Abstract
The article is the first part of a survey of problems in compressible, viscous fluid dynamics as related to the dynamics of rigid and elastic bodies in a compressible, viscous fluid in the linearized formulation. The formulation of basic problems is discussed, along with a method of solution based on general solutions of the Navier-Stokes equations in vector and scalar form in dynamical problems. Forced harmonic vibrations of rigid bodies in rest and moving compressible, viscous fluids are discussed. Publications relevant to the stated problems are analyzed.
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A. É. Babaev, A. N. Guz', and V. D. Kubenko, “Wave motion of a compressible, viscous fluid between eccentric cylindrical shells,”Mat. Fiz.,32, 91–99 (1982).
A. M. Bagno, “Influence of initial stresses on wave propagation in a compressible cylinder containing a compressible fluid,”Prikl. Mekh.,20, No. 4, 103–110 (1984).
A. M. Bagno, “Influence of a compressible, viscous fluid on the propagation of Stoneley waves at a solid-liquid interface,”Prikl. Mekh.,20, No. 6, 70–74 (1984).
A. M. Bagno, “Influence of initial stresses on the wave surface in the system: prestrained compressible body + compressible viscious fluid,”Prikl. Mekh.,22, No. 6, 32–36 (1986).
A. M. Bagno, “Influence of initial stresses on the wave process in an elastic, compressible half-space interacting with a viscous, fluid layer,”Dokl. Akad. Nauk Ukr. Ser. A, No. 8, 22–25 (1989).
A. M. Bagno and A. N. Guz', “Wave propagation in a prestressed, incompressible cylinder containing a compressible, viscous fluid,”Mekh. Kompoz. Mater, No. 2, 349–355 (1982).
A. M. Bagno and A. N. Guz' “Propagation of small disturbances in the system: prestressed, compressible, rigid body + compressible, viscous fluid,”Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 1, 167–170 (1983).
A. M. Bagno and A. N. Guz', “Stoneley waves at the contact boundary of a prestressed, incompressible, rigid half-space and a compressible, viscous, fluid,”Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 3, 107–110 (1987).
A. M. Bagno and A. N. Guz', “Influence of initial stresses on the wave velocities in a prestrained, compressible layer in contact with a fluid half-space,”Dokl. Akad. Nauk SSSR,329, No. 6, 715–717 (1993).
A. M. Bagno and A. N. Guz', “Elastic waves in prestressed bodies interacting with a fluid (review),”Prikl. Mekh.,33, No. 6, 3–29 (1997) (Int. Appl. Mech.,33, No. 6, 435–465 (1997)).
A. M. Bagno, A. N. Guz', and G. I. Shchuruk, “Waves in a viscous fluid layer situated on an elastic half-space,”Prikl. Mekh.,26, No. 4, 3–7 (1990).
A. M. Bagno, A. N. Guz', and G. I. Shchuruk, “Characteristics of a nonaxisymmetric wave process in a Timoshenko-type orthotropic shell containing a viscous fluid,”Prikl. Mekh.,26, No. 12, 22–28 (1990).
A. M. Bagno, A. N. Guz', and G. I. Shchuruk, “Influence of the fluid viscosity on waves in a prestrained, elastic, compressible layer interacting with a fluid medium,”Prikl. Mekh.,30, No. 9, 3–8 (1994) (Int. Appl. Mech.,30, No. 9, 643–649 (1994)).
A. S. Basmat, “Unsteady motion of a sphere in a compressible, viscous, fluid,”Prikl. Mekh.,19, No. 8, 118–121 (1983).
A. S. Basmat, “Unsteady motion of rigid bodies in a compressible, viscous fluid,”Dokl. Akad. Nauk Ukr. Ser. A, No. 4, 36–40 (1983).
A. S. Basmat, “Unsteady motion of a rigid sphere in a compressible, viscous fluid,”Prikl. Mekh.,23, No. 1, 127–130 (1987).
