Geodesic
Self-similar waves in media with bimodular elastic nonlinearity and relaxation
Russian journal of nonlinear dynamics, Tome 11 (2015) no. 2, pp. 209-218.

Voir la notice de l'article provenant de la source Math-Net.Ru

The results of research of the propagation of longitudinal acoustic waves in media with bimodular elastic nonlinearity and relaxation are presented. Analytical exact solutions have been obtained for the profiles of asymmetrical stationary waves as well as self-similar pulses and periodical waves propagating without distortions in their form.
Keywords: bimodular nonlinearity, relaxation, nonlinear waves, self-similar solutions. 
@article{ND_2015_11_2_a1,
     author = {V. E. Nazarov and S. B. Kiyashko and A. V. Radostin},
     title = {Self-similar waves in media with bimodular elastic nonlinearity and relaxation},
     journal = {Russian journal of nonlinear dynamics},
     pages = {209--218},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2015_11_2_a1/}
}
TY  - JOUR
AU  - V. E. Nazarov
AU  - S. B. Kiyashko
AU  - A. V. Radostin
TI  - Self-similar waves in media with bimodular elastic nonlinearity and relaxation
JO  - Russian journal of nonlinear dynamics
PY  - 2015
SP  - 209
EP  - 218
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2015_11_2_a1/
LA  - ru
ID  - ND_2015_11_2_a1
ER  - 
%0 Journal Article
%A V. E. Nazarov
%A S. B. Kiyashko
%A A. V. Radostin
%T Self-similar waves in media with bimodular elastic nonlinearity and relaxation
%J Russian journal of nonlinear dynamics
%D 2015
%P 209-218
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2015_11_2_a1/
%G ru
%F ND_2015_11_2_a1
V. E. Nazarov; S. B. Kiyashko; A. V. Radostin. Self-similar waves in media with bimodular elastic nonlinearity and relaxation. Russian journal of nonlinear dynamics, Tome 11 (2015) no. 2, pp. 209-218. http://geodesic.mathdoc.fr/item/ND_2015_11_2_a1/

[1] Rudenko O. V., Soluyan S. I., Teoreticheskie osnovy nelineinoi akustiki, Nauka, Moskva, 1975, 288 pp.

[2] Landau L. D., Lifshits E. M., Teoreticheskaya fizika: V 10 tt. T. 6: Gidrodinamika, 5-e izd., Fizmatlit, Moskva, 2006, 736 pp.

[3] Naugolnykh K. A., Ostrovskii L. A., Nelineinye volnovye protsessy v akustike, Nauka, Moskva, 1990, 237 pp.

[4] Pischalnikov Yu. A., Sapozhnikov O. A., Khokhlova V. A., “Modifikatsiya spektralnogo podkhoda k opisaniyu nelineinykh akusticheskikh voln s razryvami”, Akust. zhurn., 42:3 (1996), 412–417

[5] Landau L. D., Lifshits E. M., Teoreticheskaya fizika: V 10 tt.: T. 7: Teoriya uprugosti, 5-e izd., Fizmatlit, Moskva, 2003, 264 pp.

[6] Ambartsumyan S. A., Raznomodulnaya teoriya uprugosti, Nauka, Moskva, 1982, 359 pp.

[7] Nikolaev A. V., “Seismicheskie svoistva rykhlykh sred”, Izv. AN SSSR Ser. Fizika Zemli, 1979, no. 1, 72–77

[8] Aleshin A. S., Kuznetsov V. V., “O parametrakh nelineinosti gruntov”, Nelineinaya seismologiya: Mezhdunar. simp.: Tez. dokl., Nauka, Moskva, 1986, 4 pp.

[9] Bagmet A. L., Nazarov V. E., Nikolaev A. V., “Staticheskaya deformatsiya zemnoi poverkhnosti vblizi garmonicheskogo istochnika seismicheskikh kolebanii”, Izv. AN SSSR. Ser. Fizika Zemli, 1996, no. 7, 72–74

[10] Maslov V. P., Mosolov P. P., “Obschaya teoriya reshenii uravneniya dvizheniya raznomodulnoi uprugoi sredy”, PMTF, 49:3 (1985), 419–437

[11] Nazarov V. E., Ostrovskii L. A., “Uprugie volny v sredakh s silnoi akusticheskoi nelineinostyu”, Akust. zhurn., 36:1 (1990), 106–110

[12] Gavrilov S. N., Herman G. C., “Wave propagation in a semi-infinite heteromodular elastic bar subjected to a harmonic loading”, J. Sound Vibration, 331 (2012), 4464–4480

[13] Radostin A. V., Nazarov V. E., Kiyashko S. B., “Propagation of nonlinear acoustic waves in bimodular media with linear dissipation”, Wave Motion, 50:2 (2013), 191–196

[14] Nazarov V. E., Radostin A. V., Nelineinye volnovye protsessy v uprugikh mikroneodnorodnykh sredakh, IPF RAN, Nizhnii Novgorod, 2007, 254 pp.

[15] Ryskin N. M., Trubetskov D. I., Nelineinye volny, Nauka, Moskva, 2000, 272 pp.