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On the Propagation of Shock Waves through Elastic Solids1

By
E. B. Christoffel
E. B. Christoffel
Strassburg
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Published:
January 01, 2007

Abstract

1. In the present treatise, I will apply the principles developed in my previous work (page 81 of this volume) to the propagation of shock waves in elastic solids. I begin with some preliminary remarks on how the phenomena to be developed here are to be understood, because the following analysis cannot be allowed to suffer from any ambiguity on this point.

I consider a homogeneous elastic body free of external forces in equilibrium and denote for this case by xyz the orthogonal coordinates of one of its constituent particles m, by ρ the constant density, by ℜ its volume, and by forumla its surface area. If the equilibrium of the body is disturbed, then as usual, I will represent the coordinates of the particular particle m at time t by x + u, y + v, and z + w. The variables uvw, the displacement components of m, will be interpreted as functions of txyz; that is, they will be associated with points xyz of the volume ℜ at rest, so that at each point in time t, these determine the actual position of the particle m whose equilibrium coordinates are xyz.

We accordingly restrict all the phenomena to be investigated here to this volume at rest ℜ and its surface forumla. In particular, for the propagation of shock waves, the surface of discontinuity at time t will not be defined as the actual surface which describes the dis-continuity occurring at this time.

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Contents

Society of Exploration Geophysicists Geophysics Reprint Series

Classics of Elastic Wave Theory

Michael A. Pelissier
Michael A. Pelissier
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Henning Hoeber
Henning Hoeber
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Norbert van de Coevering
Norbert van de Coevering
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Ian F. Jones
Ian F. Jones
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Society of Exploration Geophysicists
Volume
24
ISBN electronic:
9781560801931
Publication date:
January 01, 2007

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