Self-switching of displacement waves in elastic nonlinearly deformed materials

Jeremiah Rushchitsky

doi:10.1016/S1631-0721(02)01444-4

Self-switching of displacement waves in elastic nonlinearly deformed materials
[Self-commutation d'ondes de déplacement dans les milieux élastiques non-linéaires]

Jeremiah Rushchitsky ¹

¹ S.P. Timoshenko Institute of Mechanics, Nesterov str. 3, Kyiv, 03680, Ukraine

Comptes Rendus. Mécanique, Volume 330 (2002) no. 3, pp. 175-180.

Résumé
Abstract

Nous formulons le problème de self-commutation d'ondes dans des matériaux élastiques déformés non linéairement. Nous déduisons les équations d'évolution complètes et réduites décrivant l'interaction entre deux ondes, l'onde de pompage et une onde faible transportant le signal. Dans le cas de nombres d'onde concordants entre l'onde de pompage et l'onde-signal, on décrit la procédure de construction de la solution exacte aux équations d'évolution. Cette solution s'exprime en termes de fonctions elliptiques de Jacobi. On montre l'existence de la self-commutation de l'onde de pompage et on commente le résultat.

The problem of self-switching plane waves in elastic nonlinearly deformed materials is formulated. Reduced and evolution equations, which describe the interaction of two waves the power pumping wave and the faint signal wave are obtained. For the case of wave numbers matching the pumping and signal waves, a procedure of finding the exact solution of evolution equations is described. The solution is expressed by elliptic Jacobi functions. The existence of the power wave self-switching is shown and commented.

Reçu le : 2001-07-30
Révisé le : 2001-12-26
Publié le : 2002-01-01

DOI : 10.1016/S1631-0721(02)01444-4

Keywords: acoustique, ondes, interaction de deux ondes, self-commutation des ondes
Mot clés : acoustics, waves, two waves interaction, self-switching of waves

Affiliations des auteurs :

Jeremiah Rushchitsky ¹

¹ S.P. Timoshenko Institute of Mechanics, Nesterov str. 3, Kyiv, 03680, Ukraine

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     title = {Self-switching of displacement waves in elastic nonlinearly deformed materials},
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     pages = {175--180},
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Jeremiah Rushchitsky. Self-switching of displacement waves in elastic nonlinearly deformed materials. Comptes Rendus. Mécanique, Volume 330 (2002) no. 3, pp. 175-180. doi : 10.1016/S1631-0721(02)01444-4. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01444-4/

Bibliographie
Cité par

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