Geodesic
Evolution of Pulse and Periodic Elastic Waves in Media with Quadratically-Bimodular Nonlinearity
Russian journal of nonlinear dynamics, Tome 14 (2018) no. 3, pp. 331-342.

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

On the basis of the elastic contact model of rough surfaces of solids, a quadraticallybimodular equation of state for micro-inhomogeneous media containing cracks is derived. A study is made of the propagation of elastic single unipolar pulse perturbations and bipolar periodic waves in such media. Exact analytical solutions that describe the evolution of initially triangular pulses and periodic sawtooth waves are obtained. A numerical and graphical analysis of the solutions is also carried out.
Keywords: elastic contact, quadratically-bimodular nonlinearity, periodic waves.
Mots-clés : pulse perturbation 
@article{ND_2018_14_3_a3,
     author = {V. E. Nazarov and S. B. Kiyashko},
     title = {Evolution of {Pulse} and {Periodic} {Elastic} {Waves} in {Media} with {Quadratically-Bimodular} {Nonlinearity}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {331--342},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2018_14_3_a3/}
}
TY  - JOUR
AU  - V. E. Nazarov
AU  - S. B. Kiyashko
TI  - Evolution of Pulse and Periodic Elastic Waves in Media with Quadratically-Bimodular Nonlinearity
JO  - Russian journal of nonlinear dynamics
PY  - 2018
SP  - 331
EP  - 342
VL  - 14
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2018_14_3_a3/
LA  - en
ID  - ND_2018_14_3_a3
ER  - 
%0 Journal Article
%A V. E. Nazarov
%A S. B. Kiyashko
%T Evolution of Pulse and Periodic Elastic Waves in Media with Quadratically-Bimodular Nonlinearity
%J Russian journal of nonlinear dynamics
%D 2018
%P 331-342
%V 14
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2018_14_3_a3/
%G en
%F ND_2018_14_3_a3
V. E. Nazarov; S. B. Kiyashko. Evolution of Pulse and Periodic Elastic Waves in Media with Quadratically-Bimodular Nonlinearity. Russian journal of nonlinear dynamics, Tome 14 (2018) no. 3, pp. 331-342. http://geodesic.mathdoc.fr/item/ND_2018_14_3_a3/

[1] Landau, L. D. and Lifshitz, E. M., Course of Theoretical Physics: In 10 Vols., v. 6, Fluid Mechanics, 2nd ed., Butterworth-Heinemann, Oxford, 2003, 552 pp. | MR

[2] Rudenko, O. V. and Soluyan, S. I., Theoretical Foundations of Nonlinear Acoustics, Springer, New York, 2013, 274 pp. | MR

[3] Naugolnykh, K. A. and Ostrovsky, L. A., Nonlinear Wave Processes in Acoustics, Cambridge Texts Appl. Math., Cambridge Univ. Press, Cambridge, 1998, 312 pp. | MR | Zbl

[4] Ryskin, N. M. and Trubezkov, D. I., Nonlinear Waves, Fizmatlit, Moscow, 2000, 272 pp. (Russian)

[5] Isakovich, M. A., General Acoustics, Nauka, Moscow, 1973, 496 pp. (Russian)

[6] Guyer, R. A. and Johnson, P. A., Nonlinear Mesoscopic Elasticity: Behaviour of Granular Media including Rocks and Soil, Wiley/VCH, Weinheim, 2009, 410 pp.

[7] Nazarov, V. E. and Radostin, A. V., Nonlinear Acoustic Waves in Micro-Inhomogeneous Solids, Wiley, Chichester, 2015, 264 pp.

[8] Inzh. Zh. Mekh. Tverd. Tela, 1966, no. 6, 64–67 (Russian) | MR

[9] Beresnev, I. A. and Nikolaev, A. V., “Experimental Investigations of Nonlinear Seismic Effects”, Phys. Earth Planet. Inter., 50:1 (1988), 83–87 | DOI

[10] Benveniste, Y., “One-Dimensional Wave Propagation in Materials with Different Moduli in Tension and Compression”, Int. J. Eng. Sci., 18:6 (1980), 815–827 | DOI | MR | Zbl

[11] Prikl. Mat. Mekh., 49:3 (1985), 419–437 | DOI | MR | Zbl

[12] Akust. Zh., 35:4 (1989), 711–716

[13] Akust. Zh., 36:1 (1990), 106–110 (Russian)

[14] Gavrilov, S. N. and Herman, G. C., “Wave Propagation in a Semi-Infinite Heteromodular Elastic Bar Subjected to a Harmonic Loading”, J. Sound Vibration, 331:20 (2012), 4464–4480 | DOI

[15] Radostin, A., Nazarov, V., and Kiyashko, S., “Propagation of Nonlinear Acoustic Waves in Bimodular Media with Linear Dissipation”, Wave Motion, 50:2 (2013), 191–196 | DOI | MR | Zbl

[16] Nazarov, V. E., Kiyashko, S. B., and Radostin, A. V., “Self-Similar Waves in Media with Bimodular Elastic Nonlinearity and Relaxation”, Nelin. Dinam., 11:2 (2015), 209–218 (Russian) | DOI | Zbl

[17] Izv. Vyssh. Uchebn. Zaved. Radiofizika, 59:3 (2016), 275–285 (Russian) | DOI | MR

[18] Dokl. Akad. Nauk, 474:6 (2017), 671–674 (Russian) | DOI | MR | Zbl

[19] Dokl. Akad. Nauk, 471:6 (2016), 651–654 (Russian) | DOI | MR | Zbl

[20] Hedberg, C. M. and Rudenko, O. V., “Collisions, Mutual Losses and Annihilation of Pulses in a Modular Nonlinear Medium”, Nonlinear Dynam., 90:3 (2017), 2083–2091 | DOI | MR

[21] Nazarov, V. E. and Sutin, A. M., “Nonlinear elastic constants of solids with cracks”, J. Acoust. Soc. Am., 102:6 (1997), 3349–3354 | DOI

[22] Johnson, K. L., Contact Mechanics, Cambridge Univ. Press, Cambridge, 1985, 468 pp. | Zbl

[23] Sneddon, I. N., Fourier Transformations, McGraw-Hill, New York, 1951, 542 pp. | MR

[24] Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, 3rd ed., McGraw-Hill, New York, 1970, 591 pp. | MR | Zbl

[25] Landau, L. D. and Lifshitz, E. M., Course of Theoretical Physics: Vol. 7. Theory of Elasticity, 3rd ed., Butterworth/Heinemann, Oxford, 1986, 195 pp. | MR

[26] Mathews, J. and Walker, R. L., Mathematical Methods of Physics, 2nd ed., Addison-Wesley, Reading, Mass., 1971, 501 pp.