An asymptotic analysis of the dispersion relation of a prestressed incompressible elastic plate
type: Item
instance of: scholarly article
title: An asymptotic analysis of the dispersion relation of a prestressed incompressible elastic plate
zbMATH Open document ID: 0859.73021
DOI: 10.1007/BF01187727
author: Graham A. Rogerson
author: Yibin Fu
published in: Acta Mechanica
publication date: 1997-04-09T00:00:00Z
review text: The interest in the wave propagation in prestressed incompressible elastic plates has been growing with the advent of fibre-reinforced composites. This paper gives an analysis of the asymptotic behaviour of the dispersion relation (i.e. an algebraic relation involving the wave speed, the wave number, and a parameter characterizing the prestress) for such structures. Some important conclusions are derived: a) the fundamental modes (both symmetric and antisymmetric) tend to the associated Rayleigh surface mode; b) while the lower modes are very sensitive to prestress changes, the higher harmonics are very little affected; c) in the linear theory (the present one being such) an instability phenomenon can appear. The last effect provides an exponential growth, so that future studies in this area have to be corrected by taking into account the inherent nonlinearity of the elastic field for finite amplitude displacements. We think the paper brings a basic contribution to the area of wave propagation in prestressed plates.
Mathematics Subject Classification ID: 74J10
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 923807
zbMATH Keywords: fundamental modes
zbMATH Keywords: Rayleigh surface mode
zbMATH Keywords: lower modes
zbMATH Keywords: higher harmonics
zbMATH Keywords: linear theory
zbMATH Keywords: instability
reviewed by: Dumitru Stanomir
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01187727
OpenAlex ID: W2011897014
description: scientific article; zbMATH DE number 923807