A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions

Chen, Guoqiang and Dunne, J F (2016) A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions. Journal of Sound and Vibration, 385. pp. 284-299. ISSN 0022-460X

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Abstract

A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with non-expansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracing-out frequency response functions with high accuracy and efficiency.

Item Type: Article
Keywords: Nonlinear, oscillator, fast tracing, frequency, response.
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Research Centres and Groups: Dynamics, Control and Vehicle Research Group
Subjects: T Technology > TJ Mechanical engineering and machinery
T Technology > TJ Mechanical engineering and machinery > TJ0170 Mechanics applied to machinery. Dynamics
Depositing User: Julian Dunne
Date Deposited: 25 Sep 2016 12:16
Last Modified: 01 Nov 2017 09:43
URI: http://sro.sussex.ac.uk/id/eprint/63581

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