Journal ArticleDOI
On the convergence of the Volterra-series representation of the Duffing's oscillators subjected to harmonic excitations
Zhike Peng,Zi-Qiang Lang +1 more
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TLDR
In this paper, the authors investigated the convergence issue of the Volterra-series representations of the Duffing's oscillator subjected to harmonic inputs and proposed a simple criterion to determine the upper limit of the magnitude of the harmonic inputs.About:
This article is published in Journal of Sound and Vibration.The article was published on 2007-08-07. It has received 42 citations till now. The article focuses on the topics: Duffing equation & Harmonic oscillator.read more
Citations
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Journal ArticleDOI
Volterra-series-based nonlinear system modeling and its engineering applications: A state-of-the-art review
TL;DR: In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts derived from the VOLTERRA series, including the general frequency response function (GFRF), the nonlinear output frequency response functions (NOFRF) and associated frequency response (AFRF), and a detailed review is then given on the applications of Volterras in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.
Journal ArticleDOI
Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis
TL;DR: In this article, the harmonic components in the nonlinear system response to a sinusoidal input calculated using nonlinear output frequency response functions (NOFRFs) are one of the solutions obtained using the harmonic balance method (HBM).
Journal ArticleDOI
Feasibility study of structural damage detection using NARMAX modelling and Nonlinear Output Frequency Response Function based analysis
TL;DR: In this article, a feasibility study of the application of the well-known Nonlinear Auto-Regressive Moving Average with eXogenous Inputs (NARMAX) modelling method and the NOFRFs-based analyses to the detection of damage in engineering structures is presented.
Journal ArticleDOI
A novel approach for nonlinearity detection in vibrating systems
Zi-Qiang Lang,Zhike Peng +1 more
TL;DR: In this paper, the authors proposed a novel approach for nonlinearity detection in vibrating systems based on nonlinear output frequency response functions (NOFRFs) and the properties of the NOFRFs for systems with multiple degrees of freedom (mdof).
Journal ArticleDOI
Analysis of nonlinear oscillators using Volterra series in the frequency domain
L. M. Li,Stephen A. Billings +1 more
TL;DR: In this paper, the authors extended the time-domain criterion to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic excitation, and used the new frequency domain criterion to predict the onset point of the jump.
References
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Book
The Volterra and Wiener Theories of Nonlinear Systems
TL;DR: In this article, a complete and detailed development of the analysis, design and characterization of non-linear systems using the Volterra and Wiener theories, as well as gate functions, is presented.
Book
Nonlinear Problems in Random Theory
Norbert Wiener,T. Teichmann +1 more
TL;DR: A series of lectures on the role of nonlinear processes in physics, mathematics, electrical engineering, physiology, and communication theory was given in this article, where the last few of these were devoted to the application of my ideas to problems in the statistical mechanics of gases.
Journal ArticleDOI
Modal analysis of a cracked beam
TL;DR: In this paper, a piecewise-linear two-degree-of-freedom model of a cantilever beam with a transverse edge crack is considered and a bilinear frequency is defined for each of the linear pieces of the piecewise linear system.
Journal ArticleDOI
Recursive algorithm for computing the frequency response of a class of non-linear difference equation models
TL;DR: In this paper, a recursive algorithm is developed which is both computationally compact and enables the nth-order frequency response functions of a large class of nonlinear difference equation models to be found without restriction on the order n.
Book ChapterDOI
Output Frequency Characteristics of Nonlinear Systems
Xingjian Jing,Zi-Qiang Lang +1 more
TL;DR: In this paper, some interesting properties of output frequencies of Volterra-type nonlinear systems are particularly investigated, and the results provide a very novel and useful insight into the super-harmonic and inter-modulation phenomena in output frequency response with consideration of the effects incurred by different nonlinear components in the system.
Related Papers (5)
Fading memory and the problem of approximating nonlinear operators with Volterra series
Stephen Boyd,Leon O. Chua +1 more