Skip to main content
SpringerLink
Log in

Nonlinear problems of the dynamics of elastic shells partialiy filled with a liquid

  • Published:
International Applied Mechanics Aims and scope

Abstract

Theoretical and experimental investigations of the nonlinear vibrations and dynamic stability of thin shells partially filled with a liquid are reviewed. The paper deals with the basic laws governing the dynamic high-deflection deformation of carrying shell structures and the considerable vibrations of the free liquid surface due to the natural, forced, and parametrically excited vibrations of the combined system and also due to impulse loads acting on the carrying object. The nonlinear dynamic interaction of shells with a liquid filler is analyzed with allowance for the wave motions of the free liquid surface.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. A. Abgaryan and I. M. Rapoport,Rocket Dynamics [in Russian], Mashinostroyeniye, Moscow (1969).

    Google Scholar 

  2. H. N. Abramson and D. D. Kana, “Some experimental investigations of the dynamic stability of thin shells containing a liquid,” in:Problems of the Mechanics of a Deformable Solid [Russian translation], Sudostroyeniye, Leningrad (1970), pp. 11–19.

    Google Scholar 

  3. A. A. Andronov, A. A. Vitt, and S. É. Haikin,Vibration Theory [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  4. Yu. N. Anosov, “The nonlinear vibrations of a liquid in a cylindrical cavity,”Prikl. Mekh.,2, No. 10, 22–28 (1966).

    Google Scholar 

  5. G. E. Bagdasaryan and V. Ts. Gnuni, “The parametric vibrations of a cylindrical shell filled with a liquid to different depths,”Prikl. Mekh.,2, No. 3, 21–26 (1966).

    Google Scholar 

  6. A. M. Bagno and A. N. Guz', “Elastic waves in prestressed bodies interacting with a liquid (review),”Prikl. Mekh.,33, No. 6, 3–39 (1997).

    MATH  MathSciNet  Google Scholar 

  7. L. I. Balabukh, “Interaction of shells with a liquid and gas,” in:Proc. All-Union Conf. on the Theory of Shells and Plates (Baku, 1966) [in Russian], Nauka, Moscow (1966), pp. 935–944.

    Google Scholar 

  8. N. N. Bogolyubov and Yu. A. Mitropol'skii,Asymptotic Methods in the Theory of Nonlinear Vibrations [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  9. I. B. Bogoryad,The Dynamics of a Viscous Liquid with a Free Surface [in Russian], Izd. Tomskogo Univ., Tomsk (1980).

    Google Scholar 

  10. I. B. Bogoryad, I. A. Druzhinin, G. Z. Druzhinina, and É. E. Libin,Introduction to the Dynamics of Vessels Filled with a Liquid [in Russian], Izd. Tomskogo Univ., Tomsk (1977).

    Google Scholar 

  11. V. V. Bolotin,The Dynamic Stability of Elastic Systems [in Russian], Gostekhizdat, Moscow (1956).

    Google Scholar 

  12. V. V. Bolotin, “The motion of a liquid in an oscillating vessel,”Prikl. Mat. Mekh.,20, No. 2, 293–296 (1956).

    MATH  MathSciNet  Google Scholar 

  13. V. V. Bolotin, Yu. N. Novichkov, and Yu. Yu. Shveiko,The Theory of Aerohydroelasticity, Vol. 3 of the three-volume seriesHardness, Stability, and Vibrations: A Reference Book [in Russian], Mashinostroyeniye, Moscow (1968).

    Google Scholar 

  14. L. G. Boyarshina, “The resonance phenomena in the nonlinear vibrations of cylindrical shells with a liquid,”Prikl. Mekh.,20, No. 8, 99–104 (1984).

    Google Scholar 

  15. L. G. Boyarshina, “The nonlinear wave modes of an elastic cylindrical shell with a liquid under resonance conditions,”Prikl. Mekh.,24, No. 5, 105–111 (1988).

    Google Scholar 

  16. L. G. Boyarshina, “The nonlinear wave motions of a liquid in a cylindrical vessel with an elastic bottom,”Prikl. Mekh.,30, No. 5, 69–75 (1994).

    MathSciNet  Google Scholar 

  17. L. G. Boyarshina and R. F. Ganiev, “The nonlinear vibrations of moving deformable bodies containing a liquid,”Prikl. Mekh.,12, No. 7, 62–69 (1976).

    Google Scholar 

  18. L. G. Boyarshina and P. S. Koval'chuk, “The wave modes of the free surface of a liquid contained in a cylindrical vessel,”Prikl. Mekh.,22, No. 3, 113–116 (1986).

    Google Scholar 

  19. L. G. Boyarshina, P. S. Koval'chuk, G. N. Puchka, and V. V. Kholopova, “Constructing periodic solutions of one class of nonautonomous systems of nonlinear second-order equations in a resonance case,” in:Proc. M. Kravchuk 7th Int. Sci. Conf. [in Russian] (May 14–16, 1998), Kiev (1998), p. 66.

  20. B. N. Bublik and V. I. Merkulov, “The dynamic stability of thin elastic shells filled with a liquid,”Prikl. Mat. Mekh.,24, No. 5, 941–946 (1960).

