Computation of dynamic deflection in thin elastic beam via symmetries
The deflection profiles governed by Euler Bernoulli's fourth-order equations under varied applied loads are investigated in this research. This study provides essential insights for engineers designing aircraft components, bridges, and similar structures, ensuring system safety and efficiency....
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Ain Shams Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447924004623 |
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| author | Zain Majeed Adil Jhangeer F.M. Mahomed F.D. Zaman |
| author_facet | Zain Majeed Adil Jhangeer F.M. Mahomed F.D. Zaman |
| author_sort | Zain Majeed |
| collection | DOAJ |
| description | The deflection profiles governed by Euler Bernoulli's fourth-order equations under varied applied loads are investigated in this research. This study provides essential insights for engineers designing aircraft components, bridges, and similar structures, ensuring system safety and efficiency. The investigation emphasizes critical factors such as amplitude and frequency, load history, and material properties. Initially, conservation laws of the equations with applied loads are derived by expressing them in the Euler-Lagrange form, where the resultant conservation laws satisfy the divergence expression. The association between symmetries and conservation laws is demonstrated, followed by the application of double reduction theory, which reduces both the variables and the order of the equation. Graphical representations of the outcomes illustrate the impact of load variations on the beam's deflection profiles. These visual aids facilitate a deeper understanding of the influence of different loading conditions. A comparison between varying loads is presented, showcasing the impact of these variations on structural behavior. The findings are crucial for enhancing structural design and ensuring safety under varied loading conditions, showcasing the novelties in the analytical approach and the practical applications of the derived results. |
| format | Article |
| id | doaj-art-aa6c6e79f8d24f11a8aacccb13e163d6 |
| institution | Kabale University |
| issn | 2090-4479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj-art-aa6c6e79f8d24f11a8aacccb13e163d62024-12-18T08:48:19ZengElsevierAin Shams Engineering Journal2090-44792024-12-011512103081Computation of dynamic deflection in thin elastic beam via symmetriesZain Majeed0Adil Jhangeer1F.M. Mahomed2F.D. Zaman3Abdus Salam School of Mathematical Sciences, Government College University, 68-B New Muslim Town, Lahore-54600, Pakistan; Corresponding author.IT4Innovations, VSB – Technical University of Ostrava, Ostrava-Poruba, Czech RepublicAbdus Salam School of Mathematical Sciences, Government College University, 68-B New Muslim Town, Lahore-54600, PakistanAbdus Salam School of Mathematical Sciences, Government College University, 68-B New Muslim Town, Lahore-54600, PakistanThe deflection profiles governed by Euler Bernoulli's fourth-order equations under varied applied loads are investigated in this research. This study provides essential insights for engineers designing aircraft components, bridges, and similar structures, ensuring system safety and efficiency. The investigation emphasizes critical factors such as amplitude and frequency, load history, and material properties. Initially, conservation laws of the equations with applied loads are derived by expressing them in the Euler-Lagrange form, where the resultant conservation laws satisfy the divergence expression. The association between symmetries and conservation laws is demonstrated, followed by the application of double reduction theory, which reduces both the variables and the order of the equation. Graphical representations of the outcomes illustrate the impact of load variations on the beam's deflection profiles. These visual aids facilitate a deeper understanding of the influence of different loading conditions. A comparison between varying loads is presented, showcasing the impact of these variations on structural behavior. The findings are crucial for enhancing structural design and ensuring safety under varied loading conditions, showcasing the novelties in the analytical approach and the practical applications of the derived results.http://www.sciencedirect.com/science/article/pii/S2090447924004623Load variationsLie symmetryDouble reductionLagrangianConservation laws |
| spellingShingle | Zain Majeed Adil Jhangeer F.M. Mahomed F.D. Zaman Computation of dynamic deflection in thin elastic beam via symmetries Ain Shams Engineering Journal Load variations Lie symmetry Double reduction Lagrangian Conservation laws |
| title | Computation of dynamic deflection in thin elastic beam via symmetries |
| title_full | Computation of dynamic deflection in thin elastic beam via symmetries |
| title_fullStr | Computation of dynamic deflection in thin elastic beam via symmetries |
| title_full_unstemmed | Computation of dynamic deflection in thin elastic beam via symmetries |
| title_short | Computation of dynamic deflection in thin elastic beam via symmetries |
| title_sort | computation of dynamic deflection in thin elastic beam via symmetries |
| topic | Load variations Lie symmetry Double reduction Lagrangian Conservation laws |
| url | http://www.sciencedirect.com/science/article/pii/S2090447924004623 |
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