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...

Full description

Saved in:
Bibliographic Details
Published in:Vestnik, St. Petersburg University. Mathematics St. Petersburg University. Mathematics, 2020-07, Vol.53 (3), p.351-357
Main Authors: Vasiliev, G. P., Smirnov, A. L.
Format: Article
Language:English
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
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
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