Free vibrations of small-scale plates with complex shape based on the nonlocal elasticity theory
type: Item
instance of: scholarly article
title: Free vibrations of small-scale plates with complex shape based on the nonlocal elasticity theory
zbMATH Open document ID: 1506.74140
author: Lidiya Kurpa
author: Olga Mazur
author: Iryna Morachkovska
author: Jan Awrejcewicz
published in: Acta Mechanica
publication date: 2022-11-04T00:00:00Z
review text: In the present paper, vibrations of orthotropic nano/microplates of complex shapes are studied. The governing equations are based on the Kirchhoff-Love hypothesis, and the nonlocal theory is used to take into account small-scale effects. The proposed approach uses a variational statement in combination with the Ritz method. A coordinate system is constructed based on the R-functions theory. Plates of various geometric shapes as well as the influence of different types of boundary conditions are studied. The proposed method is applied to the study of an orthotropic plate with two cutouts. The linear frequencies are obtained for a rectangular plate with two cutouts on opposite sides, while the boundary conditions are considered of several types, including simply supported and clamped edges. The small-scale effects for various sizes of cutouts are discussed.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K20
zbMATH DE Number: 7612115
zbMATH Keywords: Ritz method
zbMATH Keywords: orthotropic Kirchhoff-Love nanoplate
zbMATH Keywords: R-function theory
reviewed by: Girish Kumar Ramaiah
MaRDI profile type: Publication
full work available at URL: s00707-022-03361-w
OpenAlex ID: W4304193876
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DOI: 10.1007/S00707-022-03361-W
description: scientific article; zbMATH DE number 7612115