    Google Scholar 

  21. Variation Methods in Problems on the Vibrations of a Liquid and a Body with a Liquid [in Russian], VTs Akad. Nauk SSSR, Moscow (1962).

  22. B. L. Venediktov and R. A. Shibanov, “Self-excitation of low-frequency vibrations in a liquid due to the high-frequency vibrations of a vessel,” in:The Dynamics of Spacecraft and Extraterrestrial Investigations [in Russian], Mashinostroyeniye, Moscow (1986), pp. 215–227.

    Google Scholar 

  23. V. Z. Vlasov,The General Theory of Shells and Its Application in Engineering [in Russian], Gostekhizdat, Moscow (1949).

    Google Scholar 

  24. A. S. Vol'mir,The Nonlinear Dynamics of Plates and Shells [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  25. A. S. Vol'mir,Shells in a Liquid-Gas Flow. Problems of Aeroelasticity [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  26. A. S. Vol'mir,Shells in a Liquid-Gas Flow. Problems of Hydroelasticity [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  27. Sh. U. Galiev,The Dynamics of the Interaction of Structural Elements with a Pressure Wave in a Liquid [in Russian], Naukova Dumka, Kiev (1977).

    Google Scholar 

  28. Sh. U. Galiev,The Dynamics of Hydroelastoplastic Systems [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  29. R. F. Ganiev, “The nonlinear resonance vibrations of bodies with a liquid,”Prikl. Mekh.,13, No. 10, 23–29 (1977).

    Google Scholar 

  30. R. F. Ganiev and P. S. Koval'chuk,The Dynamics of Systems of Rigid and Elastic Bodies [in Russian], Mashinostroyeniye, Moscow (1980).

    Google Scholar 

  31. R. F. Ganiev, P. S. Koval'chuk, V. M. Kuz'ma, and V. S. Pavlovskii, “The resonance phenomena in the nonlinear vibrations of rigid and deformable bodies,”Abstracts of Papers Read at the 8th Int. Conf. on Nonlinear Vibrations, Prague (1978), p. 16.

  32. R. F. Ganiev and V. O. Kononenko,The Vibrations of Solids [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  33. Yu. A. Gorbunov, “Experimental investigation of the vibrations of spherical and cylindrical shells with a liquid in the presence of internal pressure,”Abstracts of Papers Read at the 5th All-Union Conf. on the Theory of Plates and Shells [in Russian], Nauka, Moscow (1965), pp. 57–61.

    Google Scholar 

  34. V. A. Gribkov,The Basic Results of Investigations of the Dynamic Characteristics of Shells Filled with a Liquid: Analysis and Systematization of Studies, Deposit in VINITI No. 4577-82, Moscow (1982).

  35. É. M. Grigolyuk, “Problems of interaction of shells with a liquid,” in:Proc. 7th All-Union Conf. on the Theory of Shells and Plates [in Russian], (Dnepropetrovsk, 1969), Nauka, Moscow (1970), pp. 755–778.

    Google Scholar 

  36. É. I. Grigolyuk and A. G. Gorshkov,The Nonstationary Hydroelasticity of Shells [in Russian], Sudostroyeniye Moscow (1974).

    Google Scholar 

  37. É. I. Grigolyuk and A. G. Gorshkov,The Interaction of Elastic Structures with a Liquid [in Russian], Sudostroyeniye, Leningrad (1976).

    Google Scholar 

  38. É. I. Grigolyuk, A. G. Gorshkov, and F. N. Shklyarchuk, “One method of analysis of the vibrations of a liquid partially filling an elastic shell of revolution,”Izv. Akad. Nauk SSSR, Mekh. Zhid. Gaza, No. 3, 74–80 (1968).

    Google Scholar 

  39. É. I. Grigolyuk and V. V. Kabanov,The Stability of Shells [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  40. E. T. Grigor'ev, “The axisymmetric vibrations of a shell with a liquid,”Prikl. Mekh.,2, No. 4, 39–49 (1966).

    Google Scholar 

  41. E. T. Grigor'ev, “The stability of the longitudinal vibrations of a shell with a liquid,”Prikl. Mekh.,6, No. 3, 23–30 (1967).

    Google Scholar 

  42. A. N. Guz', “Present-day trends in the mechanics of a rigid deformable body,”Prikl. Mekh.,21, No. 9, 3–10 (1985).

    MathSciNet  Google Scholar 

  43. A. N. Guz' (ed.), V. A. Zarutskii (ed.), I. Ya. Amiro, et al.,Experimental Investigations of Thin-Walled Structures [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  44. A. N. Guz' and V. D. Kubenko,The Theory of Nonstationary Aerohydroelasticity of Shells: Methods of Shell Design [in Russian], Vol. 5, Naukova Dumka, Kiev (1982).

    Google Scholar 

  45. A. N. Guz', V. D. Kubenko, and A. É. Babaev,The Hydroelasticity of Shell Systems [in Russian], Vyshcha Shk., Kiev (1984).

    Google Scholar 

  46. A. N. Guz' (ed.), Sh. Markush, L. Pust, et al.,The Dynamics of Bodies Interacting with a Medium [in Russian], Naukova Dumka, Kiev (1991).

    Google Scholar 

  47. L. V. Dokuchaev,The Nonlinear Dynamics of Aircraft with Deformable Elements [in Russian], Mashinostroyeniye, Moscow (1987).

