Transverse decay of solutions in an elastic cylinder

R. J. Knops, P. Villaggio

Research output: Contribution to journalArticle

Abstract

In a semi-infinite cylinder composed of anisotropic linearised elastic material, loaded on the base and clamped along the lateral surface, it is known that the solution as measured, for example, by the strain-energy flux through a plane cross-section decays longitudinally at most exponentially with respect to the axial distance from the base. There is, however, also a transverse radial decay of the solution, again measured for example by the strain-energy, occurring from the region close to the cylinder's axis to the region near the lateral surface, where the energy vanishes. This problem is considered in the present paper which discusses a circular semi-infinite cylinder and derives an estimate for the strain-energy contained in a cylindrical annulus at a given distance from the base and of variable height, and whose outer surface coincides with the lateral surface of the cylinder. It is shown that the strain-energy decays at most algebraically to zero as the inner radius of the annulus increases to that of the cylinder.

Original languageEnglish
Pages (from-to)577-585
Number of pages9
JournalMeccanica
Volume33
Issue number6
DOIs
Publication statusPublished - Dec 1998

Fingerprint

elastic cylinders
decay
annuli
energy
radii
cross sections
estimates

Cite this

Knops, R. J. ; Villaggio, P. / Transverse decay of solutions in an elastic cylinder. In: Meccanica. 1998 ; Vol. 33, No. 6. pp. 577-585.
@article{f4b7a21d1e8946f39d6a7bf5af6a88c4,
title = "Transverse decay of solutions in an elastic cylinder",
abstract = "In a semi-infinite cylinder composed of anisotropic linearised elastic material, loaded on the base and clamped along the lateral surface, it is known that the solution as measured, for example, by the strain-energy flux through a plane cross-section decays longitudinally at most exponentially with respect to the axial distance from the base. There is, however, also a transverse radial decay of the solution, again measured for example by the strain-energy, occurring from the region close to the cylinder's axis to the region near the lateral surface, where the energy vanishes. This problem is considered in the present paper which discusses a circular semi-infinite cylinder and derives an estimate for the strain-energy contained in a cylindrical annulus at a given distance from the base and of variable height, and whose outer surface coincides with the lateral surface of the cylinder. It is shown that the strain-energy decays at most algebraically to zero as the inner radius of the annulus increases to that of the cylinder.",
author = "Knops, {R. J.} and P. Villaggio",
year = "1998",
month = "12",
doi = "10.1023/A:1004343004833",
language = "English",
volume = "33",
pages = "577--585",
journal = "Meccanica",
issn = "0025-6455",
publisher = "Springer",
number = "6",

}

Transverse decay of solutions in an elastic cylinder. / Knops, R. J.; Villaggio, P.

In: Meccanica, Vol. 33, No. 6, 12.1998, p. 577-585.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Transverse decay of solutions in an elastic cylinder

AU - Knops, R. J.

AU - Villaggio, P.

PY - 1998/12

Y1 - 1998/12

N2 - In a semi-infinite cylinder composed of anisotropic linearised elastic material, loaded on the base and clamped along the lateral surface, it is known that the solution as measured, for example, by the strain-energy flux through a plane cross-section decays longitudinally at most exponentially with respect to the axial distance from the base. There is, however, also a transverse radial decay of the solution, again measured for example by the strain-energy, occurring from the region close to the cylinder's axis to the region near the lateral surface, where the energy vanishes. This problem is considered in the present paper which discusses a circular semi-infinite cylinder and derives an estimate for the strain-energy contained in a cylindrical annulus at a given distance from the base and of variable height, and whose outer surface coincides with the lateral surface of the cylinder. It is shown that the strain-energy decays at most algebraically to zero as the inner radius of the annulus increases to that of the cylinder.

AB - In a semi-infinite cylinder composed of anisotropic linearised elastic material, loaded on the base and clamped along the lateral surface, it is known that the solution as measured, for example, by the strain-energy flux through a plane cross-section decays longitudinally at most exponentially with respect to the axial distance from the base. There is, however, also a transverse radial decay of the solution, again measured for example by the strain-energy, occurring from the region close to the cylinder's axis to the region near the lateral surface, where the energy vanishes. This problem is considered in the present paper which discusses a circular semi-infinite cylinder and derives an estimate for the strain-energy contained in a cylindrical annulus at a given distance from the base and of variable height, and whose outer surface coincides with the lateral surface of the cylinder. It is shown that the strain-energy decays at most algebraically to zero as the inner radius of the annulus increases to that of the cylinder.

UR - http://www.scopus.com/inward/record.url?scp=0032318326&partnerID=8YFLogxK

U2 - 10.1023/A:1004343004833

DO - 10.1023/A:1004343004833

M3 - Article

VL - 33

SP - 577

EP - 585

JO - Meccanica

JF - Meccanica

SN - 0025-6455

IS - 6

ER -