Vibrations of Plates and Shells with Attached Mass
The problem of vibrations of plates and shells with a mass attached to the point was solved. A mathematical model was developed based on the hypothesis of nondeformable normals. The latter was used to derive a system of resolvable dynamic equations for the shell with a mass, where the unknowns are t...
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| Language: | English |
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Kazan Federal University
2024-10-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/101 |
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| _version_ | 1832543058498945024 |
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| author | L. U. Sultanov I. R. Garifullin |
| author_facet | L. U. Sultanov I. R. Garifullin |
| author_sort | L. U. Sultanov |
| collection | DOAJ |
| description | The problem of vibrations of plates and shells with a mass attached to the point was solved. A mathematical model was developed based on the hypothesis of nondeformable normals. The latter was used to derive a system of resolvable dynamic equations for the shell with a mass, where the unknowns are the dynamic deflection and stress function. The problem was solved numerically and analytically. In accordance with the boundary conditions, the shell deflection was expressed as double trigonometric series. The transition from the initial dynamic system to the solution of the final system of nonlinear ordinary differential equations was achieved by the Bubnov–Galerkin method. For time integration, the finite difference method was used. |
| format | Article |
| id | doaj-art-fd43752d950345c3b2bbd8016777c3b2 |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-fd43752d950345c3b2bbd8016777c3b22025-02-03T12:00:35ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982024-10-01166342643610.26907/2541-7746.2024.3.426-43659Vibrations of Plates and Shells with Attached MassL. U. Sultanov0I. R. Garifullin1Kazan Federal University; FRC Kazan Scientific Center, Russian Academy of SciencesKazan Federal UniversityThe problem of vibrations of plates and shells with a mass attached to the point was solved. A mathematical model was developed based on the hypothesis of nondeformable normals. The latter was used to derive a system of resolvable dynamic equations for the shell with a mass, where the unknowns are the dynamic deflection and stress function. The problem was solved numerically and analytically. In accordance with the boundary conditions, the shell deflection was expressed as double trigonometric series. The transition from the initial dynamic system to the solution of the final system of nonlinear ordinary differential equations was achieved by the Bubnov–Galerkin method. For time integration, the finite difference method was used.https://uzakufismat.elpub.ru/jour/article/view/101plateshellattached massfinite difference methodbubnov–galerkin method |
| spellingShingle | L. U. Sultanov I. R. Garifullin Vibrations of Plates and Shells with Attached Mass Учёные записки Казанского университета: Серия Физико-математические науки plate shell attached mass finite difference method bubnov–galerkin method |
| title | Vibrations of Plates and Shells with Attached Mass |
| title_full | Vibrations of Plates and Shells with Attached Mass |
| title_fullStr | Vibrations of Plates and Shells with Attached Mass |
| title_full_unstemmed | Vibrations of Plates and Shells with Attached Mass |
| title_short | Vibrations of Plates and Shells with Attached Mass |
| title_sort | vibrations of plates and shells with attached mass |
| topic | plate shell attached mass finite difference method bubnov–galerkin method |
| url | https://uzakufismat.elpub.ru/jour/article/view/101 |
| work_keys_str_mv | AT lusultanov vibrationsofplatesandshellswithattachedmass AT irgarifullin vibrationsofplatesandshellswithattachedmass |