    Google Scholar 

  48. L. H. Donnel,Beams, Plates, and Shells, McGraw-Hill, New York (1976).

    Google Scholar 

  49. M. A. Il'gamov,The Vibrations of Elastic Shells Containing a Liquid and Gas [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  50. M. A. Il'gamov, “Boundary conditions on the shell-liquid interface in the Euler-Lagrange form,” in:Proc. 10th All-Union Conf. on the Theory of Shells and Plates [in Russian], Vol. 2, Metsniereba, Tbilisi (1975), pp. 170–180.

    Google Scholar 

  51. Ya. F. Kayuk, “The dynamics of a shell of revolution with a viscous incompressible liquid,”Prikl. Mekh.,31, No. 11, 58–64 (1995).

    Google Scholar 

  52. Ya. F. Kayuk, Yu. A. Ivanov, and M. K. Shekera, “Nonstationary dynamic processes in a cylindrical reservoir containing a viscous liquid,”Prikl. Mekh.,32, No. 8, 72–79 (1996).

    Google Scholar 

  53. P. S. Koval'chuk, “The dynamic instability of thin-walled cylindrical shells carrying a liquid,”Abstracts of Papers Read at the All-Union Conf. on the Nonlinear Vibrations of Mechanical Systems [in Russian], Gor'kii (1990), p. 42.

  54. P. S. Koval'chuk, “The dynamic instability of thin-walled cylindrical liquid-carrying shells under combined periodic loading,”Abstracts of Papers Read at the Sci.-Tech. Conf. on the Aerohydroelasticity of Components of Machines and Buildings [in Russian], Sevastopol' (1990), p. 50.

  55. P. S. Koval'chuk, L. G. Boyarshina, and V. V. Kholopova, “Using complex resonance flow regimes in technological processes,”Inform. Nov. Tekhnol., No. 2, 27–30 (1995).

    Google Scholar 

  56. P. S. Koval'chuk, V. V. Krishtalev, and N. P. Podchasov, “Analysis of the energy interchange between the natural modes of a liquid in a cylindrical vessel attached to elastic supports,”Prikl. Mekh.,33, No. 4, 54–61 (1997).

    Google Scholar 

  57. P. S. Koval'chuk and L. A. Kruk, “Nonlinear energy interchange between the natural modes of circular cylindrical shells filled with a liquid,”Prikl. Mekh.,36, No. 1, 115–122 (2000).

    MATH  Google Scholar 

  58. P. S. Koval'chuk and L. A. Kubenko, “Interaction of oscillating cylindrical shells containing a liquid,” in:The Dynamics of Bodies Interacting with a Medium [in Russian], (A. N. Guz' (ed.), Sh. Markush, L. Pust, et al.), Naukova Dumka, Kiev (1991), pp. 168–214.

    Google Scholar 

  59. P. S. Koval'chuk and V. S. Pavlovskii, “The wave modes of the nonlinear deformation of liquid-containing shells under radial dynamic pressure,”Dokl. Akad. Nauk Ukrainy, Ser. A, No. 11, 24–28 (1992).

    Google Scholar 

  60. P. S. Koval'chuk and V. S. Pavlovskii, “The nonlinear wave deformation of cylindrical liquid-containing shells under impulse radial pressure,”Prikl. Mekh., 29, No. 12, 43–50 (1993).

    Google Scholar 

  61. P. S. Koval'chuk and V. S. Pavlovskii, “Nonlinear wave processes in cylindrical liquid-containing shells under short-term dynamic loading,” in:Technical-Physical Problems of New Engineering: Abstract Book [in Russian], Izd. MVTU, Moscow (1994).

    Google Scholar 

  62. P. S. Koval'chuk, V. S. Pavlovskii, and V. G. Filin, “The nonlinear dynamics of cylindrical bodies carrying liquid masses and subject to periodic and impulse radial perturbation,” in:Fundamental and Applied Problems of Space Exploration [in Russian], Zhitomir (1993), p. 23.

  63. P. S. Koval'chuk and V. S. Pavlovskii, and V. G. Filin, “Analysis of resonance regimes of the wave deformation of cylindrical shells carrying a liquid,”Prikl. Mekh.,30, No. 2, 49–54 (1994).

    Google Scholar 

  64. P. S. Koval'chuk V. S. Pavlovskii, and V. G. Filin, “Stability analysis of resonance regimes of the nonlinear vibrations of liquid-containing cylindrical shells under longitudinally transversal periodic excitation,”Dokl. NAN Ukrainy, No. 3, 31–34 (2000).

    Google Scholar 

  65. P. S. Koval'chuk and N. P. Podchasov, “Simulation of the nonlinear multimodal vibrations of thin cylindrical shells with close fundamental frequencies,”Abstract of Papers Read at the Int. Conf. on Modeling and Investigation of System Stability (May, 1999) [in Russian], Kiev (1999), p. 40.

  66. P. S. Koval'chuk and N. P. Podchasov, “Nonlinear bending waves in cylindrical shells under periodic excitation,”Prikl. Mekh.,24, No. 11, 58–62 (1988).

