Natural frequencies of an inhomogeneous square thin plate
type: Item
instance of: scholarly article
title: Natural frequencies of an inhomogeneous square thin plate
zbMATH Open document ID: 1475.74062
DOI: 10.1134/S1063454121020138
author: G. P. Vasiliev
author: Andreĭ Leonidovich Smirnov
published in: Vestnik St. Petersburg University. Mathematics
publication date: 2021-08-20T00:00:00Z
review text: The purpose of this paper 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 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 finite element method using the COMSOL software package. The objective of the study is to obtain asymptotic formulas describing the effect of inhomogeneity of a thin plate thickness or stiffness parameters on its natural frequencies. In the study, it is assumed that the geometric and physical parameters of the plate are smooth functions of coordinates, constant in one direction and close to constant in the other. The asymptotic formulas make it possible to determine, which of the two multiple frequencies corresponding to wave numbers \(n\) and \(m\) varies faster with the variations of the small parameter. Only the homogeneous boundary conditions at the plate edges (\(\xi^* = 0\) or \(\xi^*=1\)) of the simply supported (S) or clamped (C) type are considered in this paper.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74H10
Mathematics Subject Classification ID: 74E05
zbMATH DE Number: 7384027
zbMATH Keywords: asymptotic perturbation method
zbMATH Keywords: rectangular plate
zbMATH Keywords: linearly varying thickness
zbMATH Keywords: finite element COMSOL software package
reviewed by: Girish Kumar Ramaiah
MaRDI profile type: Publication
cites work: Numerical and experimental analysis of natural vibrations of rectangular plates of variable thickness.
cites work: Vibration analysis of moderate-thick plates with slowly varying thickness
cites work: Asymptotic methods in mechanics of solids
cites work: Free vibration frequencies of a circular thin plate with variable parameters
full work available at URL: s1063454121020138
OpenAlex ID: W4285476277
description: scientific article; zbMATH DE number 7384027