On the dynamics of flexure and stretch in the theory of elastic rods
type: Item
instance of: scholarly article
title: On the dynamics of flexure and stretch in the theory of elastic rods
zbMATH Open document ID: 0872.73020
DOI: 10.1007/BF00379919
author: Bernard D. Coleman
author: David Swigon
author: Ellis H. Dill
published in: Archive for Rational Mechanics and Analysis
publication date: 1995-06-01T00:00:00Z
review text: A theory of planar motions of straight elastic rods is presented where the strains are assumed to remain small, although displacements and rotations may be large. It is a specialization of the Kirchhoff-Clebsch theory without the usual assumption of inextensibility, i.e., of temporal invariance of arc length. Its origin as an approximation to the theory of nonlinearly elastic slender bodies is discussed, various alternative formulations of the theory are presented, and a list of conservation laws is given. Then, after discussing the general theory of traveling waves, the authors analyze in detail solitary waves and noninflexional as well as inflexional waves. In particular, it is shown that under some conditions supersonic traveling-wave solutions may be rejected as inadmissible, i.e., not physically meaningful.
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 760205
zbMATH Keywords: straight rods
zbMATH Keywords: Kirchhoff-Clebsch theory
zbMATH Keywords: theory of nonlinearly elastic slender bodies
zbMATH Keywords: conservation laws
zbMATH Keywords: solitary waves
zbMATH Keywords: supersonic traveling-wave solutions
reviewed by: H. Antes
MaRDI profile type: Publication
cites work: Travelling waves in hyperelastic rods
cites work: Kirchhoff's theory of rods
cites work: On the dynamics of rods in the theory of Kirchhoff and Clebsch
cites work: Hamiltonian dynamics of an elastica and the stability of solitary waves
cites work: Conservation laws in the dynamics of rods
full work available at URL: https://doi.org/10.1007/bf00379919
OpenAlex ID: W1968672345
description: scientific article; zbMATH DE number 760205