    Google Scholar 

  67. P. S. Koval'chuk and N. P. Podchasov, “The nonstationary wave motions of a liquid in an oscillating cylindrical vessel passing a resonance band,”Prikl. Mekh.,32, No. 1, 36–41 (1995).

    Google Scholar 

  68. P. S. Koval'chuk and N. P. Podchasov, “The nonlinear interaction of bending waves in shells of revolution under resonance conditions,”,Abstracts of Papers Read at the Int. Conf. on Modeling and Investigation of System Stability (May, 1997) [in Russian], Kiev (1997), p. 74.

  69. P. S. Koval'chuk and N. P. Podchasov, “Analysis of the nonlinear interaction of the bending modes of circular cylidrical shells under periodic excitation,”Prikl. Mekh.,34, No. 12, 62–69 (1998) (Int. Appl. Mech.,34, No. 12, 1233–1240 (1998)).

    MATH  Google Scholar 

  70. P. S. Koval'chuk, G. N. Puchka, and V. V. Kholopova, “The nonlinear resonance vibrations of a liquid in a cylindrical vessel under longitudinally transversal periodic excitation,”Prikl. Mekh.,23, No. 8, 95–100 (1987).

    Google Scholar 

  71. P. S. Koval'chuk, G. N. Puchka, and V. V. Kholopova, “The nonlinear wave motions of a liquid in axisymmetric cavities subject to vibrations,”Izv. Akad. Nauk SSSR, Mekh. Zhid. Gaza, No. 3, 120–125 (1989).

    MathSciNet  Google Scholar 

  72. P. S. Koval'chuk, G. N. Puchka, and V. V. Kholopova, “Nonstationary wave motions of a liquid in longitudinally oscillating cylindrical vessel,”Dokl. NAN Ukrainy, No. 11, 26–31 (1999).

    Google Scholar 

  73. P. S. Koval'chuk and V. V. Kholopova, “Analysis of energy interchange between the natural modes of a liquid in a cylindrical tank,”Dokl. Akad. Nauk Ukrainy, Ser. A, No. 1, 36–41 (1997).

    Google Scholar 

  74. K. S. Kolesnikov,Longitudinal Vibrations of a Rocket with a Liquid-Propellant Engine [in Russian], Mashinostroyeniye, Moscow (1971).

    Google Scholar 

  75. K. S. Kolesnikov,Rocket Dynamics [in Russian], Mashinostroyeniye, Moscow (1980).

    Google Scholar 

  76. V. O. Kononenko,Nonlinear Vibrations of Mechanical Systems: Selected Workds [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  77. A. V. Kochetkov,Numerical Simulation of Nonlinear Processes of Nonstationary Interaction of Shell Structures with Compressible Media [in Russian], Author's Abstract of Doctoral Dissertation, Moscow (1993).

  78. T. S. Krasnopol'skaya and K. A. Lavrov, “The nonlinear vibrations of a liquid-containing cylindrical shell under limited excitation,”Prikl. Mekh.,24, No. 11, 50–58 (1988).

    MathSciNet  Google Scholar 

  79. T. S. Krasnopol'skaya and N. P. Podchasov, “Waves in a liquid between two coaxial cylindrical shells due to the vibrations of the inner cylinder,”Prikl. Mekh.,28, No. 3, 61–70 (1992).

    MATH  Google Scholar 

  80. T. S. Krasnopol'skaya and N. P. Podchasov, “The forced vibrations of a liquid between two cylinders excited by the vibrations of the inner shell,”Prikl. Mekh.,28, No. 4, 42–48 (1992).

    MATH  Google Scholar 

  81. T. S. Krasnopol'skaya and N. P. Podchasov, “Resonances and chaos in nonaxisymmetric dynamic processes in hydroelastic systems,”Prikl. Mekh.,29, No. 12, 72–77 (1993).

    Google Scholar 

  82. T. S. Krasnopol'skaya and A. Yu. Shvets, “Regular and chaotic surface waves due to limited excitation of vibrations of a cylindrical tank,”Prikl. Mekh.,26, No. 8, 85–93 (1990).

    MathSciNet  Google Scholar 

  83. T. S. Krasnopol'skaya and A. Yu. Shvets, “The properties of chaotic vibrations of a liquid in cylindrical tanks,”Prikl. Mekh.,28, No. 6, 52–61 (1992).

    MATH  MathSciNet  Google Scholar 

  84. V. D. Kubenko,The Nonstationary Interaction of Structural Elements with a Medium [in Russian], Naukova Dumka, Kiev (1979).

    Google Scholar 

  85. V. D. Kubenko and P. S. Koval'chuk, “The nonlinear vibrations and wave modes of deformation of cylindrical shells filled with a liquid”,Abstracts of Invited Lectures and Short Communications Read at the 11th Int. Conf. on Nonlinear Oscillations (August, 17–23), Budapest (1987), p. 44.

  86. V. D. Kubenko and P. S. Koval'chuk, “Nonlinear problems on the vibrations of thin shells (review),”Prikl. Mekh.,34, No. 8, 3–31 (1998) (Int. Appl. Mech.,34, No. 8, 703–728 (1998)).

    MATH  MathSciNet  Google Scholar 

  87. V. D. Kubenko, P. S. Koval'chuk, L. G. Boyarshina, et al.,The Nonlinear Dynamics of Axisymmetric Bodies Carrying a Liquid [in Russian], Naukova Dumka, Kiev (1992).

