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Book Chapter

On the Laws of Equilibrium and Motion of Elastic Solid Bodies

By
M. Navier
M. Navier
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Published:
January 01, 2007

Abstract

1) If one considers an elastic body, and supposing that forces are applied to points of this body and that these are in mutual equilibrium, one may ask what changes the shape of the body has undergone as a result of the action of these forces. One may also ask, supposing that after the change in shape the body is released, what are the laws of the oscillatory motion which occur as a result of the forces which constitute elasticity.

The solution to these questions is composed of two parts: (1) the search for the differential equations which express the laws of the equilibrium or of the motion and (2) the integration of these equations. The search for the differential equations is the objective of this memoir. This must be founded on an exact understanding of the nature of those forces because of which a body is elastic, and of the internal structure of this body.

One considers an elastic solid body as a collection of material molecules positioned at very small distances. These molecules exert on one another two opposing actions, to wit, an intrinsic force of attraction and a force of repulsion resulting from the principle of heat. Between a molecule M and any neighboring molecule M′ there exists an action P, which is the difference between those two forces. In the initial state of the body, all the actions P are null or reciprocally cancel each other out, because the molecule M is at rest. When the

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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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