Frequency Domain Analysis And Design Of Nonlinear Systems Based On Volterra Series Expansion
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Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion
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.
Analysis and Design of Nonlinear Systems in the Frequency Domain
This book focuses on the development of three novel approaches to build up a framework for the frequency domain analysis and design of nonlinear systems. The concepts are derived from Volterra series representation of nonlinear systems which are described by nonlinear difference or differential equations. Occupying the middle ground between traditional linear approaches and more complex nonlinear system theories, the book will help readers to have a good start to analyse and exploit the nonlinearities. Analysis and Design of Nonlinear Systems in the Frequency Domain provides clear illustrations and examples at the beginning and the end of each chapter, respectively, making it of interest to both academics and practicing engineers.
The Bio-Inspired X-Structure/Mechanism Approach for Exploring Nonlinear Benefits in Engineering
This book presents a unique approach to the design and analysis of beneficial nonlinearity, which can take an important and critical role in engineering systems and thus cannot be simply ignored in structural design, dynamic response analysis, and parameter selection. A key issue in the area is thus systematically addressed about how to analyze and design potential nonlinearities introduced to or inherent in a system of under study, which is a must-do task in many practical applications involving vibration control, energy harvesting, sensor systems and robots etc. This book, together with several other books in this book series, is to present an up-to-date summary on the most recent development of a cutting-edge method for nonlinearity manipulation and employment developed in recent several years, named as the X-shaped structure or mechanism approach. The X-shaped structure or mechanism is a generic structure or mechanism representing a class of beneficial geometric nonlinearity with realizable and flexible linkage mechanism or structural design of different variants or forms (quadrilateral, diamond, polygon, K/Z/S/V-shape, or others) which all share similar geometric nonlinearity and thus similar nonlinear stiffness/damping properties, flexible in design, and easy to implement. This book is particularly to present a systematic frequency domain analysis, design and optimization method of critical structural or control parameters in nonlinear systems including the X-structure/mechanism dynamics, aiming at better dynamic performance and special nonlinear response as expected in engineering practice. Cases studies in vehicle suspension, energy harvesting, fault detection and fuzzy membership optimization are all showcased. The new analysis and design method introduced in this book definitely present a totally new and powerful approach to optimization and understanding of a class of nonlinear systems from a special frequency domain point of view.