    Google Scholar 

  88. V. D. Kubenko, P. S. Koval'chuk, and T. S. Krasnopol'skaya,The Nonlinear Interaction between the Modes of the Flexural Vibrations of Cylidrical Shells [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  89. V. D. Kubenko, P. S. Koval'chuk, and N. P. Podchasov,The Nonlinear Vibrations of Cylindrical Shells [in Russian], Vyshcha Shk., Kiev (1989).

    Google Scholar 

  90. V. D. Kubenko, V. D. Lakiza, V. S. Pavlovskii, et al.,The Dynamics of Elastic Gas-Liquid Systems under Vibrational Actions [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  91. E. V. Ladygina and A. I. Manevich, “The free vibrations of a nonlinear cubical system with two degrees of freedom and close fundamental frequencies,”Prikl. Mat. Mekh.,57, No. 2, 40–49 (1993).

    MathSciNet  Google Scholar 

  92. H. Lamb,Hydrodynamics [Russian translation]. Gostekhizdat, Moscow-Leningrad (1947).

    Google Scholar 

  93. A. D. Lizarev and N. B. Rostanina,The Vibrations of Metal-Polymeric and Homogeneous Spherical Shells [in Russian] Nauka i Tekhnika, Minsk (1984).

    Google Scholar 

  94. O. S. Limarchenko,Using Direct Methods in the Solution of Applied Problems of the Nonlinear Dynamics of Bodies Partially Filled with a Liquid [in Russian] Preprint 87.8, Inst. Mat., Kiev (1987).

    Google Scholar 

  95. O. S. Limarchenko and V. V. Yasinskii,The Nonlinear Dynamics of Structures with a Liquid [in Russian] KPI, Kiev (1997).

    Google Scholar 

  96. L. G. Loitsyanskii,Fluid Mechanics [in Russian] Nauka, Moscow (1973).

    Google Scholar 

  97. I. A. Lukovskii,The Nonlinear Vibrations of a Liquid in Vessels of Complex Geometry [in Russian] Naukova Dumka, Kiev (1975).

    Google Scholar 

  98. I. A. Lukovskii,Introduction to the Nonlinear Dynamics of a Rigid Body with Cavities Containing a Liquid [in Russian] Naukova Dumka, Kiev (1990).

    Google Scholar 

  99. I. A. Lukovskii, V. A. Trotsenko, and V. I. Usyukin,Intraction of Thin-Walled Elastic Elements with a Liquid in Mobile Cavities [in Russian] Naukova Dumka, Kiev (1989).

    Google Scholar 

  100. A. I. Lurie,Analytical Mechanics [in Russian] Fizmatgiz, Moscow (1961).

    Google Scholar 

  101. A. M. Lyapunov,The General Problem on Motion Stability [in Russian] Gostekhizdat, Moscow-Leningrad (1950).

    Google Scholar 

  102. I. G. Malkin,Some Problems of the Theory of Nonlinear Vibrations [in Russian] Fizmatgiz, Moscow (1956).

    Google Scholar 

  103. I. G. Malkin,The Theory of Motion Stability [in Russian] Nauka, Moscow (1966).

    Google Scholar 

  104. N. A. Kil'chevskii (ed.),The Mechanics of Shell-Liquid-Heated-Gas Systems [in Russian] Naukova Dumka, Kiev (1970).

    Google Scholar 

  105. G. N. Mikishev,Experimental Methods in Spacecraft Dynamics [in Russian] Mashinostroyeniye, Moscow (1978).

    Google Scholar 

  106. G. N. Mikishev and B. I. Rabinovich,The Dynamics of Solids with Cavities Partially Filled with a Liquid [in Russian], Mashinostroyeniye, Moscow (1968).

    Google Scholar 

  107. G. N. Mikishev and B. I. Rabinovich,The Dynamics of Thin-Walled Structures with Compartments Containing a Liquid [in Russian], Mashinostroyeniye, Moscow (1971).

    Google Scholar 

  108. Yu. A. Mitropol'skii,The Averaging Method in Nonlinear Mechanics [in Russian] Naukova Dumka, Kiev (1971).

    Google Scholar 

  109. E. N. Mnev and A. K. Pertsev,Shell Hydroelasticity [in Russian] Sudostroyeniye, Leningrad (1970).

    Google Scholar 

  110. N. N. Moiseev, “Variation problems of the vibration theory of a liquid and body with a liquid,” in:Variation Methods in Problems on the Vibrations of a Liquid and Body with a Liquid [in Russian], VTs Akad. Nauk SSSR, Moscow (1962), pp. 9–118.

    Google Scholar 

  111. N. N. Moiseev,Asymptotic Methods of Nonlinear Mechanics [in Russian], Nauka, Moscow (1969).

    MATH  Google Scholar 

  112. N. N. Moiseev and A. A. Petrov,Numerical Methods of Calculation of the Fundamental Frequencies of the Vibrations of a Limited Liquid Volume [in Russian], VTs Akad. Nauk SSSR, Moscow (1966).

