Nonlinear analysis of forced responses of an axially moving beam by incremental harmonic balance method

J. L. Huang; S. H. Chen; R. K. L. Su; Y. Y. Lee

doi:10.1063/1.3452306

Nonlinear analysis of forced responses of an axially moving beam by incremental harmonic balance method

J. L. Huang, S. H. Chen, R. K. L. Su, Y. Y. Lee

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

1 Citation (Scopus)

Abstract

This paper analyzes nonlinear vibration of an axially moving beam subject to periodic lateral forces by Incremental Harmonic Balance (IHB) method. Attention is paid to the fundamental resonance as the force frequency is close to the first frequencies ω₁ of the system. Galerkin method is used to discretize the governing equations and the IHB method is used to illustrate the nonlinear dynamic behavior of the axially moving beam. The stable and unstable periodic solutions for given parameters are determined by the multivariable Floquet theory. Hsu's method is applied for computing the transition matrix at the end of one period. The effects of internal resonance on the beam responses are discussed. The periodic solutions obtained from the IHB method are in good agreement with the results obtained from numerical integration.

Original language	English
Title of host publication	AIP Conference Proceedings
Publisher	AIP Publishing
Pages	941-946
Volume	1233
ISBN (Print)	978-0-7354-0778-7
DOIs	https://doi.org/10.1063/1.3452306
Publication status	Published - Nov 2009
Event	2nd International Symposium on Computational Mechanics (ISCM II) and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science ( EPMESC XII) - Hong Kong, Macau, China Duration: 30 Nov 2009 → 3 Dec 2009

Conference

Conference	2nd International Symposium on Computational Mechanics (ISCM II) and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science ( EPMESC XII)
Place	China
City	Hong Kong, Macau
Period	30/11/09 → 3/12/09

Research Keywords

an axially moving beam
IHB method
internal resonance
Nonlinear vibration
stability

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title = "Nonlinear analysis of forced responses of an axially moving beam by incremental harmonic balance method",

abstract = "This paper analyzes nonlinear vibration of an axially moving beam subject to periodic lateral forces by Incremental Harmonic Balance (IHB) method. Attention is paid to the fundamental resonance as the force frequency is close to the first frequencies ω1 of the system. Galerkin method is used to discretize the governing equations and the IHB method is used to illustrate the nonlinear dynamic behavior of the axially moving beam. The stable and unstable periodic solutions for given parameters are determined by the multivariable Floquet theory. Hsu's method is applied for computing the transition matrix at the end of one period. The effects of internal resonance on the beam responses are discussed. The periodic solutions obtained from the IHB method are in good agreement with the results obtained from numerical integration.",

keywords = "an axially moving beam, IHB method, internal resonance, Nonlinear vibration, stability",

author = "Huang, {J. L.} and Chen, {S. H.} and Su, {R. K. L.} and Lee, {Y. Y.}",

year = "2009",

month = nov,

doi = "10.1063/1.3452306",

language = "English",

isbn = "978-0-7354-0778-7",

volume = "1233",

pages = "941--946",

booktitle = "AIP Conference Proceedings",

publisher = "AIP Publishing",

address = "United States",

note = "2nd International Symposium on Computational Mechanics (ISCM II) and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science ( EPMESC XII) ; Conference date: 30-11-2009 Through 03-12-2009",

}

Huang, JL, Chen, SH, Su, RKL & Lee, YY 2009, Nonlinear analysis of forced responses of an axially moving beam by incremental harmonic balance method. in AIP Conference Proceedings. vol. 1233, AIP Publishing, pp. 941-946, 2nd International Symposium on Computational Mechanics (ISCM II) and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science ( EPMESC XII), Hong Kong, Macau, China, 30/11/09. https://doi.org/10.1063/1.3452306

Nonlinear analysis of forced responses of an axially moving beam by incremental harmonic balance method. / Huang, J. L.; Chen, S. H.; Su, R. K. L. et al.
AIP Conference Proceedings. Vol. 1233 AIP Publishing, 2009. p. 941-946.

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Nonlinear analysis of forced responses of an axially moving beam by incremental harmonic balance method

AU - Huang, J. L.

AU - Chen, S. H.

AU - Su, R. K. L.

AU - Lee, Y. Y.

PY - 2009/11

Y1 - 2009/11

N2 - This paper analyzes nonlinear vibration of an axially moving beam subject to periodic lateral forces by Incremental Harmonic Balance (IHB) method. Attention is paid to the fundamental resonance as the force frequency is close to the first frequencies ω1 of the system. Galerkin method is used to discretize the governing equations and the IHB method is used to illustrate the nonlinear dynamic behavior of the axially moving beam. The stable and unstable periodic solutions for given parameters are determined by the multivariable Floquet theory. Hsu's method is applied for computing the transition matrix at the end of one period. The effects of internal resonance on the beam responses are discussed. The periodic solutions obtained from the IHB method are in good agreement with the results obtained from numerical integration.

AB - This paper analyzes nonlinear vibration of an axially moving beam subject to periodic lateral forces by Incremental Harmonic Balance (IHB) method. Attention is paid to the fundamental resonance as the force frequency is close to the first frequencies ω1 of the system. Galerkin method is used to discretize the governing equations and the IHB method is used to illustrate the nonlinear dynamic behavior of the axially moving beam. The stable and unstable periodic solutions for given parameters are determined by the multivariable Floquet theory. Hsu's method is applied for computing the transition matrix at the end of one period. The effects of internal resonance on the beam responses are discussed. The periodic solutions obtained from the IHB method are in good agreement with the results obtained from numerical integration.

KW - an axially moving beam

KW - IHB method

KW - internal resonance

KW - Nonlinear vibration

KW - stability

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U2 - 10.1063/1.3452306

DO - 10.1063/1.3452306

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 978-0-7354-0778-7

VL - 1233

SP - 941

EP - 946

BT - AIP Conference Proceedings

PB - AIP Publishing

T2 - 2nd International Symposium on Computational Mechanics (ISCM II) and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science ( EPMESC XII)

Y2 - 30 November 2009 through 3 December 2009

ER -

Nonlinear analysis of forced responses of an axially moving beam by incremental harmonic balance method

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