A new detailed explanation of the Tacoma collapse and some optimization problems to improve the stability of suspension bridges
We give a new full explanation of the Tacoma Narrows Bridge collapse, occurred on November 7, 1940. Our explanation involves both structural phenomena, such as parametric resonances, and sophisticated mathematical tools, such as the Floquet theory. Contrary to all previous attempts, our explanation...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-07-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023045?viewType=HTML |
| _version_ | 1797824620404932608 |
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| author | Filippo Gazzola Mohamed Jleli Bessem Samet |
| author_facet | Filippo Gazzola Mohamed Jleli Bessem Samet |
| author_sort | Filippo Gazzola |
| collection | DOAJ |
| description | We give a new full explanation of the Tacoma Narrows Bridge collapse, occurred on November 7, 1940. Our explanation involves both structural phenomena, such as parametric resonances, and sophisticated mathematical tools, such as the Floquet theory. Contrary to all previous attempts, our explanation perfectly fits, both qualitatively and quantitatively, with what was observed that day. With this explanation at hand, we set up and partially solve some optimal control and shape optimization problems (both analytically and numerically) aiming to improve the stability of bridges. The control parameter to be optimized is the strength of a partial damping term whose role is to decrease the energy within the deck. Shape optimization intends to give suggestions for the design of future bridges. |
| first_indexed | 2024-03-13T10:41:42Z |
| format | Article |
| id | doaj.art-124cb1430b1047ad888ec8650c71efa6 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-13T10:41:42Z |
| publishDate | 2023-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-124cb1430b1047ad888ec8650c71efa62023-05-18T01:31:51ZengAIMS PressMathematics in Engineering2640-35012023-07-015213510.3934/mine.2023045A new detailed explanation of the Tacoma collapse and some optimization problems to improve the stability of suspension bridgesFilippo Gazzola 0Mohamed Jleli1Bessem Samet21. Dipartimento di Matematica del Politecnico, Piazza L. da Vinci 32 - 20133 Milano, Italy2. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia2. Department of Mathematics, King Saud University, Riyadh, Saudi ArabiaWe give a new full explanation of the Tacoma Narrows Bridge collapse, occurred on November 7, 1940. Our explanation involves both structural phenomena, such as parametric resonances, and sophisticated mathematical tools, such as the Floquet theory. Contrary to all previous attempts, our explanation perfectly fits, both qualitatively and quantitatively, with what was observed that day. With this explanation at hand, we set up and partially solve some optimal control and shape optimization problems (both analytically and numerically) aiming to improve the stability of bridges. The control parameter to be optimized is the strength of a partial damping term whose role is to decrease the energy within the deck. Shape optimization intends to give suggestions for the design of future bridges.https://www.aimspress.com/article/doi/10.3934/mine.2023045?viewType=HTMLpartial dampingstabilityoptimal controlshape optimizationplates |
| spellingShingle | Filippo Gazzola Mohamed Jleli Bessem Samet A new detailed explanation of the Tacoma collapse and some optimization problems to improve the stability of suspension bridges Mathematics in Engineering partial damping stability optimal control shape optimization plates |
| title | A new detailed explanation of the Tacoma collapse and some optimization problems to improve the stability of suspension bridges |
| title_full | A new detailed explanation of the Tacoma collapse and some optimization problems to improve the stability of suspension bridges |
| title_fullStr | A new detailed explanation of the Tacoma collapse and some optimization problems to improve the stability of suspension bridges |
| title_full_unstemmed | A new detailed explanation of the Tacoma collapse and some optimization problems to improve the stability of suspension bridges |
| title_short | A new detailed explanation of the Tacoma collapse and some optimization problems to improve the stability of suspension bridges |
| title_sort | new detailed explanation of the tacoma collapse and some optimization problems to improve the stability of suspension bridges |
| topic | partial damping stability optimal control shape optimization plates |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2023045?viewType=HTML |
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