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Type: Journal article
Title: Analytical approximation of the primary resonance response of a periodically excited piecewise non-linear-linear oscillator
Author: Ji, J.
Hansen, C.
Citation: Journal of Sound and Vibration, 2004; 278(1-2):327-342
Publisher: Academic Press Ltd Elsevier Science Ltd
Issue Date: 2004
ISSN: 0022-460X
Statement of
J. C. Ji and Colin H. Hansen
Abstract: An analytical approximate solution is constructed for the primary resonance response of a periodically excited non-linear oscillator, which is characterized by a combination of a weakly non-linear and a linear differential equation. Without eliminating the secular terms, a valid asymptotic expansion solution for the weakly non-linear equation is analytically determined for the case of primary resonances. Then, a symmetric periodic solution for the overall system is obtained by imposing continuity and matching conditions. The stability characteristic of the symmetric periodic solution is investigated by examining the asymptotic behaviour of perturbations to the steady state solution. The validity of the developed analysis is highlighted by comparing the first order approximate solutions with the results of numerical integration of the original equations.
RMID: 0020041097
DOI: 10.1016/j.jsv.2003.10.022
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Appears in Collections:Mechanical Engineering publications
Environment Institute publications

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