A. S. Basmat, “Unsteady motion of an impulse-excited rigid sphere in a compressible, viscous fluid,”Prikl. Mekh.,23, No. 6, 107–111 (1987).
A. S. Basmat, “Investigation of transient problems for a compressible, viscous fluid,”Prikl. Mekh.,25, No. 4, 111–115 (1989).
A. S. Basmat and A. N. Guz', “Interaction of an unsteady wave with a rigid sphere immersed in a compressible fluid,”Prikl. Mat. Mekh.,54, No. 2, 239–244 (1990).
A. S. Basmat, A. N. Guz', and A. P. Zhuk, “Unsteady motion of a rigid bodies in a compressible, viscous fluid,”Mat. Fiz.,36, No. 2, 37–43 (1984).
A. S. Basmat, A. N. Guz', and A. P. Zhuk, “Unsteady motion of a rigid cylinder in a compressible, viscous fluid,”Prikl. Mekh.,21, No. 10, 109–114 (1985).
A. S. Basmat and A. P. Zhuk, “Unsteady motion of rigid bodies in a compressible medium,”Prikl. Mekh.,20, No. 3, 114–116 (1984).
R. F. Ganiev and L. E. Ukrainskii,Particle Dynamics in the Interaction of Vibrations [in Russian], Naukova Dumka, Kiev (1975).
A. N. Guz', “Hydroelasticity problems for a viscous, fluid and initially stressed elastic bodies,”Dokl. Akad. Nauk SSSR,251, No. 2, 305–308 (1980).
A. N. Guz', “Representation of the solutions of the linearized Navier-Stokes equations,”Dokl. Akad. Nauk SSSR,253 No. 4, 825–827 (1980).
A. N. Guz', “Representation of the solutions of the linearized Navier-Stokes equations for a moving fluid,”Dokl. Akad. Nauk SSSR,255, No. 5, 1066–1068 (1980).
A. N. Guz', “Hydroelasticity problems for initially stressed bodies,”Prikl. Mekh.,16, No. 3, 3–21 (1980).
A. N. Guz', “Wave propagation in a cylindrical shell containing a viscous, compressible fluid,”Prikl. Mekh.,16, No. 10, 10–20 (1980).
A. N. Guz', “Hydroelasticity problems for a compressible, viscous, fluid in spherical coordinates,”Prikl. Mekh.,16, No. 11, 3–10 (1980).
A. N. Guz', “Dynamics of rigid bodies in a moving compressible, viscous fluid,”Dokl. Akad. Nauk SSSR,259, No. 2, 314–315 (1981).
A. N. Guz', “Dynamics of rigid bodies in a compressible, viscous fluid (fluid at rest),”Prikl. Mekh.,17, No. 3, 3–22 (1981).
A. N. Guz', “Dynamics of rigid bodies in a compressible, viscous, fluid (moving fluid),”Prikl. Mekh.,17, No. 10, 20–30 (1981).
A. N. Guz', “An analog in continuum mechanics,”Dokl. Akad. Nauk SSSR,263, No. 3, 563–565 (1982).
A. N. Guz', “Vibrations of a circular cylinder in compressible, viscous, fluid flow,”Prikl. Mekh.,19, No. 3, 50–59 (1983).
A. N. Guz',Elastic Waves in Initially Stressed Bodies, Vol. 1:General Aspects [in Russian], Naukova Dumka, Kiev (1986).
A. N. Guz', “Elastic Waves in Initially Stressed Bodies, Vol. 2:Propagation Laws [in Russian], Naukova Dumka, Kiev (1986).
A. N. Guz', “Hydroelasticity problems for a compressible, viscous, fluid,”Prikl. Mekh.,27, No. 1, 3–15 (1991).
A. N. Guz', “Representation of the general solutions of the dynamical equations for a moving, compressible, viscous fluid in spherical coordinates,”Dokl. Akad. Nauk SSSR,329, No. 5, 559–561 (1993).
