Nonlinear oscillator with power-form elastic-term: Fourier series expansion of the exact solution

Please use this identifier to cite or link to this item:
Información del item - Informació de l'item - Item information
Title: Nonlinear oscillator with power-form elastic-term: Fourier series expansion of the exact solution
Authors: Beléndez, Augusto | Francés, Jorge | Beléndez, Tarsicio | Bleda, Sergio | Pascual, Carolina | Arribas Garde, Enrique
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 | Universidad de Castilla-La Mancha. Departamento de Física Aplicada
Keywords: Dynamical systems | Nonlinear oscillators | Conservative systems | Truly nonlinear oscillators | Fourier series expansion | Approximate solutions | Symbolic computation
Knowledge Area: Física Aplicada | Matemática Aplicada
Date Created: Aug-2014
Issue Date: 1-May-2015
Publisher: Elsevier
Citation: Communications in Nonlinear Science and Numerical Simulation. 2015, 22(1-3): 134-148. doi:10.1016/j.cnsns.2014.10.012
Abstract: A family of conservative, truly nonlinear, oscillators with integer or non-integer order nonlinearity is considered. These oscillators have only one odd power-form elastic-term and exact expressions for their period and solution were found in terms of Gamma functions and a cosine-Ateb function, respectively. Only for a few values of the order of nonlinearity, is it possible to obtain the periodic solution in terms of more common functions. However, for this family of conservative truly nonlinear oscillators we show in this paper that it is possible to obtain the Fourier series expansion of the exact solution, even though this exact solution is unknown. The coefficients of the Fourier series expansion of the exact solution are obtained as an integral expression in which a regularized incomplete Beta function appears. These coefficients are a function of the order of nonlinearity only and are computed numerically. One application of this technique is to compare the amplitudes for the different harmonics of the solution obtained using approximate methods with the exact ones computed numerically as shown in this paper. As an example, the approximate amplitudes obtained via a modified Ritz method are compared with the exact ones computed numerically.
Sponsor: This work was supported by the “Generalitat Valenciana” of Spain, under projects PROMETEO/2011/021 and ISIC/2012/013, and by the “Vicerrectorado de Tecnologías de la Información” of the University of Alicante, Spain, under project GITE-09006-UA.
ISSN: 1007-5704 (Print) | 1878-7274 (Online)
DOI: 10.1016/j.cnsns.2014.10.012
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Publisher version:
Appears in Collections:INV - GHPO - Artículos de Revistas
INV - GMECA - Artículos de Revistas

Files in This Item:
Files in This Item:
File Description SizeFormat 
ThumbnailCNSNS_v22_p134_2015.pdfVersión final (acceso restringido)380,91 kBAdobe PDFOpen    Request a copy
ThumbnailCNSNS-D-14-00408R1-RUA.pdfVersión revisada (acceso abierto)3,27 MBAdobe PDFOpen Preview

Items in RUA are protected by copyright, with all rights reserved, unless otherwise indicated.