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.
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