Residue harmonic balance analysis for the damped Duffing resonator driven by a van der Pol oscillator

A. Y T Leung; Zhongjin Guo; H. X. Yang

doi:10.1016/j.ijmecsci.2012.06.011

Author(s)

A. Y T Leung
Zhongjin Guo
H. X. Yang

Detail(s)

Original language	English
Pages (from-to)	59-65
Journal / Publication	International Journal of Mechanical Sciences
Volume	63
Issue number	1
Publication status	Published - Oct 2012

Link(s)

DOI	DOI https://doi.org/10.1016/j.ijmecsci.2012.06.011 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-84864618176&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(a70bfdd6-2186-44b8-a0a3-1adedba4c44a).html

Abstract

The residue harmonic balance is developed for coupled systems exemplified by the damped Duffing resonator driven by a van der Pol oscillator. This technique combines the features of harmonic balance and parameter bookkeeping to obtain approximate solutions to any desired accuracy. For the two degrees of freedom system, the zeroth-order approximation uses just one Fourier term resulting in a set of two nonlinear algebraic equations that can be solved analytically. The unbalanced residue due to Fourier truncation is improved by solving linear equations that automatically increase the number of terms to balance the previous truncation completely. Highly accurate bifurcation frequencies for various parameters are obtained and are verified by numerical integration results. The effects of the coupling stiffness on the angular frequency and amplitude of steady state response are investigated. The effects of the nonlinear damping are also studied. © 2012 Elsevier Ltd. All rights reserved.

Research Area(s)

Approximate periodic solution, Damped Duffing resonator, Residue harmonic balance, Van der Pol oscillator

Citation Format(s)

[ RIS ] [ BibTeX ]

Residue harmonic balance analysis for the damped Duffing resonator driven by a van der Pol oscillator. / Leung, A. Y T; Guo, Zhongjin; Yang, H. X.
In: International Journal of Mechanical Sciences, Vol. 63, No. 1, 10.2012, p. 59-65.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review

Leung, AYT, Guo, Z & Yang, HX 2012, 'Residue harmonic balance analysis for the damped Duffing resonator driven by a van der Pol oscillator', International Journal of Mechanical Sciences, vol. 63, no. 1, pp. 59-65. https://doi.org/10.1016/j.ijmecsci.2012.06.011

Leung, A. Y. T., Guo, Z., & Yang, H. X. (2012). Residue harmonic balance analysis for the damped Duffing resonator driven by a van der Pol oscillator. International Journal of Mechanical Sciences, 63(1), 59-65. https://doi.org/10.1016/j.ijmecsci.2012.06.011

Leung AYT, Guo Z, Yang HX. Residue harmonic balance analysis for the damped Duffing resonator driven by a van der Pol oscillator. International Journal of Mechanical Sciences. 2012 Oct;63(1):59-65. doi: 10.1016/j.ijmecsci.2012.06.011

Leung, A. Y T ; Guo, Zhongjin ; Yang, H. X. / Residue harmonic balance analysis for the damped Duffing resonator driven by a van der Pol oscillator. In: International Journal of Mechanical Sciences. 2012 ; Vol. 63, No. 1. pp. 59-65.