Analytical approximate solutions for conservative nonlinear oscillators by modified rational harmonic balance method
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Título: | Analytical approximate solutions for conservative nonlinear oscillators by modified rational harmonic balance method |
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Autor/es: | Beléndez, Augusto | Gimeno, Encarnación | Alvarez, Mariela L. | Yebra Calleja, María Soledad | Méndez Alcaraz, David Israel |
Grupo/s de investigación o GITE: | Holografía y Procesado Óptico |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal |
Palabras clave: | Nonlinear oscillators | Analytical approximate solutions | Trully nonlinear oscillators | Conservative oscillators | Rational harmonic balance method |
Área/s de conocimiento: | Física Aplicada | Matemática Aplicada |
Fecha de creación: | feb-2008 |
Fecha de publicación: | 22-jun-2009 |
Editor: | Taylor & Francis |
Cita bibliográfica: | BELÉNDEZ VÁZQUEZ, Augusto, et al. "Analytical approximate solutions for conservative nonlinear oscillators by modified rational harmonic balance method". International Journal of Computer Mathematics. ISSN 1029-0265, First published on 22 June 2009 |
Resumen: | An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the generalized harmonic balance method in which analytical approximate solutions have rational form. This approach gives us not only a truly periodic solution but also the frequency of the motion as a function of the amplitude of oscillation. Three truly nonlinear oscillators including cubic Duffing oscillator, fractional-power restoring force and anti-symmetric quadratic nonlinear oscillators are presented to illustrate the usefulness and effectiveness of the proposed technique. We find that this method works very well for the cubic 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 0.0046%. 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. For the other two nonlinear oscillators considered the relative errors in the analytical approximate frequencies are 0.098% and 0.066%, respectively. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems. |
Patrocinador/es: | This work was supported by the "Ministerio de Educación y Ciencia", Spain, under project FIS2005-05881-C02-02. The authors express their gratitude to the reviewers for their useful suggestions and for their comments, which significantly improved the original manuscript. |
URI: | http://hdl.handle.net/10045/11920 |
ISSN: | 0020-7160 (Print) | 1029-0265 (Online) |
DOI: | 10.1080/00207160802380942 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | This is an electronic version of an article published in the International Journal of Computer Mathematics ©2008 Copyright Taylor & Francis; International Journal of Computer Mathematics is available online at http://www.informaworld.com |
Revisión científica: | si |
Versión del editor: | http://dx.doi.org/10.1080/00207160802380942 |
Aparece en las colecciones: | INV - GHPO - Artículos de Revistas INV - Acústica Aplicada - Artículos de Revistas INV - GMECA - Artículos de Revistas INV - GIRS - Artículos de Revistas |
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IJCM_belendez_2009pruebas.pdf | Versión revisada (acceso libre) | 278,46 kB | Adobe PDF | Abrir Vista previa |
IJCM_v87_n7_p1497_2010.pdf | Versión final (acceso restringido) | 241,16 kB | Adobe PDF | Abrir Solicitar una copia |
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