Rational harmonic balance based method for conservative nonlinear oscillators: application to the Duffing equation
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Title: | Rational harmonic balance based method for conservative nonlinear oscillators: application to the Duffing equation |
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Authors: | Beléndez, Augusto | Gimeno, Encarnación | Beléndez, Tarsicio | Hernández Prados, Antonio |
Research Group/s: | Holografía y Procesado Óptico |
Center, Department or Service: | Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal | Universidad de Alicante. Instituto Universitario de Física Aplicada a las Ciencias y las Tecnologías |
Keywords: | Nonlinear oscillators | Approximate solutions | Rational harmonic balance method | Duffing oscillator |
Knowledge Area: | Física Aplicada |
Date Created: | 12-Nov-2008 |
Issue Date: | 11-Mar-2009 |
Publisher: | Elsevier |
Citation: | BELÉNDEZ VÁZQUEZ, Augusto et al. “Rational harmonic balance based method for conservative nonlinear oscillators: application to the Duffing equation". Mechanics Research Communications. Vol. 36, Issue 6 (Sept. 2009). ISSN 0093-6413, pp. 728-734 |
Abstract: | A second-order modified rational harmonic balance method is used to approximately solve the nonlinear differential equation that governs the oscillations of a conservative autonomous system with one degree of freedom. The Duffing oscillator is analyzed to illustrate the usefulness and effectiveness of the proposed technique. We find that this method works very well for this oscillator, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. For the second-order approximation we have shown that the relative error in the analytical approximate frequency is as low as 0.0055% when A tends to infinity. We also compared the Fourier series expansions of the analytical approximate solution and the exact one. This has allowed us to compare the coefficients for the different harmonic terms in these solutions. |
Sponsor: | This work was supported by the "Generalitat Valenciana" of Spain, under Project GREP/2007/020. |
URI: | http://hdl.handle.net/10045/11911 |
ISSN: | 0093-6413 (Print) | 1873-3972 (Online) |
DOI: | 10.1016/j.mechrescom.2009.03.001 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1016/j.mechrescom.2009.03.001 |
Appears in Collections: | INV - GHPO - Artículos de Revistas INV - GMECA - Artículos de Revistas INV - GIRS - Artículos de Revistas |
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File | Description | Size | Format | |
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MRC_v36_n6_p728_2009.pdf | Versión final (acceso restringido) | 214 kB | Adobe PDF | Open Request a copy |
MRC_v36_n6_p728_2009pre.pdf | Versión revisada (acceso libre) | 197,04 kB | Adobe PDF | Open Preview |
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