A perturbation-incremental method for strongly non-linear non-autonomous oscillators

K. W. Chung; C. L. Chan; Z. Xu; J. Xu

doi:10.1016/j.ijnonlinmec.2004.10.002

Author(s)

K. W. Chung
C. L. Chan
Z. Xu
J. Xu

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	845-859
Journal / Publication	International Journal of Non-Linear Mechanics
Volume	40
Issue number	6
Publication status	Published - Jul 2005

Link(s)

DOI	DOI https://doi.org/10.1016/j.ijnonlinmec.2004.10.002 Final Published version
	Check@CityULib
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-15344342878&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(01e378ef-2cbb-4d84-baec-5833d9e170fa).html

Abstract

A perturbation-incremental method is extended for the analysis of strongly non-linear non-autonomous oscillators of the form ẍ+g(x)=εf(x,ẋ, Ωt), where g(x) and f(x,ẋ,Ωt) are arbitrary non-linear functions of their arguments, and ε can take arbitrary values. Limit cycles of the oscillators can be calculated to any desired degree of accuracy and their stabilities are determined by the Floquet theory. Branch switching at period-doubling bifurcation along a frequency-response curve is made simple by the present method. Subsequent continuation of an emanating branch is also discussed. © 2004 Elsevier Ltd. All rights reserved.

Research Area(s)

Floquet method, Frequency-response curve, Limit cycles, Period-doubling bifurcation, Strongly non-linear non-autonomous oscillators

Citation Format(s)

[ RIS ] [ BibTeX ]

A perturbation-incremental method for strongly non-linear non-autonomous oscillators. / Chung, K. W.; Chan, C. L.; Xu, Z.; Xu, J.

In: International Journal of Non-Linear Mechanics, Vol. 40, No. 6, 07.2005, p. 845-859.

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

Chung, KW, Chan, CL, Xu, Z & Xu, J 2005, 'A perturbation-incremental method for strongly non-linear non-autonomous oscillators', International Journal of Non-Linear Mechanics, vol. 40, no. 6, pp. 845-859. https://doi.org/10.1016/j.ijnonlinmec.2004.10.002

Chung, K. W., Chan, C. L., Xu, Z., & Xu, J. (2005). A perturbation-incremental method for strongly non-linear non-autonomous oscillators. International Journal of Non-Linear Mechanics, 40(6), 845-859. https://doi.org/10.1016/j.ijnonlinmec.2004.10.002

Chung KW, Chan CL, Xu Z, Xu J. A perturbation-incremental method for strongly non-linear non-autonomous oscillators. International Journal of Non-Linear Mechanics. 2005 Jul;40(6):845-859. https://doi.org/10.1016/j.ijnonlinmec.2004.10.002

Chung, K. W. ; Chan, C. L. ; Xu, Z. ; Xu, J. / A perturbation-incremental method for strongly non-linear non-autonomous oscillators. In: International Journal of Non-Linear Mechanics. 2005 ; Vol. 40, No. 6. pp. 845-859.