly-used methods such as harmonic balance and describing functions A large amount of analysis and design results which demonstrate how to employ nonlinearity for a better system performance, and there is no other similar book for this topic A very engineering point of view, which can greatly facilitate nonlinear analysis and design in practice Includes supplementary material: sn.pub/extras