Cargando…

Studying highly nonlinear oscillators using the non-perturbative methodology

Due to the growing concentration in the field of the nonlinear oscillators (NOSs), the present study aims to use the general He's frequency formula (HFF) to examine the analytical representations for particular kinds of strong NOSs. Three real-world examples are demonstrated by a variety of eng...

Descripción completa

Detalles Bibliográficos
Autores principales: Moatimid, Galal M., Amer, T. S., Galal, A. A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10662384/
https://www.ncbi.nlm.nih.gov/pubmed/37985730
http://dx.doi.org/10.1038/s41598-023-47519-5
_version_ 1785148534108979200
author Moatimid, Galal M.
Amer, T. S.
Galal, A. A.
author_facet Moatimid, Galal M.
Amer, T. S.
Galal, A. A.
author_sort Moatimid, Galal M.
collection PubMed
description Due to the growing concentration in the field of the nonlinear oscillators (NOSs), the present study aims to use the general He's frequency formula (HFF) to examine the analytical representations for particular kinds of strong NOSs. Three real-world examples are demonstrated by a variety of engineering and scientific disciplines. The new approach is evidently simple and requires less computation than the other perturbation techniques used in this field. The new methodology that is termed as the non-perturbative methodology (NPM) refers to this innovatory strategy, which merely transforms the nonlinear ordinary differential equation (ODE) into a linear one. The method yields a new frequency that is equivalent to the linear ODE as well as a new damping term that may be produced. A thorough explanation of the NPM is offered for the reader's convenience. A numerical comparison utilizing the Mathematical Software (MS) is used to verify the theoretical results. The precise numeric and theoretical solutions exhibited excellent consistency. As is commonly recognized, when the restoration forces are in effect, all traditional perturbation procedures employ Taylor expansion to expand these forces and then reduce the complexity of the specified problem. This susceptibility no longer exists in the presence of the non-perturbative solution (NPS). Additionally, with the NPM, which was not achievable with older conventional approaches, one can scrutinize examining the problem's stability. The NPS is therefore a more reliable source when examining approximations of solutions for severe NOSs. In fact, the above two reasons create the novelty of the present approach. The NPS is also readily transferable for additional nonlinear issues, making it a useful tool in the fields of applied science and engineering, especially in the topic of the dynamical systems.
format Online
Article
Text
id pubmed-10662384
institution National Center for Biotechnology Information
language English
publishDate 2023
publisher Nature Publishing Group UK
record_format MEDLINE/PubMed
spelling pubmed-106623842023-11-20 Studying highly nonlinear oscillators using the non-perturbative methodology Moatimid, Galal M. Amer, T. S. Galal, A. A. Sci Rep Article Due to the growing concentration in the field of the nonlinear oscillators (NOSs), the present study aims to use the general He's frequency formula (HFF) to examine the analytical representations for particular kinds of strong NOSs. Three real-world examples are demonstrated by a variety of engineering and scientific disciplines. The new approach is evidently simple and requires less computation than the other perturbation techniques used in this field. The new methodology that is termed as the non-perturbative methodology (NPM) refers to this innovatory strategy, which merely transforms the nonlinear ordinary differential equation (ODE) into a linear one. The method yields a new frequency that is equivalent to the linear ODE as well as a new damping term that may be produced. A thorough explanation of the NPM is offered for the reader's convenience. A numerical comparison utilizing the Mathematical Software (MS) is used to verify the theoretical results. The precise numeric and theoretical solutions exhibited excellent consistency. As is commonly recognized, when the restoration forces are in effect, all traditional perturbation procedures employ Taylor expansion to expand these forces and then reduce the complexity of the specified problem. This susceptibility no longer exists in the presence of the non-perturbative solution (NPS). Additionally, with the NPM, which was not achievable with older conventional approaches, one can scrutinize examining the problem's stability. The NPS is therefore a more reliable source when examining approximations of solutions for severe NOSs. In fact, the above two reasons create the novelty of the present approach. The NPS is also readily transferable for additional nonlinear issues, making it a useful tool in the fields of applied science and engineering, especially in the topic of the dynamical systems. Nature Publishing Group UK 2023-11-20 /pmc/articles/PMC10662384/ /pubmed/37985730 http://dx.doi.org/10.1038/s41598-023-47519-5 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Moatimid, Galal M.
Amer, T. S.
Galal, A. A.
Studying highly nonlinear oscillators using the non-perturbative methodology
title Studying highly nonlinear oscillators using the non-perturbative methodology
title_full Studying highly nonlinear oscillators using the non-perturbative methodology
title_fullStr Studying highly nonlinear oscillators using the non-perturbative methodology
title_full_unstemmed Studying highly nonlinear oscillators using the non-perturbative methodology
title_short Studying highly nonlinear oscillators using the non-perturbative methodology
title_sort studying highly nonlinear oscillators using the non-perturbative methodology
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10662384/
https://www.ncbi.nlm.nih.gov/pubmed/37985730
http://dx.doi.org/10.1038/s41598-023-47519-5
work_keys_str_mv AT moatimidgalalm studyinghighlynonlinearoscillatorsusingthenonperturbativemethodology
AT amerts studyinghighlynonlinearoscillatorsusingthenonperturbativemethodology
AT galalaa studyinghighlynonlinearoscillatorsusingthenonperturbativemethodology