A. N. Guz', “Limiting transitions in the dynamics of rigid and elastic bodies in a compressible, viscous fluid,”Prikl. Mekh.,29, No. 7, 74–80 (1993) (Int. Appl. Mech. 29, No. 7, 569–574 (1993)).
A. N. Guz', “Vibrations of a sphere in compressible, viscous fluid flow,”Prikl. Mekh.,29, No. 12, 3–14 (1993).
A. N. Guz', “Dynamics of bodies in a moving compressible, viscous fluid,”Dokl. Akad. Nauk Ukr., No. 10, 44–47 (1994).
A. N. Guz', “Construction of solutions in the dynamics of a moving compressible, viscous fluid,” in:Modern Problems in Continuum Mechanics: To the 75th Birthday of I. I. Vorovich [in Russian], MP “Kniga,” Rostov-on-Don (1995), pp. 80–85.
A. N. Guz', “Identification of Lagrangian and Eulerian coordinates in continuum mechanics,”Prikl. Mekh.,34, No. 10, 50–54 (1998) (Int. Appl. Mech.,34, No. 10, 965–968 (1998)).
A. N. Guz',Compressible, Viscous Fluid Dynamics [in Russian], A.S.K., Kiev (1998).
A. N. Guz' and A. M. Bagno, “Stoneley waves at the interface of an initially stressed elastic half-space and a compressible, viscous fluid,”Prikl. Mekh.,20, No. 12, 3–7 (1984).
A. N. Guz', A. M. Bagno, and G. I. Shchuruk, “Axisymmetric elastic waves in an orthotropic cylindrical shell containing a compressible, viscous fluid,”Dokl. Akad. Nauk Ukr. Ser. A, No. 9, 40–45 (1989).
A. N. Guz' and A. S. Basmat, “Interaction of unsteady waves with a rigid sphere in a compressible, viscous fluid,”Dokl. Akad. Nauk SSSR,306, No. 4, 813–816 (1989).
A. N. Guz' and V. T. Golovchan,Diffraction of Elastic Waves in Multiply Connected Bodies [in Russian], Naukova Dumka, Kiev (1972).
A. N. Guz' and A. P. Zhuk, “Hydrodynamic forces in a sound field in a viscous fluid,”Dokl. Akad. Nauk SSSR,266, No. 1, 32–35 (1982).
A. N. Guz' and A. P. Zhuk, “Forces acting on a spherical particle in a sound field in a viscous fluid,”Dokl. Akad. Nauk SSSR,274, No. 6, 1313–1316 (1984).
A. N. Guz' and A. P. Zhuk, “Hydrodynamic interaction of two spherical particles in an ideal fluid in a sound field,”Dokl. Akad. Nauk SSSR,279, No. 3, 566–570 (1984).
A. N. Guz' and A. P. Zhuk, “Nonlinear problems in the theory of small vibrations of particles in a compressible, viscous fluid,” in:Ninth International Conference on Nonlinear Vibrations [in Russian], Vol. 3, Naukova Dumka, Kiev (1984), pp. 85–88.
A. N. Guz' and A. P. Zhuk, “Motion of two parallel circular cylinders in a viscous fluid in a sound field,”Izv. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 6, 158–164 (1990).
A. N. Guz' and A. P. Zhuk, “Influence of an acoustic wave on rigid particles in a fluid,” in:Nonlinear Problems in the Dynamics of Machines: To the 60th Birthday of K. V. Frolov [in Russian], Inst. Mashinoved. Ross. Akad. Nauk, Moscow (1992), pp. 43–52.
A. N. Guz' and A. P. Zhuk, “Dynamics of rigid particles in a fluid in the presence of a sound field: model of a piecewise-homogeneous medium (review),”Prikl. Mekh.,29, No. 5, 3–20 (1993) (Int. Appl. Mech.,29, No. 5, 329–344 (1993)).
A. N. Guz' and A. P. Zhuk, “Dynamics of particles near a plane boundary in an acoustic radiation field,”Prikl. Mekh.,35, No. 10, 74–79 (1999) (Int. Appl. Mech.,35, No. 10, (1999)).
