Comptes Rendus
no. 3
Self-switching of displacement waves in elastic nonlinearly deformed materials
[Self-commutation d'ondes de déplacement dans les milieux élastiques non-linéaires]
Jeremiah Rushchitsky1
1 S.P. Timoshenko Institute of Mechanics, Nesterov str. 3, Kyiv, 03680, Ukraine
Comptes Rendus. Mécanique, Volume 330 (2002) no. 3, pp. 175-180.

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 :
Révisé le :
Publié le :
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
Jeremiah Rushchitsky 1

1 S.P. Timoshenko Institute of Mechanics, Nesterov str. 3, Kyiv, 03680, Ukraine 
@article{CRMECA_2002__330_3_175_0,
     author = {Jeremiah Rushchitsky},
     title = {Self-switching of displacement waves in elastic nonlinearly deformed materials},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {175--180},
     publisher = {Elsevier},
     volume = {330},
     number = {3},
     year = {2002},
     doi = {10.1016/S1631-0721(02)01444-4},
     language = {en},
}
TY  - JOUR
AU  - Jeremiah Rushchitsky
TI  - Self-switching of displacement waves in elastic nonlinearly deformed materials
JO  - Comptes Rendus. Mécanique
PY  - 2002
SP  - 175
EP  - 180
VL  - 330
IS  - 3
PB  - Elsevier
DO  - 10.1016/S1631-0721(02)01444-4
LA  - en
ID  - CRMECA_2002__330_3_175_0
ER  - 
%0 Journal Article
%A Jeremiah Rushchitsky
%T Self-switching of displacement waves in elastic nonlinearly deformed materials
%J Comptes Rendus. Mécanique
%D 2002
%P 175-180
%V 330
%N 3
%I Elsevier
%R 10.1016/S1631-0721(02)01444-4
%G en
%F CRMECA_2002__330_3_175_0
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/

[1] J.J. Rushchitsky Nonlinear waves in solid mixtures (review), Internat. Appl. Mech., Volume 33 (1997) no. 1, pp. 3-38

[2] J.J. Rushchitsky Interaction of waves in solid mixtures, Appl. Mech. Rev., Volume 52 (1999) no. 2, pp. 35-74

[3] J.J. Rushchitsky Extension of the microstructural theory of two-phase mixtures to composite materials (review), Internat. Appl. Mech., Volume 36 (2000) no. 5, pp. 586-614

[4] N. Bloembergen Nonlinear Optics. A Lecture Note, Benjamin, New York, 1965

[5] A. Yariv Quantum Electronics, Wiley, New York, 1967

[6] M. Schubert; B. Wilgelmi Einfuhrung in der nichtlineare Optik, Teil I, Klassische Beschreibung, Teubner, Leipzig, 1971

[7] A.A. Maier Experimental observation of the optical self-switching of unidirectional distributively coupled waves (review), Progr. Phys. Sci., Volume 166 (1996) no. 11, pp. 1171-1196 (in Russian)

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Signed symmetric covariation coefficient for alpha-stable dependence modeling

Bernard Garel; Bernédy Kodia

C. R. Math (2009)

Exact controllability for systems describing plate vibrations. A perturbation approach

Marius Tucsnak; Megane Bournissou; Sylvain Ervedoza

C. R. Math (2024)