Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator
https://doi.org/10.26907/2541-7746.2023.2.153-166
Abstract
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.
Keywords
eigenvibration,
shallow shell,
oscillator,
eigenvalue,
eigenvector,
eigenvalue problem,
finite element method,
Hermite finite element
Supporting agencies: This study was supported by the Kazan Federal University Strategic Academic Leadership Program (PRIORITY-2030).
About the Authors
D. M. Korosteleva
Kazan State Power Engineering University
Russian Federation
Russian Federation
Kazan, 420066
S. I. Solov’ev
Kazan Federal University
Russian Federation
Russian Federation
Kazan, 420008
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Review
For citations:
Korosteleva D.M., Solov’ev S.I. Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2023;165(2):153–166. (In Russ.) https://doi.org/10.26907/2541-7746.2023.2.153-166
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