Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity
Our model is based on an Euler-Bernoulli beam clamped at one end and subjected at its free end to a control in displacement and velocity. In this work, relative of the control parameters, we study the stabilization in displacement and then in energy of the model using a stable numerical scheme that...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/7647568 |
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| _version_ | 1849304845015580672 |
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| author | Yeo Brahima Dakouri Narcisse Adou Jérôme |
| author_facet | Yeo Brahima Dakouri Narcisse Adou Jérôme |
| author_sort | Yeo Brahima |
| collection | DOAJ |
| description | Our model is based on an Euler-Bernoulli beam clamped at one end and subjected at its free end to a control in displacement and velocity. In this work, relative of the control parameters, we study the stabilization in displacement and then in energy of the model using a stable numerical scheme that we implement. This numerical scheme results from the Crank–Nicolson algorithm for the discretization in time and from the finite element method based on the approximation by Hermith cubic functions for the discretization in space. The study shows that, compared to the velocity control, the displacement control has an almost negligible effect on the stabilization of the beam. This result is confirmed later by a sensitivity study on the control parameters involved in our model. |
| format | Article |
| id | doaj-art-3fbac7a59e88447b9efc1045fc716250 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3fbac7a59e88447b9efc1045fc7162502025-08-20T03:55:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/7647568Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and VelocityYeo Brahima0Dakouri Narcisse1Adou Jérôme2UFR Mathématiques et InformatiqueÉcole Supérieure Africaine des Technologies de l’Information et de la CommunicationUFR Mathématiques et InformatiqueOur model is based on an Euler-Bernoulli beam clamped at one end and subjected at its free end to a control in displacement and velocity. In this work, relative of the control parameters, we study the stabilization in displacement and then in energy of the model using a stable numerical scheme that we implement. This numerical scheme results from the Crank–Nicolson algorithm for the discretization in time and from the finite element method based on the approximation by Hermith cubic functions for the discretization in space. The study shows that, compared to the velocity control, the displacement control has an almost negligible effect on the stabilization of the beam. This result is confirmed later by a sensitivity study on the control parameters involved in our model.http://dx.doi.org/10.1155/2022/7647568 |
| spellingShingle | Yeo Brahima Dakouri Narcisse Adou Jérôme Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity International Journal of Mathematics and Mathematical Sciences |
| title | Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity |
| title_full | Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity |
| title_fullStr | Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity |
| title_full_unstemmed | Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity |
| title_short | Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity |
| title_sort | numerical study of an euler bernoulli beam stabilization controlled in displacement and velocity |
| url | http://dx.doi.org/10.1155/2022/7647568 |
| work_keys_str_mv | AT yeobrahima numericalstudyofaneulerbernoullibeamstabilizationcontrolledindisplacementandvelocity AT dakourinarcisse numericalstudyofaneulerbernoullibeamstabilizationcontrolledindisplacementandvelocity AT adoujerome numericalstudyofaneulerbernoullibeamstabilizationcontrolledindisplacementandvelocity |