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

L. 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

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

Duke University

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

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.

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
Externally published	Yes

Keywords

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

Access to Document

10.1016/j.jcp.2005.10.026

Cite this

@article{fae9c8c675c64c06867935324385edf5,

title = "A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator",

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.",

keywords = "Duffing's oscillator, Dynamical systems, Harmonic balance method, Limit cycle oscillations, Numerical analysis",

author = "L. Liu and Thomas, \{J. P.\} and Dowell, \{E. H.\} and P. Attar and Hall, \{K. C.\}",

year = "2006",

month = jun,

day = "10",

doi = "10.1016/j.jcp.2005.10.026",

language = "English",

volume = "215",

pages = "298--320",

journal = "Journal of Computational Physics",

issn = "0021-9991",

number = "1",

}

TY - JOUR

T1 - A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator

AU - Liu, L.

AU - Thomas, J. P.

AU - Dowell, E. H.

AU - Attar, P.

AU - Hall, K. C.

PY - 2006/6/10

Y1 - 2006/6/10

N2 - 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.

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.

KW - Duffing's oscillator

KW - Dynamical systems

KW - Harmonic balance method

KW - Limit cycle oscillations

KW - Numerical analysis

UR - https://www.scopus.com/pages/publications/33645885601

U2 - 10.1016/j.jcp.2005.10.026

DO - 10.1016/j.jcp.2005.10.026

M3 - Article

SN - 0021-9991

VL - 215

SP - 298

EP - 320

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this