Stabilization of a nonlinear Euler-Bernoulli viscoelastic beam subjected to a neutral delay
An approach is implemented in this article to analyze the decay rate of nonlinear beams according to the Euler–Bernoulli equation in the context of rheological viscoelastic damping deformations taking into account the neutral type delay. The interaction between viscoelastic and neutral type delays i...
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Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade
2024-01-01
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| Series: | Theoretical and Applied Mechanics |
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| Online Access: | https://doiserbia.nb.rs/img/doi/1450-5584/2024/1450-55842400005L.pdf |
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| author | Lakehal Ibrahim Benterki Djamila Zennir Khaled |
| author_facet | Lakehal Ibrahim Benterki Djamila Zennir Khaled |
| author_sort | Lakehal Ibrahim |
| collection | DOAJ |
| description | An approach is implemented in this article to analyze the decay rate of nonlinear beams according to the Euler–Bernoulli equation in the context of rheological viscoelastic damping deformations taking into account the neutral type delay. The interaction between viscoelastic and neutral type delays is discussed as our main aim to support a rapidly developing literature. Using the energy method and constructing an appropriate Lyapunov functional, under certain conditions on the kernel and neutral delay terms, we show that despite the destructive nature of delays in general, a very general decaying energy for the problem was obtained. |
| format | Article |
| id | doaj-art-ea890446e4924f218574d2fced5e884d |
| institution | Kabale University |
| issn | 1450-5584 2406-0925 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade |
| record_format | Article |
| series | Theoretical and Applied Mechanics |
| spelling | doaj-art-ea890446e4924f218574d2fced5e884d2025-01-30T06:46:38ZengSerbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, BelgradeTheoretical and Applied Mechanics1450-55842406-09252024-01-01512759110.2298/TAM240318005L1450-55842400005LStabilization of a nonlinear Euler-Bernoulli viscoelastic beam subjected to a neutral delayLakehal Ibrahim0Benterki Djamila1https://orcid.org/0000-0002-2249-5679Zennir Khaled2https://orcid.org/0000-0002-7895-4168Mathematical Analysis and Applications Laboratory, Department of Mathematics, Faculty of mathematics and computer science, Bordj-Bou-Arreridj-University, El-Anasser, AlgeriaMathematical Analysis and Applications Laboratory, Department of Mathematics, Faculty of mathematics and computer science, Bordj-Bou-Arreridj-University, El-Anasser, AlgeriaDepartment of Mathematics, College of Science, Qassim University, Saudi Arabia + Department of Mathematics, Faculty of Science, University 20 Août 1955, Skikda, AlgeriaAn approach is implemented in this article to analyze the decay rate of nonlinear beams according to the Euler–Bernoulli equation in the context of rheological viscoelastic damping deformations taking into account the neutral type delay. The interaction between viscoelastic and neutral type delays is discussed as our main aim to support a rapidly developing literature. Using the energy method and constructing an appropriate Lyapunov functional, under certain conditions on the kernel and neutral delay terms, we show that despite the destructive nature of delays in general, a very general decaying energy for the problem was obtained.https://doiserbia.nb.rs/img/doi/1450-5584/2024/1450-55842400005L.pdfnonlinear euler-bernoulli beamlyapunov functionsviscoelasticitygeneral decayboundary controlpartial differential equations |
| spellingShingle | Lakehal Ibrahim Benterki Djamila Zennir Khaled Stabilization of a nonlinear Euler-Bernoulli viscoelastic beam subjected to a neutral delay Theoretical and Applied Mechanics nonlinear euler-bernoulli beam lyapunov functions viscoelasticity general decay boundary control partial differential equations |
| title | Stabilization of a nonlinear Euler-Bernoulli viscoelastic beam subjected to a neutral delay |
| title_full | Stabilization of a nonlinear Euler-Bernoulli viscoelastic beam subjected to a neutral delay |
| title_fullStr | Stabilization of a nonlinear Euler-Bernoulli viscoelastic beam subjected to a neutral delay |
| title_full_unstemmed | Stabilization of a nonlinear Euler-Bernoulli viscoelastic beam subjected to a neutral delay |
| title_short | Stabilization of a nonlinear Euler-Bernoulli viscoelastic beam subjected to a neutral delay |
| title_sort | stabilization of a nonlinear euler bernoulli viscoelastic beam subjected to a neutral delay |
| topic | nonlinear euler-bernoulli beam lyapunov functions viscoelasticity general decay boundary control partial differential equations |
| url | https://doiserbia.nb.rs/img/doi/1450-5584/2024/1450-55842400005L.pdf |
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