Simple wave interaction of an elastic string

L.J.F. Broer, E.W.C. van Groesen

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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 languageEnglish
Pages (from-to)161-168
Number of pages8
JournalRheologica Acta
Volume16
Issue number2
DOIs
Publication statusPublished - 1977

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    Broer, L. J. F., & van Groesen, E. W. C. (1977). Simple wave interaction of an elastic string. Rheologica Acta, 16(2), 161-168. https://doi.org/10.1007/BF01527913