Abstract
It is substantiated that the problem formulated in the title plays a fundamental role in the rational interpretation of experiments on massive specimens. These experiments are intended for studying waves excited by a short-term harmonic pulse. The problem for a porous saturated medium is a direct analogy of the problem previously solved for composite materials. The procedure of solving the problem based on the Laplace time transform is described. An analysis of the integrands in the inverse transform is nontrivial and cannot be stated briefly. Therefore, Part 1 closes with general comments on the inverse transform. Part 2 will include a detailed description of the inverse transform and many physical conclusions: on conformity of the stationary part of the solution to plane harmonic compression–tension waves with frequency of the given harmonic pulse, on attenuation of all types of waves, and on two types of nonstationary waves
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REFERENCES
M. K. Balakirev and I. A. Gilinskii, Waves in Piezocrystals [in Russian], Nauka, Novosibirsk (1982).
R. I. Nigmatulin, Fundamentals of the Mechanics of Heterogeneous Media [in Russian], Nauka, Moscow (1978).
V. N. Nikolaevskii, The Mechanics of Porous and Cracked Media [in Russian], Nedra, Moscow (1984).
V. N. Nikolaevskii, K. S. Basniev, A. G. Gorbunov, and G. A. Zotov, The Mechanics of Saturated Porous Media [in Russian], Nedra, Moscow (1970).
Ya. Ya. Rushchitskii, Elements of Mixture Theory [in Russian], Naukova Dumka, Kiev (1991).
Ya. Ya. Rushchitskii and S. I. Tsurpal, Waves in Materials with a Microstructure [in Ukrainian], Inst. Mekh. NANU, Kiev (1998). 526
Yu. V. Sidorov, M. V. Fedoryuk, and M. I. Shabunin, Lectures on Complex Variable Theory [in Russian], Nauka, Moscow (1982).
C. Truesdell (ed.), Mechanics of Solids, Vol. 1 V/a of the Encyclopedia of Physics (S. Flugge, chief ed.), Springer-Verlag, Berlin–Heidelberg–New York (1973).
V. K. Kinra, M. S. Petraitis, and S. K. Datta, “Ultrasonic wave propagation in a random particulate composite, ” Int. J. Solids Struct., 16, No. 3, 301–312 (1980).
V. K. Kinra and E. Ker, “Effective elastic moduli of a thin-walled glass microsphere/PMMA composite, ” J. Comp. Mater., 16, No. 2, 117–138 (1982).
V. K. Kinra and E. Ker, “An experimental investigation of pass bands and stop bands in two periodic particulate composites, ” Int. J. Solids Struct., 19, No. 3, 393–409 (1983).
V. K. Kinra, E. Ker, and S. K. Datta, “Influence of particle resonance on wave propagation in a random particulate composite, ” Mech. Res. Commun., 9, No. 2, 109–114 (1982).
T. J. Plona, “Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies, ” Appl. Phys. Let., 37, No. 4, 259–261 (1980).
J. J. Rushchitsky, “On the question of applicability of the linear mixture theory, ” Soviet (Int.) Appl. Mech., 17, No. 6, 58–62 (1980).
J. J. Rushchitsky and B. B. Ergashev, “Theoretical analysis of nonstationary effects in the massive sample from fibrous composite under a short-time action of the harmonic pulse, ” Soviet (Int.) Appl. Mech., 23, No. 12, 82–89 (1987).
J. J. Rushchitsky, “Nonlinear waves in solid mixtures, ” Int. Appl. Mech., 33, No. 1, 3–38 (1997).
J. J. Rushchitsky, “Interaction of waves in solids, ” Appl. Mech. Rev., 52, No. 2, 35–74 (1999).
Ya. Ya. Rushchitskii, “On the classification of elastic waves, ” Int. Appl. Mech., 35, No. 11, 1104–1110 (1999).
Ya. Ya. Rushchitskii, “Extension of the microstructural theory of two-phase mixtures to composite materials, ” Int. Appl. Mech., 36, No. 5, 586–614 (2000).
Ya. Ya. Rushchitskii, “The wave energy in nonlinearly deformable composites, ” Int. Appl. Mech., 37, No. 1, 107–114 (2001).
C. H. Yew and P. N. Jogi, “A study of wave motion in fiber-reinforced medium, ” Int. J. Solids Struct., 12, No. 6, 694–703 (1976).
C. H. Yew and P. N. Jogi, “The determination of Biot's parameters for sandstones. P. 1. Static tests, ” Exp. Mech., 18, No. 2, 167–172 (1978).
C. H. Yew, P. N. Jogi, and K. E. Gray, “Estimation of the mechanical properties of fluid saturated porous rocks using the measured wave motion, ” J. Energy Res. Tech., 101, No. 1, 112–116 (1979).
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Rushchitskii, Y.Y., Israfilov, R.M. Waves in a Saturated Porous Half-Space. Part 1. International Applied Mechanics 37, 520–527 (2001). https://doi.org/10.1023/A:1017924515909
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DOI: https://doi.org/10.1023/A:1017924515909