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Efficient determination of higher-order periodic solutions using n-mode harmonic balance

Publication ,  Journal Article
Donescu, P; Virgin, LN
Published in: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
January 1, 1996

This paper presents a systematic procedure to explicitly determine the algebraic equations arising from the method of harmonic balance with an arbitrary number of modes in the assumed solutions. The technique can be used for a wide variety of nonlinear oscillators (including systems of ordinary differential equations). The method is illustrated in the case of second-order differential equations with nonlinear restoring force. Although numerical methods have been employed to solve the resulting systems of algebraic equations, the general approach is analytic. As such, this study confirms independently (i.e. nonsimulation) the period-doubling cascade of an escape equation including the bifurcation universal scaling laws.

Duke Scholars

Published In

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

DOI

ISSN

0272-4960

Publication Date

January 1, 1996

Volume

56

Issue

1

Start / End Page

21 / 32

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0199 Other Mathematical Sciences
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Donescu, P., & Virgin, L. N. (1996). Efficient determination of higher-order periodic solutions using n-mode harmonic balance. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 56(1), 21–32. https://doi.org/10.1093/imamat/56.1.21
Donescu, P., and L. N. Virgin. “Efficient determination of higher-order periodic solutions using n-mode harmonic balance.” IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) 56, no. 1 (January 1, 1996): 21–32. https://doi.org/10.1093/imamat/56.1.21.
Donescu P, Virgin LN. Efficient determination of higher-order periodic solutions using n-mode harmonic balance. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications). 1996 Jan 1;56(1):21–32.
Donescu, P., and L. N. Virgin. “Efficient determination of higher-order periodic solutions using n-mode harmonic balance.” IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), vol. 56, no. 1, Jan. 1996, pp. 21–32. Scopus, doi:10.1093/imamat/56.1.21.
Donescu P, Virgin LN. Efficient determination of higher-order periodic solutions using n-mode harmonic balance. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications). 1996 Jan 1;56(1):21–32.
Journal cover image

Published In

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

DOI

ISSN

0272-4960

Publication Date

January 1, 1996

Volume

56

Issue

1

Start / End Page

21 / 32

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0199 Other Mathematical Sciences
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics