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A study of ½-subharmonic oscillations by the method of harmonic balance

✍ Scribed by D.G. Ashwell; A.P. Chauhan

Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
540 KB
Volume
27
Category
Article
ISSN
0022-460X

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Solution of a Duffing-harmonic oscillator by the method of harmonic balance
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The first-order harmonic balance method via first Fourier coefficient is used to construct an approximate frequency–amplitude relation for a Duffing-harmonic oscillator. This relation is in agreement with the result obtained by the Ritz procedure.

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The harmonic balance method is commonly used to analyze the steady state periodic solutions of strongly non-linear systems. Mostly, only a few leading harmonics are used in the truncated Fourier series employed with this method. For the forced oscillations, this assumed solution can fail to uncover

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The incremental harmonic balance method is improved by (i) reversing the order of increment and linearization to find the bifurcated solution branches, (ii) using a fast Fourier transform to compute the solution increments and the Floquet matrix, and (iii) finding the secondary path after a bifurcat