The dynamic deformation of three-component porous media

Victor S. Polenov   ; Lyubov A. Kukarskikh   ; Dmitry A. Nitsak

Ural mathematical journal, Tome 6 (2020) no. 1, pp. 130-136

Résumé

A mathematical model of the dynamic deformation of three-component elastic media saturated with liquid and gas, given by elastic moduli and coefficients characterizing the porosity and compressibility of the liquid and gas, is considered. Formulas for determining the propagation velocity of monochromatic waves in ternary porous media are obtained. The existence of three longitudinal waves depends on the discriminant of a cubic equation and the velocity ratio.

Détail

Keywords: Elasticity, Medium, Fluid, Stress, Deformation, Displacement.

Bibliographie

[1] Biot M. A., “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-Frequency Range”, J. Acoust. Soc. America, 28:2 (1956), 168–178 | DOI | MR

[2] Biot M. A., “Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher Frequency Range”, J. Acoust. Soc. America, 28:2 (1956), 179–191 | DOI | MR

[3] Biot M. A., “Mechanics of deformation and acoustic propagation in porous media”, J. Appl. Phys., 33:4 (1962), 1483–1498 | DOI | MR

[4] Bronstein K. A., Semendyaev I. N., Spravochnik po matematike dlya inzhenerov i uchashchihsya vtuzov [Maths Reference for Engineers and University Students], Moscow, 1964, 608 pp. (in Russian)

[5] Bykovtsev G. I., Verveiko N. D., “O rasprostranenii voln v uprugo-vyazko-plasticheskoi crede [On the propagation of waves in an elastic-viscous-plastic medium]”, Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, 1966, no. 4, 111–123 (in Russian)

[6] Frenkel Ya. I., “K teorii seysmichescikh i seysmoelectrichescikh yavleny vo vlazhnoi pochve [Toward a theory of seismic and seismoelectric phenomena in the moist soil]”, Izv. ANSSR. Ser. Gegr. Geophis [Proceedings of the SSR Academy of Sciences. The Series of Geography and Geophysics], 8:4 (1944), 133–150 (in Russian) | MR | Zbl

[7] Kukarskikh L. A., Polenov V. S., “Advance of waves in fluid saturated elastic–viscoplastic porous medium”, Bull. Voronezh St. Tekh. Univ., 9:8 (2012), 57–60 (in Russian)

[8] Maslikova T. I., Polenov V. S., “The propagation of unsteady elastic waves in homogeneous porous media”, Mech. Solids., 40:1 (2005), 86–89

[9] Polenov V. S., “Osnovnye uravneniya dinamichesckogo demphirovaniya trekhkomponentnykh sred [The basic equations of the dynamic deformation of three-component media]”, Sovremennye tendentsii razvitiya estesvoznaniya i tekhnicheskikh nayk: Sbornik nauchnykh trudov po materialam MNPK.[Modern trends in the development of natural sciences and technical sciences: A collection of scientific papers based on materials of the IPPC], Belgorod, 2018, 31–34 (in Russian)

[10] Polenov V. S., Chigarev A. V., “Mathematical modeling of shock waves in inhomogeneous viscoelastic two–component media”, Appl. Math. Phys., 6:5 (2018), 997–1005 | DOI

[11] Polenov V. S., Nitsak D. A., “Metematicheskoe modelirovanie akusticheskoi emissii v nasyschennych zhidkostew dvukhkomponentnykh sredach”, Proc. XI Int. Sci. Pract. Conf. “Science of Russia: goals and objectives” (Oct. 10, 2018, Ekaterinburg, Russia), v. 2, 2018, 52–58 (in Russian) | DOI

[12] Rakhmatulin Kh. A., Gazovaya i volnovaya dinamika [Gas and Wave Dynamics], MSU, M., 1983, 200 pp. (in Russian)

[13] Reznichenko Yu. V., “O rasprostranenii seysmichescikh voln v discretnykh i heterogennykh sredakh [On the propagation of seismic waves in discrete and heterogeneous media]”, Izv. Akad. Nauk SSSR. Ser. Geogr. Geophys., 13 (1949), 115–128 (in Russian)

[14] Thomas T. Y., Plastic Flow and Fracture in Solids, Acad. Press, New York, 1961, 267 pp. | MR | Zbl