A. N. Guz' and V. D. Kubenko,Theory of the Unsteady-State Aerohydroelasticity of Shells (Computational Methods for Shells, in five volumes, Vol. 5) [in Russian], Naukova Dumka, Kiev (1982).
A. N. Guz', V. D. Kubenko, and A. É. Babaev,Hydroelasticity of Shell Systems [in Russian], Vyshcha Shkola, Kiev (1984).
A. N. Guz', V. D. Kubenko, and M. A. Cherevko,Diffraction of Elastic Waves [in Russian], Naukova Dumka, Kiev (1978).
A. N. Guz', Sh. Markush, L. Pust et al.,Dynamics of Bodies Interacting With a Medium [in Russian], Naukova Dumka, Kiev (1991).
I. G. Guseinov and A. N. Guz', “Effect of acoustic waves on a cylindrical shell filled, with a compressible, viscous fluid,”Prikl. Mekh.,22, No. 5, 34–42 (1986).
A. P. Zhuk, “Interaction of a solid particle with a sound wave in a viscous fluid,”Prikl. Mekh.,19, No. 11, 92–99 (1983).
A. P. Zhuk, “Average hydrodynamic force acting on a spherical particle in a sound field in a viscous fluid,”Prikl. Mekh.,20, No. 1, 126–127 (1984).
A. P. Zhuk, “Interaction of a rigid cylinder with a sound wave in a viscous fluid,”Prikl. Mekh.,24, No. 1, 107–114 (1988).
A. P. Zhuk, “Application of the theory of viscoelasticity to the solution of problems in the interaction of an acoustic wave with rigid bodies in a viscous fluid,”Dokl. Akad. Nauk Ukr. Ser. A, No. 6, 35–38.
A. P. Zhuk, “Investigation of the interaction of an acoustic wave with a cylinder in a viscous fluid, based on the theory of viscoelasticity,”Dokl. Akad. Nauk Ukr. Ser. A, No. 3, 49–52 (1990).
A. P. Zhuk, “Investigation, based on the theory of viscoelasticity, of the interaction of two parallel cylinders during the transmission of an acoustic wave in a viscous fluid,”Dokl. Akad. Nauk Ukr. Ser. A, No. 4, 42–45 (1990).
A. P. Zhuk, “Investigation of the interaction of an acoustic wave with a spherical particle in a viscous fluid, based on the theory of viscoelasticity,”Dokl. Akad. Nauk Ukr. Ser. A, No. 2, 3–34 (1991).
V. D. Kubenko,Transient Interaction of Structural Elements with a Medium [in Russian], Naukova Dumka, Kiev (1979).
V. D. Kubenko, “Solution of transient hydroelasticity problems in the case of a compressible, viscous fluid,”Prikl. Mekh.,18, No. 3, 119–122 (1982).
V. D. Kubenko, V. M. Kuz'ma, and G. N. Puchka,Dynamics of Spherical Bodies in a Fluid in the Presence of Vibrations [in Russian], Naukova Dumka, Kiev (1989).
V. D. Kubenko, V. D. Lakiza, V. S. Pavlovskii, and N. A. Pelekh,Dynamics of Elastic Gas-Liquid Systems Subjected to Vibrations [in Russian], Naukova Dumka, Kiev (1988).
V. D. Kubenko, Yu. N. Ryabukha, and I. V. Savina, “Diffraction of acoustic waves by coaxial, cylindrical, piezoceramic shells filled, with a viscous fluid,”Prikl. Mekh.,24, No. 10, 28–34 (1988).
