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Shock and Vibration
Volume 17, Issue 3, Pages 251-267
http://dx.doi.org/10.3233/SAV-2010-0510

Analytical Stationary Acoustic Wave in a Liquid over Which a Moving Pressure Runs

André Langlet, Jérôme Renard, and Olivier Pennetier

Institut PRISME/RES UPRES EA 4229, Université d'Orléans, 63, Avenue de Lattre de Tassigny, F-18020 Bourges Cedex, France

Received 10 April 2009; Revised 8 September 2009

Copyright © 2010 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents an analytical study of the stationary response of a liquid loaded on its free surface by an ideal pressure step moving in a constant direction at a constant velocity. The acoustic pressure in the liquid is found, in four different examples, by means of the Fourier Transform. Two loading regimes are considered; subsonic and supersonic. Two configurations of liquid domains are also studied, the first one is a half infinite space while the second one is bounded by a rigid bottom at a finite depth. For the two supersonic cases, a simple reasoning based on the existence of a front of discontinuity in the liquid and on the property of reflection of waves confirms the result of the mathematical investigations. The results obtained for the steady state case are of intererest, even when the loading is not exactly stationary, such as the presure produced by an explosion occurring in the vicinity of the surface of a liquid. Two numerically resolved examples are presented, which confirm this assumption.

For the two supersonic cases, a simple reasoning based on the existence of a front of discontinuity in the liquid and on the property of reflection of waves confirms the result of the mathematical investigations.

The results obtained for the steady state case are of intererest, even when the loading is not exactly stationary, such as the presure produced by an explosion occurring in the vicinity of the surface of a liquid. Two numerically resolved examples are presented, which confirm this assumption.