    Google Scholar 

  113. N. N. Moiseev and V. V. Rumyantsev,The Dynamics of a Body with Cavities Containing a Liquid [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  114. F. Moon,Chaotic Vibrations [Russian translation], Mir, Moscow (1990).

    MATH  Google Scholar 

  115. Kh. M. Mushtari and K. Z. Galimov,The Nonlinear Theory of Elastic Shells [in Russian], Tatknigoizdat, Kazan' (1957).

    Google Scholar 

  116. G. S. Narimanov, “The motion of a solid whose cavity is partially filled with a liquid,”Prikl. Mat. Mekh.,20, No. 1, 21–38 (1956).

    MATH  MathSciNet  Google Scholar 

  117. G. S. Narimanov, “The vibrations of a liquid in mobile cavities,”Izv. Akad. Nauk SSSR, Mekh. Mashinostr., No. 10 71–74 (1957).

    Google Scholar 

  118. G. S. Narimanov, L. V. Dokuchaev, and I. A. Lukovskii,The Nonlinear Dynamics of an Aircraft with a Liquid [in Russian], Mashinostroyeniye, Moscow (1977).

    Google Scholar 

  119. Yu. I. Neimark and P. S. Landa,Stochastic and Chaotic Vibrations [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  120. A. V. Kornishin (ed.),The Nonstationary Aeroelasticity of Thin-Walled Structures [in Russian], Mashinostroyeniye, Moscow (1982).

    Google Scholar 

  121. S. K. Nikitin,The Nonstationary Interaction of Elastic Solids of Revolution Partially Filled with a Liquid [in Russian], Author's Abstract of Doctoral Dissertation, Kiev (1987).

  122. N. A. Nikolaenko,Probability Methods in Dynamic Design of Machine-Building Structures [in Russian], Mashinostroyeniye, Moscow (1967).

    Google Scholar 

  123. V. V. Novozhilov,The Theory of Thin Shells [in Russian], Sudpromgiz, Leiningrad (1962).

    Google Scholar 

  124. E. I. Obraztsova, “The forced nonlinear vibrations of a cylindrical shell with a liquid,” in:Proc. 3rd Symp. on Vibration of Elastic Structures with a Liquid (Novosibirsk, 1976) [in Russian], Moscow (1976), pp. 314–319.

  125. E. I. Obraztsova, “Nonlinear parametric vibrations of a liquid-containing cylindrical shell under longitudinal excitation,”Izv. Vuzov, Aviats. Tekhn., No. 3, 87–93 (1976).

    Google Scholar 

  126. E. I. Obraztsova and F. N. Shklyarchuk, “The nonlinear parametric vibrations of a cylindrical tank with a liquid,”Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 133–145 (1979).

    MathSciNet  Google Scholar 

  127. E. I. Obraztsova and F. N. Shklyarchuk, “The nonlinear parametric vibrations of an orthotropic cylindrical tank partially filled with a liquid,” in:Proc. 4th Symp. (Novosibirsk, 1979) [in Russian], Moscow (1980), pp. 216–224.

  128. V. S. Pavlovskii and V. G. Filin, “The vibrational stability of a cylindrical shell with a liquid under nonlinear-resonance conditions,”Prikl. Mekh.,15, No. 8, 46–55 (1979).

    Google Scholar 

  129. V. S. Pavlovskii and V. G. Filin, “The nonlinear resonance vibrations of liquid-containing cylindrical, shells under transversal loads,” in:Proc. 4th Workshop on the Dynamics of Elastic and Rigid Bodies Interacting with a Liquid [in Russian], Izd. Tomskogo Univ., Tomsk (1981), pp. 158–163.

    Google Scholar 

  130. V. S. Pavlovskii and V. G. Filin, “The nonlinear parametric vibrations of liquid-containing cylindrical shells with an initial deflection,”Prikl. Mekh.,21, No. 3, 46–56 (1985).

    Google Scholar 

  131. V. I. Perekhrest and G. M. Ulitin, “The exact solutions of the axisymmetric problem of the hydroelasticity of a cylindrical shell,”Prikl. Mekh.,16, No. 8, 99–104 (1980).

    MathSciNet  Google Scholar 

  132. M. P. Petrenko, “The natural vibrations of a liquid with a free surface and the elastic bottom of a cylindrical cavity,”Prikl. Mekh.,5, No. 6, 44–50 (1969).

    Google Scholar 

  133. M. P. Petrenko, “The concurrent vibrations of a liquid and the elastic bottom of a cylindrical tank,” in:Proc. 7th All-Union Conf. on the Theory of Shells and Plates (Dnepropetrovsk, 1969) [in Russian], Nauka, Moscow (1970), pp. 474–478.

    Google Scholar 

  134. M. P. Petrenko, “Resonance vibrations of the free liquid surface in a tank with an elastic bottom,]rd in:Proc. 3rd Workshop on the Dynamics of Elastic and Rigid Bodies Interacting with a Liquid (Tomsk, 1977) [in Russian], Tomsk (1978), pp. 91–97.

  135. B. I. Rabinovich, “The equations of lateral vibrations of shells with a liquid filler,”Izv. Akad. Nauk SSSR, Mekh. Mashinostr., No. 1, 166–169 (1964).

