Solution of the relativistic (an)harmonic oscillator using the harmonic balance method

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Title: Solution of the relativistic (an)harmonic oscillator using the harmonic balance method
Authors: Beléndez, Augusto | Pascual, Carolina | Méndez Alcaraz, David Israel | Neipp, Cristian
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
Keywords: Nonlinear oscillators | Approximate solutions | Relativistic oscillator | Harmonic balance method
Knowledge Area: Física Aplicada
Date Created: 7-May-2007
Issue Date: 7-Nov-2007
Publisher: Elsevier
Citation: BELÉNDEZ VÁZQUEZ, Augusto, et al. "Solution of the relativistic (an)harmonic oscillator using the harmonic balance method". Journal of Sound and Vibration. Vol. 311, Issues 3-5 (Apr. 2008). ISSN 0022-460X, pp. 1447-1456
Abstract: The harmonic balance method is used to construct approximate frequency–amplitude relations and periodic solutions to the relativistic oscillator. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes, A, while the discrepancy between the second approximate frequency and the exact one never exceeds 0.82% and tends to 0.52% when A tends to infinity. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed.
Sponsor: This work was supported by the "Ministerio de Educación y Ciencia", Spain, under Project FIS2005-05881-C02-02, and by the "Generalitat Valenciana", Spain, under Project ACOMP-2007-020.
ISSN: 0022-460X (Print) | 1095-8568 (Online)
DOI: 10.1016/j.jsv.2007.10.010
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
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INV - GMECA - Artículos de Revistas

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