Dynamic version of Saint-Venant's principle—historical account and recent results

Abstract

Possible existence of a dynamic version of the quasi-static Saint-Venant's principle (DSVP) has been raised by Boley five decades ago. Since then, relatively few papers have been dedicated to the possible validity of a DSVP. These papers are reviewed in the first part of a present communication. An apparent observation is the absence of any consensus on whether there is a dynamic counterpart to the classical Saint-Venant's principle (SVP) with the same generality and validity. On the other hand, there is experimental support (and numerical simulations) regarded by several researchers as evidence for the existence and validity of a DSVP in conservative systems. Nevertheless, no coherent versions of SVP for dynamic problem in non-dissipative systems have been proposed, and those proposed, are proved to be not valid. The historical account emphasizes the apparent gap between the theoretical approach and the experimental insights. In the second part of the present communication a new definition of a dynamic version of SVP is suggested, bridging over the apparent gap between the theoretical approach and experimental insights. This is achieved by introducing the concept of “dynamically equivalent system of loads” analogous to the “statically equipollent system of loads” introduced by Saint-Venant.