Dynamical behavior of fractionalized simply supported beam: An application of fractional operators to Bernoulli-Euler theory

Dynamical behavior of fractionalized simply supported beam: An application of fractional operators to Bernoulli-Euler theory

The complex structures usually depend upon unconstrained and constrained simply supported beams because the passive damping is applied to control vibrations or dissipate acoustic energies involved in aerospace and automotive industries. This manuscript aims to present an analytic study of a simply s...

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Autores principales: Abro Kashif Ali, Atangana Abdon, Khoso Ali Raza
Formato: article
Lenguaje:EN
Publicado: De Gruyter 2021
Materias:
simply supported beam
integral transform
analytic solutions
fractional approaches
rheological analysis
Engineering (General). Civil engineering (General)
TA1-2040
Acceso en línea:https://doaj.org/article/e867a57876b8485a913bc988a0dda247
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spelling oai:doaj.org-article:e867a57876b8485a913bc988a0dda2472021-12-05T14:10:57ZDynamical behavior of fractionalized simply supported beam: An application of fractional operators to Bernoulli-Euler theory2192-80102192-802910.1515/nleng-2021-0017https://doaj.org/article/e867a57876b8485a913bc988a0dda2472021-10-01T00:00:00Zhttps://doi.org/10.1515/nleng-2021-0017https://doaj.org/toc/2192-8010https://doaj.org/toc/2192-8029The complex structures usually depend upon unconstrained and constrained simply supported beams because the passive damping is applied to control vibrations or dissipate acoustic energies involved in aerospace and automotive industries. This manuscript aims to present an analytic study of a simply supported beam based on the modern fractional approaches namely Caputo-Fabrizio and Atanagna-Baleanu fractional differential operators. The governing equation of motion is fractionalized for knowing the vivid effects of principal parametric resonances. The powerful techniques of Laplace and Fourier sine transforms are invoked for investigating the exact solutions with fractional and non-fractional approaches. The analytic solutions are presented in terms of elementary as well as special functions and depicted for graphical illustration based on embedded parameters. Finally, effects of the amplitude of vibrations and the natural frequency are discussed based on the sensitivities of dynamic characteristics of simply supported beam.Abro Kashif AliAtangana AbdonKhoso Ali RazaDe Gruyterarticlesimply supported beamintegral transformanalytic solutionsfractional approachesrheological analysisEngineering (General). Civil engineering (General)TA1-2040ENNonlinear Engineering, Vol 10, Iss 1, Pp 231-239 (2021)
institution DOAJ
collection DOAJ
language EN
topic simply supported beam
integral transform
analytic solutions
fractional approaches
rheological analysis
Engineering (General). Civil engineering (General)
TA1-2040
spellingShingle simply supported beam
integral transform
analytic solutions
fractional approaches
rheological analysis
Engineering (General). Civil engineering (General)
TA1-2040
Abro Kashif Ali
Atangana Abdon
Khoso Ali Raza
Dynamical behavior of fractionalized simply supported beam: An application of fractional operators to Bernoulli-Euler theory
description The complex structures usually depend upon unconstrained and constrained simply supported beams because the passive damping is applied to control vibrations or dissipate acoustic energies involved in aerospace and automotive industries. This manuscript aims to present an analytic study of a simply supported beam based on the modern fractional approaches namely Caputo-Fabrizio and Atanagna-Baleanu fractional differential operators. The governing equation of motion is fractionalized for knowing the vivid effects of principal parametric resonances. The powerful techniques of Laplace and Fourier sine transforms are invoked for investigating the exact solutions with fractional and non-fractional approaches. The analytic solutions are presented in terms of elementary as well as special functions and depicted for graphical illustration based on embedded parameters. Finally, effects of the amplitude of vibrations and the natural frequency are discussed based on the sensitivities of dynamic characteristics of simply supported beam.
format article
author Abro Kashif Ali
Atangana Abdon
Khoso Ali Raza
author_facet Abro Kashif Ali
Atangana Abdon
Khoso Ali Raza
author_sort Abro Kashif Ali
title Dynamical behavior of fractionalized simply supported beam: An application of fractional operators to Bernoulli-Euler theory
title_short Dynamical behavior of fractionalized simply supported beam: An application of fractional operators to Bernoulli-Euler theory
title_full Dynamical behavior of fractionalized simply supported beam: An application of fractional operators to Bernoulli-Euler theory
title_fullStr Dynamical behavior of fractionalized simply supported beam: An application of fractional operators to Bernoulli-Euler theory
title_full_unstemmed Dynamical behavior of fractionalized simply supported beam: An application of fractional operators to Bernoulli-Euler theory
title_sort dynamical behavior of fractionalized simply supported beam: an application of fractional operators to bernoulli-euler theory
publisher De Gruyter
publishDate 2021
url https://doaj.org/article/e867a57876b8485a913bc988a0dda247
work_keys_str_mv AT abrokashifali dynamicalbehavioroffractionalizedsimplysupportedbeamanapplicationoffractionaloperatorstobernoullieulertheory
AT atanganaabdon dynamicalbehavioroffractionalizedsimplysupportedbeamanapplicationoffractionaloperatorstobernoullieulertheory
AT khosoaliraza dynamicalbehavioroffractionalizedsimplysupportedbeamanapplicationoffractionaloperatorstobernoullieulertheory
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