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Addendum to the paper ?two dimensional wave front shape induced in a homogeneously strained elastic body by a point perturbing body force?

Authors :
Robert G. Payton
Source :
Archive for Rational Mechanics and Analysis. 35:402-408
Publication Year :
1969
Publisher :
Springer Science and Business Media LLC, 1969.

Abstract

In a previous paper PAYTON [1] (hereafter referred to as WF for wave front) considered the shape of the two dimensional wave front induced in a finitely strained elastic body by an impulsive point body force. This problem was characterized by three parameters ct, fl and ~ which were dependent upon the initial strain and the constitutive relations for the material in question. For certain regions of the (~t, fl, ~) space it was shown that the wave front normal curve possessed inflection points and that the associated wave front curve carried cuspoidal triangles. In WF the wave front shape was classified by the number (and location) of normal curve inflection points. It was remarked (through a note added in proof) that the classification of cases n. 5, n. 8 and n. 13, where n = 1, 2, 3 and 4, was incomplete. In cases 1.8 and 4.8 (where ct =fl) and in cases 2.8 and 3.8 (where ctf l=l) this incompleteness was removed but the remaining eight cases were left open. It is now possible to complete this classification through a unified approach.

Details

ISSN :
14320673 and 00039527
Volume :
35
Database :
OpenAIRE
Journal :
Archive for Rational Mechanics and Analysis
Accession number :
edsair.doi...........55d64ecddd8685130b417ea87b152efa