Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator

D. M. Korosteleva, S. Solov’ev
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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.
附带振子的浅壳特征振动数学建模
针对附带振子的浅壳的特征振动问题,提出了一种新的希尔伯特空间对称变分法。研究证实,存在一串有限倍率的正特征值,其极限点位于无穷大,并存在相应的完整正交特征向量系统。该问题用有限元法的网格方案与 Hermite 有限元进行了近似。证明了近似解的理论误差估计值。数值实验结果验证了理论结论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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