Abstract
The propagation of harmonic waves along the interface of an initially stressed, compressible layer and a viscous, compressible fluid half-space is investigated. A dispersion relation that does not depend on the form of the elastic potential is derived on the basis of the three-dimensional linearized elasticity equations for elastic bodies with uniform initial deformations and on the linearized Navier-Stokes equations for a viscous Newtonian fluid at rest. The phase velocities and attenuation coefficients of the elastic modes are determined numerically as functions of the thickness of the elastic layer using a Murnaghan-type three-invariant elastic potential.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Yu. Babich, A. N. Guz', and A. P. Zhuk, "Elastic waves in initially stressed bodies," Prikl. Mekh.,15, No. 4, 3–23 (1979).
L. M. Brekhovskikh, Waves in Layered Media, 2nd ed., Academic Press, New York (1980).
L. M. Brekhovskikh and O. A. Godin, Acoustics of Layered Media, Vol. I: Plane and Quasi-Plane Waves; Vol. II: Point Sources and Wave Beams, Springer-Verlag, Berlin-New York (1990, 1992).
L. M. Brekhovskikh and V. S. Goncharov, Mechanics of Continua and Wave Dynamics, Springer-Verlag, Berlin-New York (1985).
I. A. Viktorov, Acoustic Surface Waves in Solids [in Russian], Nauka, Moscow (1981).
G. A. Grachev, E. A. Rivels, and A. V. Rozenberg, "Influence of thin ice on the propagation of low-frequency sound in shallow water," in: Mathematical Methods of Underwater Acoustics [in Russian], No. 2, Izd. Rost. Univ., Rostov-on-Don (1990), pp. 33–37.
A. N. Guz', Elasticity of Elastic Bodies with Finite Deformations [in Russian], Naukova Dumka, Kiev (1973).
A. N. Guz', "Representation of the general solutions of the linearized theory of elasticity of compressible bodies," Dokl. Akad. Nauk Ukr. Ser. A, No. 6, 700–704 (1975).
A. N. Guz', Stability of Elastic Bodies in Hydrostatic Compression [in Russian], Naukova Dumka, Kiev (1979).
A. N. Guz', "Hydroelasticity problems for a viscous fluid and initially stressed elastic bodies," Dokl. Akad. Nauk,251, No. 2, 305–308 (1980).
A. N. Guz', "Representation of the solutions of the linearized Navier-Stokes equations," Dokl. Akad. Nauk,253, No. 4, 825–827 (1980).
A. N. Guz', "Aerohydroelasticity problems for initially stressed bodies," Prikl. Mekh.,16, No. 3, 3–21 (1980).
A. N. Guz', Elastic Waves in Initially Stressed Solids [in Russian], Naukova Dumka, Kiev (1986) Vols. 1 and 2.
A. N. Guz' and A. P. Zhuk, "Influence of initial stresses on the velocities of Stoneley waves," Prikl. Mat. Mekh.44, No. 6, 1095–1099 (1980).
A. N. Guz', A. P. Zhuk, and F. G. Makhort, Waves in an Initially Stressed Layer [in Russian], Naukova Dumka, Kiev (1976).
A. N. Guz', F. G. Makhort, and O. I. Gushcha, Introduction to Acoustoelasticity [in Russian], Naukova Dumka, Kiev (1977).
A. N. Guz', F. G. Makhort, O. I. Gushcha, and V. K. Lebedev, Fundamentals of Nondestructive Ultrasonic Stress Characterization in Solids [in Russian], Naukova Dumka, Kiev (1974).
A. P. Zhuk, "Stoneley waves in an initially stressed medium," Prikl. Mekh.,16, No. 1, 113–116 (1990).
L. N. Zakharov, "Sound propagation in a layer of a fresh-water reservoir under wintertime conditions," Akust. Zh.,20, No. 1, 132–133 (1974).
V. N. Krasil'nikov, "Influence of a thin elastic layer on sound propagation in a fluid half-space," Akust. Zh.,6, No. 2, 220–228 (1960).
L. A. Molotkov, "Dispersion relations for layered inhomogeneous elastic and fluid systems," in: Dynamical Problems in the Theory of Seismic Wave Propagation [in Russian], No. 5, Leningrad (1962), pp. 240–280.
L. A. Molotkov, Matrix Method in the Theory of Wave Propagation in Layered Elastic and Fluid Media [in Russian], Nauka, Leningrad (1984).
G. I. Petrashen', L. A. Molotkov, and P. V. Krauklis, Waves in Layered Homogeneous, Isotropic, Elastic Media [in Russian], in two volumes, Nauka, Leningrad (1985).
F. D. Murnaghan, Finite Deformations of an Elastic Solid, Wiley, New York (1951).
J. W. Rayleigh, "On waves propagated along the plane surface of an elastic solid," Proc. London Math. Soc.,17, No. 253, 4–11 (1985/86).
R. Stoneley, "The elastic waves at the interface of separation of two solids," Proc. R. Soc. London Ser. A,106, No. 732, 416–429 (1924).
Additional information
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 9, pp. 3–9, September, 1994.
Rights and permissions
About this article
Cite this article
Bagno, A.M., Guz', A.N. & Shchuruk, G.I. Influence of fluid viscosity on waves in an initially deformed, compressible, elastic layer interacting with a fluid medium. Int Appl Mech 30, 643–649 (1994). https://doi.org/10.1007/BF00847075
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00847075