Simple wave interaction of an elastic string

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Abstract

The equations for the two-dimensional motion of a completely flexible elastic string can be derived from a Lagrangian. The equations of motion possess four characteristic velocities, to which the following four simple wave solutions correspond: leftward and rightward propagating longitudinal and transverse waves. The latter are exceptional (constant shape). By expanding the solution about a steady solution the interaction of simple waves may be studied. A typical result is the following: As a consequence of their interaction two transverse waves running into opposite directions emit a longitudinal wave and undergo themselves a translation over a finite distance but remain otherwise unchanged. The results are also valuable for a full comprehension of the interaction process of simple waves on inextensible strings.
Original languageUndefined
Pages (from-to)161-168
JournalRheologica acta
Volume16
DOIs
Publication statusPublished - 1977

Keywords

  • IR-56157

Cite this

@article{f1e8d517060a4bf18c0681434c146bab,
title = "Simple wave interaction of an elastic string",
abstract = "The equations for the two-dimensional motion of a completely flexible elastic string can be derived from a Lagrangian. The equations of motion possess four characteristic velocities, to which the following four simple wave solutions correspond: leftward and rightward propagating longitudinal and transverse waves. The latter are exceptional (constant shape). By expanding the solution about a steady solution the interaction of simple waves may be studied. A typical result is the following: As a consequence of their interaction two transverse waves running into opposite directions emit a longitudinal wave and undergo themselves a translation over a finite distance but remain otherwise unchanged. The results are also valuable for a full comprehension of the interaction process of simple waves on inextensible strings.",
keywords = "IR-56157",
author = "L.J.F. Broer and {van Groesen}, {Embrecht W.C.}",
year = "1977",
doi = "10.1007/BF01527913",
language = "Undefined",
volume = "16",
pages = "161--168",
journal = "Rheologica acta",
issn = "0035-4511",
publisher = "Springer",

}

Simple wave interaction of an elastic string. / Broer, L.J.F.; van Groesen, Embrecht W.C.

In: Rheologica acta, Vol. 16, 1977, p. 161-168.

Research output: Contribution to journalArticleAcademic

TY - JOUR

T1 - Simple wave interaction of an elastic string

AU - Broer, L.J.F.

AU - van Groesen, Embrecht W.C.

PY - 1977

Y1 - 1977

N2 - The equations for the two-dimensional motion of a completely flexible elastic string can be derived from a Lagrangian. The equations of motion possess four characteristic velocities, to which the following four simple wave solutions correspond: leftward and rightward propagating longitudinal and transverse waves. The latter are exceptional (constant shape). By expanding the solution about a steady solution the interaction of simple waves may be studied. A typical result is the following: As a consequence of their interaction two transverse waves running into opposite directions emit a longitudinal wave and undergo themselves a translation over a finite distance but remain otherwise unchanged. The results are also valuable for a full comprehension of the interaction process of simple waves on inextensible strings.

AB - The equations for the two-dimensional motion of a completely flexible elastic string can be derived from a Lagrangian. The equations of motion possess four characteristic velocities, to which the following four simple wave solutions correspond: leftward and rightward propagating longitudinal and transverse waves. The latter are exceptional (constant shape). By expanding the solution about a steady solution the interaction of simple waves may be studied. A typical result is the following: As a consequence of their interaction two transverse waves running into opposite directions emit a longitudinal wave and undergo themselves a translation over a finite distance but remain otherwise unchanged. The results are also valuable for a full comprehension of the interaction process of simple waves on inextensible strings.

KW - IR-56157

U2 - 10.1007/BF01527913

DO - 10.1007/BF01527913

M3 - Article

VL - 16

SP - 161

EP - 168

JO - Rheologica acta

JF - Rheologica acta

SN - 0035-4511

ER -