Natural Frequencies of an Inhomogeneous Square Thin Plate

The purpose of the study is to analyze the inhomogeneity effect on the natural transverse vibrations of square thin plates using asymptotic methods, when the thickness and/or stiffness of the plate can be assumed almost constant. The results of calculations by asymptotic formulas, which are determin...

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Bibliographic Details
Published in:Vestnik, St. Petersburg University. Mathematics St. Petersburg University. Mathematics, 2021-04, Vol.54 (2), p.119-124
Main Authors: Vasiliev, G. P., Smirnov, A. L.
Format: Article
Language:English
Subjects:
Analysis
Asymptotic methods
Finite element method
Inhomogeneity
Mathematics
Mathematics and Statistics
Perturbation methods
Resonant frequencies
Stiffness
Thin plates
To the Memory of P. E. Tovstik
Transverse oscillation
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Summary:The purpose of the study is to analyze the inhomogeneity effect on the natural transverse vibrations of square thin plates using asymptotic methods, when the thickness and/or stiffness of the plate can be assumed almost constant. The results of calculations by asymptotic formulas, which are determined by the perturbation method, are compared with the numerical results obtained by the finite element method using the COMSOL software package.
ISSN:1063-4541
1934-7855
DOI:10.1134/S1063454121020138