Abstract
A plane harmonic problem of vertical vibrations of a rigid permeable stamp on a liquid saturated poroelastic base is considered. The equations of two-phase Biot media, which take into account inertial and viscous interactions of phases, are used. The asymptotic properties of the contact stress at low vibration frequencies are studied.
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REFERENCES
M. A. Biot, “Theory of propagation of elastic waves in fluid-saturated porous solid,” J. Acoust. Soc. Am., 28, No. 2, 168-191 (1956).
V. M. Seimov, A. N. Trofimchuk, and O. A. Savitsky, Vibration of a Wave in Layered Media [in Russian], Naukova Dumka, Kiev (1990).
R. D. Stoll and G. M. Bryan, “Wave attenuation in saturated sediments,” J. Acoust. Soc. Am., 47, No. 5, Part 2, 1440-;1447 (1970).
T. Yamamoto, “Acoustic propagation in the ocean with a poroelastic bottom,” J. Acoust. Soc. Am., 73, No. 5, 1578-1596 (1983).
L. Ya. Kosachevsky, “About propagation of elastic waves in two-component mediums,” Appl. Math. Mech., 23, No. 6, 1115-1123 (1959).
V. N. Nikolaevsky, K. S. Basniev, A. T. Gorbunov, et al., Mechanics of Saturated Porous Media [in Russian], Nedra, Moscow (1970).
A. N. Trofimchuk, “Dynamical interaction of rigid plate with poroelastic water-saturated base,” Appl. Mech., 32, No. 1, 69-74 (1996).
V. M. Seimov, Dynamical Contact Problems [in Russian], Naukova Dumka, Kiev (1976).
S. G. Krein, Linear Equations in Banach Spaces [in Russian], Nauka, Moscow (1971).
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Derivatives of Fractional Order [in Russian], Nauka i Tekhnika, Minsk (1987).
F. D. Gakhov, Boundary-Value Problems [in Russian], Nauka, Moscow (1977).
V. M. Aleksandrov and E. V. Kovalenko, Problems with Mixed Boundary Conditions in Continuum Mechanics [in Russian], Nauka, Moscow (1986).
E. Jahnke, F. Emde, and F. Losch, Special Functions [Russian translation], Nauka, Moscow (1968).
V. M. Lyatkher and Yu. S. Yakovlev (editors), Dynamic Continuous Media in Calculation of Hydrotechnical Structures [in Russian], Énergiya, Moscow (1976).
A. N. Trofimchuk, “Asymptotic solutions of nonstationary contact problems for fluid-saturated poroelastic media,” in: Abstracts of the Fourth All-Union Conference on Mixed Problems in Mechanics of Elastic Solids, Part II, Odessa (1989), p. 111.
P. I. Klubin, “Calculation of Beam and Circular Plates on an Elastic Base,” Inzh. Sb., No. 12, 95-136 (1952).
G. Ya. Popov, Concentration of Elastic Stresses near Stamp. Thin Insertion and Refreshment [in Russian], Nauka, Moscow (1982).
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Gomilko, A.M., Savitsky, O.A. & Trofimchuk, A.N. Asymptotic Solution of a Harmonic Contact Problem for a Permeable Stamp on a Liquid Saturated Base. Nonlinear Oscillations 5, 1–19 (2002). https://doi.org/10.1023/A:1014692925506
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DOI: https://doi.org/10.1023/A:1014692925506