By Xingjian Jing, Ziqiang Lang
This publication is a scientific precis of a few new advances within the sector of nonlinear research and layout within the frequency area, targeting the applying orientated thought and techniques according to the GFRF notion, that is usually performed through the writer long ago eight years. the most effects are formulated uniformly with a parametric attribute method, which gives a handy and novel perception into nonlinear impact on process output reaction by way of attribute parameters and therefore facilitate nonlinear research and layout within the frequency area. The booklet begins with a short advent to the history of nonlinear research within the frequency area, via recursive algorithms for computation of GFRFs for various parametric types, and nonlinear output frequency homes. Thereafter the parametric attribute research technique is brought, which results in the recent realizing and formula of the GFRFs, and nonlinear attribute output spectrum (nCOS) and the nCOS dependent research and layout technique. in line with the parametric attribute technique, nonlinear effect within the frequency area should be investigated with a unique perception, i.e., alternating sequence, that's through a few software leads to vibration keep watch over. importance bounds of frequency reaction capabilities of nonlinear platforms can be studied with a parametric attribute method, which bring about novel parametric convergence standards for any given parametric nonlinear version whose input-output dating permits a convergent Volterra sequence enlargement. This publication objectives these readers who're operating within the components relating to nonlinear research and layout, nonlinear sign processing, nonlinear approach identity, nonlinear vibration keep an eye on, etc. It really serves as a very good reference when you are learning frequency area tools for nonlinear systems.
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Additional info for Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion: A Parametric Characteristic Approach
3a–c. The output harmonics incurred by different single cubic nonlinear term in input or output both demonstrate the periodicity. The output harmonics incurred by single input nonlinearity are finite (see Fig. 3a) while the ones incurred by output nonlinearity are infinite (Fig. 3b). When both the two cubic nonlinearities work together, the output harmonics are still periodic but demonstrate coupling effect such that the output magnitude at the frequencies 6, 7, 8 are coincidently 1. 38 3 Output Frequency Characteristics of Nonlinear Systems Fig.
16). 13) can also be written as H n, p ðjω1 , Á Á Á, jωn Þ ¼ nÀpþ1 X p Y rP 1 Á Á Ár p ¼ 1 ri ¼ n i¼1 H ri ðjωXþ1 , Á Á Á, jωXþri Þ expðÀjðωXþ1 þ Á Á Á þ ωXþri Þki Þ where X ¼ iÀ1 X ð2:18Þ rx . 2 Computation of the GFRFs for NDE Models Similarly, the computation of the GFRFs for the NDE model can be recursively conducted in terms of model parameters as follows (Billings and PeytonJones1990; Jing et al. 2008e): K X c0, n ðk1 ; Á Á Á; kn Þðjω1 Þk1 Á Á Áðjωn Þkn k1 , kn ¼1 ! nÀq X q nÀ1 X K X À Á Y À Ákpþi À Á þ cp, q k1 ; Á Á Á; kpþq jωnÀqþi H nÀq, p jω1 , Á Á Á, jωnÀq q¼1 p¼1 k1 , kpþq ¼0 i¼1 n K X X À Á þ cp, 0 k1 ; Á Á Á; kp H n, p ðjω1 , Á Á Á, jωn Þ p¼2 k1 , kp ¼0 Ln ðjω1 þ Á Á Á þ jωn Þ Á H n ðjω1 , Á Á Á, jωn Þ ¼ ð2:19Þ 2 The Generalized Frequency Response Functions and Output Spectrum of.
N ð3:4bÞ where V ¼ ÀV [ V. This is an analytical expression for the super-harmonics and inter-modulations in the nth-order output frequencies of nonlinear systems. 4a–c), V represents the theoretical input frequency range including both positive and negative frequencies contributing to high order (larger than 1) output spectra (involving only positive frequencies), V is the physical input frequency range contributing to every order output spectrum and W1 represents the output frequencies incurred by the linear part of the system.