Analytical Approximant to a Quadratically Damped Duffing Oscillator

The Duffing oscillator of a system with strong quadratic damping is considered. We give an elementary approximate analytical solution to this oscillator in terms of exponential and trigonometric functions. We compare the analytical approximant with the Runge–Kutta numerical solution. We also solve t...

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Autor principal: Salas S, Alvaro H.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi 2022
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8844348/
https://www.ncbi.nlm.nih.gov/pubmed/35177958
http://dx.doi.org/10.1155/2022/3131253
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author Salas S, Alvaro H.
author_facet Salas S, Alvaro H.
author_sort Salas S, Alvaro H.
collection PubMed
description The Duffing oscillator of a system with strong quadratic damping is considered. We give an elementary approximate analytical solution to this oscillator in terms of exponential and trigonometric functions. We compare the analytical approximant with the Runge–Kutta numerical solution. We also solve the oscillator by menas of He's homotopy method and the famous Krylov–Bogoliubov–Mitropolsky method. The approximant allows estimating the points at which the solution crosses the horizontal axis.
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spelling pubmed-88443482022-02-16 Analytical Approximant to a Quadratically Damped Duffing Oscillator Salas S, Alvaro H. ScientificWorldJournal Research Article The Duffing oscillator of a system with strong quadratic damping is considered. We give an elementary approximate analytical solution to this oscillator in terms of exponential and trigonometric functions. We compare the analytical approximant with the Runge–Kutta numerical solution. We also solve the oscillator by menas of He's homotopy method and the famous Krylov–Bogoliubov–Mitropolsky method. The approximant allows estimating the points at which the solution crosses the horizontal axis. Hindawi 2022-02-07 /pmc/articles/PMC8844348/ /pubmed/35177958 http://dx.doi.org/10.1155/2022/3131253 Text en Copyright © 2022 Alvaro H. Salas S. https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Salas S, Alvaro H.
Analytical Approximant to a Quadratically Damped Duffing Oscillator
title Analytical Approximant to a Quadratically Damped Duffing Oscillator
title_full Analytical Approximant to a Quadratically Damped Duffing Oscillator
title_fullStr Analytical Approximant to a Quadratically Damped Duffing Oscillator
title_full_unstemmed Analytical Approximant to a Quadratically Damped Duffing Oscillator
title_short Analytical Approximant to a Quadratically Damped Duffing Oscillator
title_sort analytical approximant to a quadratically damped duffing oscillator
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8844348/
https://www.ncbi.nlm.nih.gov/pubmed/35177958
http://dx.doi.org/10.1155/2022/3131253
work_keys_str_mv AT salassalvaroh analyticalapproximanttoaquadraticallydampedduffingoscillator

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