Skip to Main content Skip to Navigation
Journal articles

Frequency dependent iteration method for forced nonlinear oscillators

Abstract : A new iteration method for nonlinear vibrations has been developed by decomposing the periodic solution in two parts corresponding to low and high harmonics. For a nonlinear forced oscillator, the iteration schema is proposed with different formulations for these two parts. Then, the schema is deduced by using the harmonic balance technique. This method has proven to converge to the periodic solutions provided that a convergence condition is satisfied. The convergence is also demonstrated analytically for linear oscillators. Moreover, the new method has been applied to Duffing oscillators as an example. The numerical results show that each iteration schema converges in a domain of the excitation frequency and it can converge to different solutions of the nonlinear oscillator.
Complete list of metadatas

Cited literature [17 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01695465
Contributor : Denis Duhamel <>
Submitted on : Monday, January 29, 2018 - 1:22:03 PM
Last modification on : Wednesday, February 26, 2020 - 7:06:16 PM
Document(s) archivé(s) le : Friday, May 25, 2018 - 3:53:28 PM

File

article.pdf
Files produced by the author(s)

Identifiers

Citation

Tien Hoang, Denis Duhamel, Gilles Forêt, Honoré P. Yin, Pierre Argoul. Frequency dependent iteration method for forced nonlinear oscillators. Applied Mathematical Modelling, Elsevier, 2017, 42, pp.441 - 448. ⟨10.1016/j.apm.2016.10.012⟩. ⟨hal-01695465⟩

Share

Metrics

Record views

209

Files downloads

300