    Google Scholar 

  136. B. I. Rabinovich,Introduction to the Dynamics of Carrier Rockets [in Russian], Mashinostroyeniye, Moscow (1975).

    Google Scholar 

  137. B. I. Rabinovich, “The vibrations of elements with cavities containing a liquid,” in:The Vibrations of Machines, Structures, and Their Components, Vol. 3 of the six-volume seriesVibrations in Engineering: A Reference Book [in Russian], Mashinostroyeniye, Moscow (1980), pp. 61–89.

    Google Scholar 

  138. M. T. Rabinovich and D. I. Trubetskov,Introduction to the Theory of Vibrations and Waves [in Russian], Nauka Moscow (1984).

    Google Scholar 

  139. I. M. Rapoport,The Dynamics of an Elastic Body Partially Filled with a Liquid [in Russian], Mashinostroyeniye, Moscow (1966).

    Google Scholar 

  140. I. M. Rapoport,The Vibrations of an Elastic Shell Partially Filled with a Liquid [in Russian], Mashinostroyeniye, Moscow (1967).

    Google Scholar 

  141. Ya. Ya. Rushchytskii and S. I. Tsurpal,Waves in a Material with a Microstructure [in Ukrainian], Oranta, Kiev (1998).

    Google Scholar 

  142. A. V. Sevast'yanov, “The stability of a circular cylindrical shell filled with a liquid and subject to longitudinal dynamic compression,”Inzh. Zh. Mekh. Tverd. Tela, No. 3, 125–132 (1968).

    Google Scholar 

  143. I. T. Selezov,Simulation of Wave and Diffraction Processes in Continua [in Russian], Naukova Dumka, Kiev (1989).

    Google Scholar 

  144. I. T. Selezov and L. V. Selezova,Waves in Magnetohydroelastic Media [in Russian], Naukova Dumka, Kiev (1975).

    Google Scholar 

  145. V. F. Sivak, “Experimental investigation of the resonance and dissipative properties of a glass-fiber-reinforced plastic cylindrical shell filled with a liquid,”Prikl. Mekh.,34, No. 2, 39–42 (1998).

    MATH  Google Scholar 

  146. V. F. Sivak and A. I. Telalov, “Experimental investigation of the vibrations of a cylindrical shell contacting with a liquid,”Prikl. Mekh.,27, No. 10, 121–123 (1991).

    Google Scholar 

  147. V. F. Sivak and A. I. Telalov, “Experimental investigation of the vibration damping of a longitudinally reinforced cylindrical shell contacting with a liquid,”Prikl. Mekh.,28, No. 4, 77–80 (1992).

    Google Scholar 

  148. L. I. Slepyan,Nonstationary Elastic Waves [in Russian], Sudostroveniye, Leningrad (1972).

    Google Scholar 

  149. S. P. Timoshenko,Vibrations in Engineering [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  150. G. M. Ulitin, “The dynamic stability of a cylindrical shell filled with a liquid to different levels,”Teor. Prikl. Mekh.,17, 93–98 (1986).

    Google Scholar 

  151. S. F. Feshchenko, I. A. Lukovskii, B. I. Rabinovich, and L. V. Dokuchaev,Methods for Determination of the Apparent Additional Masses of a Liquid in Mobile Cavities, [in Russian], Naukova, Dumka, Kiev (1969).

    Google Scholar 

  152. K. V. Frolov and V. I. Antonov,Vibrations of Shells in a Liquid [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  153. F. L. Chernous'ko,The Motion of a solid with Cavities Containing a Viscous Liquid [in Russian], VTs Akad. Nauk SSSR, Moscow (1969).

    Google Scholar 

  154. Yu. S. Shkenev, “The dynamics of an elastic and elastoplastic shell filled with an ideal liquid,” in:Proc. 4th All-Union Conf. on the Theory of Shells and Plates (Yerevan, 1962) [in Russian], Izd. Akad. Nauk SSSR, Moscow (1964), pp. 997–1007.

    Google Scholar 

  155. F. N. Shklyarchuk, “The axisymmetric vibrations of a liquid inside an elastic cylindrical shell with an elastic bottom,”Izv. Vuzov, Aviats. Tekh., No. 4, 75–83 (1965).

    Google Scholar 

  156. F. N. Shklyarchuk, “An approximate method of analysis of the axisymmetric vibrations of shells of revolution with a liquid filler,”Izv. Akad. Nauk SSSR, Mekh. Mashinostr., No. 6, 123–129 (1965).

    Google Scholar 

  157. F. N. Shklyarchuk, “The dynamic stability of a cylindrical shell partially filled with a liquid and subject to longitudinal vibrations,” in:Proc. 7th All-Union Conf. on the Theory of Shells and Plates (Dnepropetrovsk, 1969) [in Russian], Nauka, Moscow (1970), pp. 619–624.

    Google Scholar 

  158. F. N. Shklyarchuk, “The effect of the compressibility of a liquid in the longitudinal vibrations of a cylindrical tank,” in:Vibrations of Elastic Structures with a Liquid, Novosib. Elektrotekh. Inst., Novosibirsk (1973), pp. 291–313.

    Google Scholar 

  159. F. N. Shklyarchuk, “The parametric vibrations of a cylindrical shell partially filled with a liquid and subject to longitudinal excitation,” in:Proc. 7th All-Union Conf. on the Theory of Shells and Plates (Dnepropetrovsk, 1969), [in Russian], Nauka, Moscow (1970), pp. 314–329.

