On Saint-Venant's principle in linear elastodynamics
type: Item
instance of: scholarly article
title: On Saint-Venant's principle in linear elastodynamics
zbMATH Open document ID: 0891.73010
DOI: 10.1007/BF00041790
published in: Journal of Elasticity
publication date: 1998-07-19T00:00:00Z
review text: The authors use the displacement characterization of linear elastodynamics for a nonhomogeneous anisotropic semi-infinite cylinder subject to homogeneous initial conditions and loaded on its plane end only (or for a long body whose boundary includes a loaded plane) in order to obtain space-time estimates for measure of energy of a portion of the cylinder beyond a distance \(z\) from the load region. Additionally, they establish an analogue of the Phragmén-Lindelöf principle for a cone-shaped semi-infinite homogeneous isotropic elastic body whose boundary includes a plane perpendicular to the cone-axis subject to a harmonically vibrating load. The reviewer remarks: (i) The authors are not aware of a dynamic pure-stress version of Saint-Venant principle formulated previously by the reviewer [cf. \([*]\) \textit{J. Ignaczak}, Bull. Acad. Polon. Sci., Sér. Sci. Tech., 22, 483-489 (1974; Zbl 0288.73010)]. In particular, the inequalities (2.18) in \([*]\) make a counterpart to the inequalities of theorem 2.1 by the authors. The inequality (2.16) by the authors with \(z_0= 0\), \(t_0>0\) can be obtained from the inequality (2.3) in \([*]\) by letting \(z= l\), \(t= t_0- z/c\), and by postulating a correspondence between the stress and displacement energies. (ii) The estimate (2.52) combined with (2.42) is not a genuine dynamic estimate, since the end load, by virtue of (2.51), belongs to a class of statically self-equilibrated tractions for every time \(t\geq 0\).
reviewed by: Józef Ignaczak
Mathematics Subject Classification ID: 74G50
Mathematics Subject Classification ID: 74B05
zbMATH DE Number: 1022663
zbMATH Keywords: analogue of Phragmén-Lindelöf principle
zbMATH Keywords: nonhomogeneous anisotropic semi-infinite cylinder
zbMATH Keywords: space-time estimates
zbMATH Keywords: measure of energy
zbMATH Keywords: cone-shaped semi-infinite homogeneous isotropic elastic body
author: S. Chiriţă
author: Ramón Quintanilla
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1022663