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Localized basis function method for computing limit cycle oscillations

Publication ,  Journal Article
Epureanu, BI; Dowell, EH
Published in: Nonlinear Dynamics
January 1, 2003

An alternate approach to the standard harmonic balance method (based on Fourier transforms) is proposed. The proposed method begins with an idea similar to the harmonic balance method, i.e. to transform the initial set of differential equations of the dynamics to a set of discrete algebraic equations. However, as distinct from previous harmonic balance techniques, the proposed method uses a set of basis functions which are localized in time and are not necessarily sinusoidal. Also as distinct from previous harmonic balance methods, the algebraic equations obtained after the transformation of the differential equations of the dynamics are solved in the time domain rather than the frequency domain. Numerical examples are provided to demonstrate the performance of the method for autonomous and forced dynamics of a Van der Pol oscillator.

Duke Scholars

Published In

Nonlinear Dynamics

DOI

ISSN

0924-090X

Publication Date

January 1, 2003

Volume

31

Issue

2

Start / End Page

151 / 166

Related Subject Headings

  • Acoustics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

Citation

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Epureanu, B. I., & Dowell, E. H. (2003). Localized basis function method for computing limit cycle oscillations. Nonlinear Dynamics, 31(2), 151–166. https://doi.org/10.1023/A:1022081101766
Epureanu, B. I., and E. H. Dowell. “Localized basis function method for computing limit cycle oscillations.” Nonlinear Dynamics 31, no. 2 (January 1, 2003): 151–66. https://doi.org/10.1023/A:1022081101766.
Epureanu BI, Dowell EH. Localized basis function method for computing limit cycle oscillations. Nonlinear Dynamics. 2003 Jan 1;31(2):151–66.
Epureanu, B. I., and E. H. Dowell. “Localized basis function method for computing limit cycle oscillations.” Nonlinear Dynamics, vol. 31, no. 2, Jan. 2003, pp. 151–66. Scopus, doi:10.1023/A:1022081101766.
Epureanu BI, Dowell EH. Localized basis function method for computing limit cycle oscillations. Nonlinear Dynamics. 2003 Jan 1;31(2):151–166.
Journal cover image

Published In

Nonlinear Dynamics

DOI

ISSN

0924-090X

Publication Date

January 1, 2003

Volume

31

Issue

2

Start / End Page

151 / 166

Related Subject Headings

  • Acoustics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences