A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator

Liping Liu; J. P. Thomas; E. H. Dowell; P. Attar; K. C. Hall

doi:10.1016/j.jcp.2005.10.026

A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator

Liping Liu
, J. P. Thomas
, E. H. Dowell
, P. Attar
, K. C. Hall

Mathematics and Statistics

Duke University

Research output: Contribution to journal › Article › peer-review

166 Scopus citations

Abstract

The present study focuses on a novel harmonic balance formulation, which is much easier to implement than the standard/classical harmonic balance method for complex nonlinear mathematical models and algorithms. Both harmonic balance approaches are applied to Duffing's oscillator to demonstrate the advantages and disadvantages of the two approaches. A fundamental understanding of the difference between these two methods is achieved, and the properties of each method are analyzed in detail. © 2005 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	298-320
Number of pages	23
Journal	Journal of Computational Physics
Volume	215
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2005.10.026
State	Published - Jun 10 2006

Keywords

Duffing's oscillator
Dynamical systems
Harmonic balance method
Limit cycle oscillations
Numerical analysis

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10.1016/j.jcp.2005.10.026

Cite this

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AB - The present study focuses on a novel harmonic balance formulation, which is much easier to implement than the standard/classical harmonic balance method for complex nonlinear mathematical models and algorithms. Both harmonic balance approaches are applied to Duffing's oscillator to demonstrate the advantages and disadvantages of the two approaches. A fundamental understanding of the difference between these two methods is achieved, and the properties of each method are analyzed in detail. © 2005 Elsevier Inc. All rights reserved.

KW - Duffing's oscillator

KW - Dynamical systems

KW - Harmonic balance method

KW - Limit cycle oscillations

KW - Numerical analysis

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A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator

Abstract

Keywords

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