    Google Scholar 

  160. F. N. Shklyarchuk,The Dynamics of Structures of Aircrafts [in Russian], Izd. Moskovskogo Aviats. Inst., Moscow (1983).

    Google Scholar 

  161. V. P. Shmakov, “The equations of axisymmetric vibrations of a cylindrical shell with a liquid filler,”Izv. Akad. Nauk SSSR, Mekh. Mashinostr., No. 1, 170–173 (1964).

    Google Scholar 

  162. V. P. Shmakov, “One technique simplifying the use of the Bubnov-Galerkin method in solving boundary-value problems,”Inzh. Zh. Mekh. Tverd. Tela, No. 5, 129–136 (1967).

    Google Scholar 

  163. H. G. Schuster,Deterministic Chaos: An Introduction [Russian translation], Mir, Moscow (1988).

    Google Scholar 

  164. H. N. Abramson, “Dynamic behavior of liquid in moving container,”Appl. Mech. Revs.,16, No. 7, 501–506 (1963).

    Google Scholar 

  165. H. N. Abramson (Ed),The Dynamic Behavior of Liquid in Moving Containers with Applications to Space Vehicle Technology, NASA, SP, 106, Washington, D. C. (1966).

  166. H. N. Abramson, W. H. Chu, and D. D. Kana, “Some studies of nonlinear lateral sloshing in rigid containers,”Trans. ASME, Ser. E,33, No. 4, 777–784 (1966).

    Google Scholar 

  167. H. F. Bauer,Fluid Oscillations in the Containers of Space Vehicles and their Influence upon Stability, NASA TR-87, Washington D. C. (1964).

  168. H. F. Bauer, S. S. Chang, and J. T. Wang, “Nonlinear liquid motion in a longitudinally excited container with elastic bottom,”AIAA J.,9, No. 12, 2333–2339 (1971).

    MATH  ADS  Google Scholar 

  169. H. F. Bauer and J. Woodward, “Fluid behavior in a longitudinally-excited cylindrical tank of arbitrary sector-annular cross section,”AIAA J.,8, No. 4, 713–719 (1970).

    Article  ADS  Google Scholar 

  170. W. H. Chu and D. D. Kana, “A theory for nonlinear transverse vibrations of a partially filled elastic tank,”AIAA J.,5, No. 10, 1828–1835 (1967).

    ADS  Google Scholar 

  171. F. T. Dodge, D. D. Kana, and H. N. Abramson, “Liquid surface oscillations in longitudinally excited rigid cylindrical containers,”AIAA J., 3, No. 4, 685–695 (1965).

    Article  MATH  Google Scholar 

  172. W. Flügge,Stresses in Shells, Springer Verlag, Berlin (1973).

    MATH  Google Scholar 

  173. R. E. Hutton, “An investigation of nonlinear, nonplanar oscillations of fluid in a cylindrical container,” in:AIAA Fifth Annual Struct. Mater. Conf. (April 1–3), Palm Springs, Calif. (1964), pp. 191–194.

  174. D. D. Kana and R. R. Craig, “Parametric oscillations of a longitudinally excited cylindrical shell containing liquid,”J. Spacecraft Rockets,5, No. 1, 13–21 (1968).

    ADS  Google Scholar 

  175. D. D. Kana, U. S. Lindholm, and H. N. Abramson, “An experimental study of liquid instability in a vibrating elastic tank,” in:AIAA Symposium on Structural Dynamics and Aeroelasticity (1965), pp. 162–168.

  176. G. Lamé,Lecons sur la theorie mathematique de l'elasticite des coprs solids, Bachelir, Paris (1852).

    Google Scholar 

  177. U. S. Lindholm, W. H. Chu, D. D. Kana, and H. N. Abramson, “Bending vibration of a circular cylindrical shell with an internal liquid having a free surface,”AIAA J.,1, No. 9, 101–110 (1963).

    Google Scholar 

  178. U. S. Lindholm, D. D. Kana, and H. N. Abramson, “Breathing vibration of a circular cylindrical shell with an internal liquid,”J. Aerospace Sci.,29, No. 9, 1052–1059 (1962).

    Google Scholar 

  179. J. W. Miles, “Nonlinear surface waves in closed basins,”J. Fluid Mech.,75, No. 3, 419–448 (1976).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  180. J. W. Miles, “Internally resonant surface, waves in circular cylinder,”J. Fluid Mech.,149, pt 1, 1–14 (1984).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  181. J. W. Miles, “Resonantly forced surface waves in circular cylinder,”J. Fluid Mech.,149, pt 2, 15–31 (1984).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  182. A. H. Nayfeh and D. T. Mook,Nonlinear Oscillations, Wiley, New York (1979).

    MATH  Google Scholar 

Download references

Authors
  1. V. D. Kubenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. S. Koval’chuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 4, pp. 3–34, April, 2000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kubenko, V.D., Koval’chuk, P.S. Nonlinear problems of the dynamics of elastic shells partialiy filled with a liquid. Int Appl Mech 36, 421–448 (2000). https://doi.org/10.1007/BF02681969

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02681969

Keywords

Search

Navigation