Effects of higher-order deformations on in-plane vibration and stability of thick circular rings
type: Item
instance of: scholarly article
title: Effects of higher-order deformations on in-plane vibration and stability of thick circular rings
zbMATH Open document ID: 0911.73037
DOI: 10.1007/BF01213017
author: D. Massart
published in: Acta Mechanica
publication date: 1999-05-09T00:00:00Z
review text: To study the title problem, the author presents a one-dimensional higher-order theory based on the expansion of deformation into power series in normal coordinate. On the basis of this power series, a set of dynamic equations is derived through Hamilton's principle. Since the equations derived are very complex, approximate theories of various orders can be considered. For example, if the normal stress is zero we obtain the Timoshenko-type ring theory. Under the assumption of plane state of stresses in the depth direction, and assuming that the shear strain vanishes through the ring depth, the lowest-order approximate theory reduces to the classical ring theory. The one-dimensional higher-order theory developed by the author can predict natural frequencies and buckling stresses of a thick ring more accurately than the previously published ring theories.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74H55
zbMATH DE Number: 1143330
zbMATH Keywords: expansion of deformation into power series in normal coordinate
zbMATH Keywords: Hamilton's principle
zbMATH Keywords: natural frequencies
zbMATH Keywords: buckling stresses
reviewed by: Yuri N. Sankin
MaRDI profile type: Publication
cites work: In-plane vibration and stability of shallow circular arches subjected to axial forces
cites work: A general nonlinear theory of elastic shells
description: scientific article; zbMATH DE number 1143330