Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator
For the problem of eigenvibrations of the shallow shell with an attached oscillator, a new symmetric variational statement in the Hilbert space was proposed. It was established that there exist a sequence of positive eigenvalues of finite multiplicity with a limit point at infinity and the correspon...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2024-01-01
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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/23 |
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| _version_ | 1832569183688196096 |
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| author | D. M. Korosteleva S. I. Solov’ev |
| author_facet | D. M. Korosteleva S. I. Solov’ev |
| author_sort | D. M. Korosteleva |
| collection | DOAJ |
| description | For the problem of eigenvibrations of the shallow shell with an attached oscillator, a new symmetric variational statement in the Hilbert space was proposed. It was established that there exist a sequence of positive eigenvalues of finite multiplicity with a limit point at infinity and the corresponding complete orthonormal system of eigenvectors. The problem was approximated by the mesh scheme of the finite element method with Hermite finite elements. Theoretical error estimates for the approximate solutions were proved. The theoretical findings were verified by the results of numerical experiments. |
| format | Article |
| id | doaj-art-441d1e89c51f40b0b60931ea34178a47 |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-441d1e89c51f40b0b60931ea34178a472025-02-02T23:06:08ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982024-01-01165210.26907/2541-7746.2023.2.153-16622Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached OscillatorD. M. Korosteleva0S. I. Solov’ev1Kazan State Power Engineering UniversityKazan Federal UniversityFor the problem of eigenvibrations of the shallow shell with an attached oscillator, a new symmetric variational statement in the Hilbert space was proposed. It was established that there exist a sequence of positive eigenvalues of finite multiplicity with a limit point at infinity and the corresponding complete orthonormal system of eigenvectors. The problem was approximated by the mesh scheme of the finite element method with Hermite finite elements. Theoretical error estimates for the approximate solutions were proved. The theoretical findings were verified by the results of numerical experiments.https://uzakufismat.elpub.ru/jour/article/view/23eigenvibrationshallow shelloscillatoreigenvalueeigenvectoreigenvalue problemfinite element methodhermite finite element |
| spellingShingle | D. M. Korosteleva S. I. Solov’ev Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator Учёные записки Казанского университета: Серия Физико-математические науки eigenvibration shallow shell oscillator eigenvalue eigenvector eigenvalue problem finite element method hermite finite element |
| title | Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator |
| title_full | Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator |
| title_fullStr | Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator |
| title_full_unstemmed | Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator |
| title_short | Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator |
| title_sort | mathematical modeling of eigenvibrations of the shallow shell with an attached oscillator |
| topic | eigenvibration shallow shell oscillator eigenvalue eigenvector eigenvalue problem finite element method hermite finite element |
| url | https://uzakufismat.elpub.ru/jour/article/view/23 |
| work_keys_str_mv | AT dmkorosteleva mathematicalmodelingofeigenvibrationsoftheshallowshellwithanattachedoscillator AT sisolovev mathematicalmodelingofeigenvibrationsoftheshallowshellwithanattachedoscillator |