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Analysis of nonlinear oscillators using volterra series in the frequency domain Part I : convergence limits

Li, L.M. and Billings, S.A. (2009) Analysis of nonlinear oscillators using volterra series in the frequency domain Part I : convergence limits. Research Report. ACSE Research Report no. 988 . Automatic Control and Systems Engineering, University of Sheffield

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Abstract

The Volterra series representation is a direct generalisation of the linear convolution integral and has been widely applied in the analysis and design of nonlinear systems, both in the time and the frequency domain. The Volterra series is associated with the so-called weakly nonlinear systems, but even within the framework of weak nonlinearity there is a convergence limit for the existence of a valid Volterra series representation for a given nonlinear differential equation. Barrett(1965) proposed a time domain criterion to prove that the Volterra series converges with a given region for a class of nonlinear systems with cubic stiffness nonlinearity. In this paper this time-domain criterion is extended to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic excitation.

Item Type: Monograph (Research Report)
Copyright, Publisher and Additional Information: The Department of Automatic Control and Systems Engineering research reports offer a forum for the research output of the academic staff and research students of the Department at the University of Sheffield. Papers are reviewed for quality and presentation by a departmental editor. However, the contents and opinions expressed remain the responsibility of the authors. Some papers in the series may have been subsequently published elsewhere and you are advised to cite the later published version in these instances.
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) > ACSE Research Reports
Depositing User: Miss Anthea Tucker
Date Deposited: 16 Oct 2012 09:21
Last Modified: 06 Jun 2014 08:21
Status: Published
Publisher: Automatic Control and Systems Engineering, University of Sheffield
URI: http://eprints.whiterose.ac.uk/id/eprint/74643

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