N. E. Kochin, I. A. Kibel', and N. V. Roze,Theoretical Fluid Mechanics [in Russian], Part 2, GIFML, Moscow (1963).
H. L. Lamb,Hydrodynamics, 6th ed., Cambridge Univ. Press (1932).
L. D. Landau and E. M. Lifshitz,Fluid Mechanics, 2nd ed., rev., Pergamon Press, Oxford-New York (1987).
N. A. Kil'chevskii (ed.),Mechanics of Shell-Liquid-Heated Gas Systems [in Russian], Naukova Dumka, Kiev (1970).
R. von Mises,Mathematical Theory of Compressible Fluid Flow, Academic Press, New York (1958).
P. M. Morse and H. Feshbach,Methods of Theoretical Physics, Vol. 2, McGraw-Hill, New York (1953).
R. I. Nigmatulin,Dynamics of Multiphase Media [in Russian], Part 1, Nauka, Moscow (1987).
R. I. Nigmatulin,Dynamics of Multiphase Media, [in Russian], Part 2, Nauka, Moscow (1987).
O. V. Rudenko and S. N. Soluyan,Theoretical Foundations of Nonlinear Acoustics, Consultants Bureau, New York (1977).
L. I. Sedov,A Course in Continuum Mechanics, Vol. 2:Physical Foundations and Formulations of Problems, Wolters-Noordhoff, Groningen (1972).
N. A. Slezkin,Incompressible, Viscous Fluid Dynamics [in Russian], Gostekhizdat, Moscow (1955).
J. Happel and H. Brenner,Low Reynolds Number Hydrodynamics, 2nd rev. ed., Noordhoff, Leiden, Netherlands (1973).
G. I. Shchuruk, “Torsional waves in a cylindrical shell containing a compressible, viscous fluid,”Prikl. Mekh.,19, No. 4, 117–121 (1983).
R. P. D'Armond and W. T. Roubeau, “Wave propagation of viscous compressible liquid confined in elastic tubes,”ASME Paper, NFF,23, NV, 6 (1972).
W. R. Dean and M. E. O'Neill, “A slow motion of viscous liquid caused by the rotation of a solid sphere,”Mathematika,10, Part 1, No. 19, 13–24 (1963).
A. N. Guz', “Problems of hydroelasticity for compressible viscous liquid,” in:Applied Mechanics, Vol. 1:Fluid Mechanics, Pergamon Press, New York (1989), pp. 436–441.
A. N. Guz', “Dynamics of rigid bodies in a compressible viscous fluid (piecewise-homogeneous medium model),” in:Second Liquid Matter Conference Abstracts, Florence, Italy (1993), p. 80.
A. N. Guz' and A. P. Zhuk, “On nonlinear interaction of solid particles with a sound wave in viscous liquids,” in:International Union of Theoretical and Applied Mechanics (IUTAM) Symposium on Nonlinear Deformation Waves, Tallin, Estonia, Springer-Verlag, Berlin-New York (1983), pp. 365–378.
L. V. King, “On the acoustic radiation pressure on spheres,”Proc. R. Soc. London Ser. A,147, 212–240 (1934).
H. Lamb, “On the uniform motion of a sphere through a viscous fluid,”Philos. Mag.,21, 120 (1911).
M. E. O'Neill, “A slow motion of viscous liquid by a slowly moving sphere,”Mathematika,11, Part 1, No. 21, 67–74 (1964).
C. W. Oseen, “Über die Stokesche Formel und über eine vervandte Aufgabe in Hydrodynamik,”Ark. Mat. Astron. Fys.,6, No. 29 (1910),7, No. 1 (1911).
C. Stokes, “On the effect of internal friction of fluids on the motion of pendulums,”Camb. Trans.,9, No. 8, 1–3 (1951).
A. P. Zhuk, “Interaction of solid bodies immersed in liquid in the acoustic wave field,” in:First International Conference on Engineering Aero-Hydroelasticity (EAHE-89), Vol. 2, Prague (1989), pp. 310–315.
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S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 1, pp. 25–52, January, 2000.
Detailed information about the author can be found in the journalPrikladnaya Mekhanika, Volume 35, No. 1, pp. 104–108 (1999).
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Guz’, A.N. Compressible, viscous fluid dynamics (review). Part 1. Int Appl Mech 36, 14–39 (2000). https://doi.org/10.1007/BF02681958
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DOI: https://doi.org/10.1007/BF02681958