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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Kazan Federal University
2024-01-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/23 |
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| Summary: | 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. |
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| ISSN: | 2541-7746 2500-2198 |