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

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posted on 2023-06-09, 03:06 authored by Guoqiang Chen, Julian DunneJulian Dunne
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of Sound and Vibration

ISSN

0022-460X

Publisher

Elsevier

Volume

385

Page range

284-299

Department affiliated with

  • Engineering and Design Publications

Research groups affiliated with

  • Dynamics, Control and Vehicle Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-09-25

First Open Access (FOA) Date

2017-11-01

First Compliant Deposit (FCD) Date

2016-09-25

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