Finite element modeling of the eigenvibrations of the square plate with attached oscillator
https://doi.org/10.26907/0021-3446-2023-11-92-97
Abstract
For the problem on eigenvibrations of the plate with an attached oscillator, the new symmetric linear variational statement is proposed. It is established the existence of the sequence of positive eigenvalues of finite multiplicity with limit point at infinity and the corresponding complete orthonormal system of eigenvectors. The new symmetric scheme of the finite element method with Hermite finite elements is formulated. Error estimates consistent with the solution smoothness for the approximate eigenvalues and approximate eigenvectors are proved. The results of numerical experiments illustrating the influence of the solution smoothness on the computation accuracy are presented.
About the Authors
D. M. Korosteleva
Kazan State Power Engineering University
Russian Federation
Russian Federation
Diana Maratovna Korosteleva
51 Krasnoselskaya str., Kazan, 420066
S. I. Solov’ev
Kazan Federal University
Russian Federation
Russian Federation
Sergey Ivanovich Solov’ev
18 Kremlevskaya str., Kazan, 420008
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Review
For citations:
Korosteleva D.M., Solov’ev S.I. Finite element modeling of the eigenvibrations of the square plate with attached oscillator. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2023;(11):92-97. (In Russ.) https://doi.org/10.26907/0021-3446-2023-11-92-97
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