Free Vibration Frequencies of a Circular Thin Plate with Variable Parameters

We study transverse vibrations of an inhomogeneous circular thin plate in this work. Using the perturbation method, asymptotic formulas are obtained for free-vibration frequencies of a plate whose thickness and Young’s modulus linearly depend on radius. The effect of the boundary conditions on frequ...

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Bibliographic Details
Published inVestnik, St. Petersburg University. Mathematics Vol. 53; no. 3; pp. 351 - 357
Main Authors Vasiliev, G. P., Smirnov, A. L.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.07.2020
Springer Nature B.V
Subjects
Analysis
Asymptotic methods
Asymptotic properties
Boundary conditions
Finite element method
Free vibration
Mathematics
Mathematics and Statistics
Mechanics
Modulus of elasticity
Perturbation methods
Thin plates
Transverse oscillation
free vibrations of plates
perturbation method
inhomogeneous circular plate
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Summary:We study transverse vibrations of an inhomogeneous circular thin plate in this work. Using the perturbation method, asymptotic formulas are obtained for free-vibration frequencies of a plate whose thickness and Young’s modulus linearly depend on radius. The effect of the boundary conditions on frequencies and the behavior of frequencies for a plate with the fixed mass are analyzed. For lower frequencies of the plate, the asymptotic results are compared with the results of analysis by finite elements.
ISSN:1063-4541
1934-7855
DOI:10.1134/S1063454120030140