Skip to main content
SpringerLink
Log in

Investigation of Forced Oscillations in Circular Cylindrical Vessels Separated by Diametrical Barriers

  • Published:
Nonlinear Oscillations

Abstract

We consider nonlinear oscillations of an ideal incompressible liquid in a partially filled vertical semicircular cylindrical tank. We construct approximate periodic solutions for a four-mode system that describes nonlinear oscillations in a semicircular cylindrical tank under the action of a perturbation force in the plane of the barrier. We construct and investigate the domains of stability and instability for the physical processes considered. We perform a numerical realization of the method and analyze the hydrodynamic interaction of the liquid with the tank. The problem considered is of interest for the investigation of nonlinear processes in a liquid in the case of tanks with diametrical barriers.

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. H. N. Abramson, L. R. Garza, and D. D. Kana, “Motion of the mass of liquid in cylindrical tanks divided into parts,” Raket. Tekh., No. 6, 155-158 (1962).

    Google Scholar 

  2. I. A. Lukovskii, “A variational method in nonlinear problems of dynamics of a bounded volume of liquid with free surface,” in: Oscillations of Elastic Structures with Liquid [in Russian], Volna, Moscow (1976), pp. 260-264.

  3. I. A. Lukovskii, Introduction to Nonlinear Dynamics of Bodies with Cavities Partially Filled with Liquid [in Russian], Naukova Dumka, Kiev (1990).

    Google Scholar 

  4. I. O. Lukovs'kyi and O. V. Solodun, “A nonlinear model of the motion of a liquid in cylindrical vessels divided into compartments,” Dop. Nats. Akad. Nauk Ukr., 51-55 (2001).

  5. N. N. Moiseev, “On the theory of nonlinear oscillations of a bounded volume of liquid,” Prikl. Mat. Mekh., 22, 612-621 (1958).

    Google Scholar 

  6. A. M. Pil'kevich, “Analysis of forced oscillations of a liquid in cylindrical coaxial reservoirs,” in: Applied Methods for Investigation of Physicomechanical Processes [in Russian], Kiev (1979), pp. 49-63.

  7. H. N. Abramson, W. H. Chu, and D. D. Kana, “Some studies of nonlinear lateral sloshing in rigid containers,” J. Appl. Mech., 33, No. 4, 66-74 (1966).

    Google Scholar 

  8. H. N. Abramson and L. R. Garza, “Some measurement of liquid frequencies and damping in compartment cylindrical tanks,” AIAA J. Spacecraft Rock., 2, No. 3, 453-455 (1965).

    Google Scholar 

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

    Google Scholar 

  10. O. M. Faltinsen, “A nonlinear theory of sloshing in rectangular tanks,” J. Ship. Res., 18, No. 4, 224-241 (1974).

    Google Scholar 

  11. O. M. Faltinsen, O. F. Rongebakke, I. A. Lukovsky, and A. N. Timokha, “Multidimensional modal analysis of nonlinear sloshing in a rectangular tanks with finite water depth,” J. Fluid Mech., 407, 201-234 (2000).

    Google Scholar 

  12. R. E. Hatton, “An investigating of nonlinear, nonplanar oscillations of liquid in cylindrical containers,” Tech. Note. Washington (NASA; D-1870), 145-153 (1963).

  13. J. C. Luce, “A variational principle for a fluid with a free surface,” J. Fluid Mech., 27, 395-397 (1967).

    Google Scholar 

  14. J. W. Miles, “Nonlinear surface waves in closed basins,” J. Fluid Mech., 75, 419-448 (1976).

    Google Scholar 

  15. J. W. Miles, “Internally resonant surface waves in a circular cylinder,” J. Fluid Mech., 149, 1-14 (1984).

    Google Scholar 

  16. J. W. Miles, “Resonantly forced surface waves in a circular cylinder,” J. Fluid Mech., 149, 15-31 (1984).

    Google Scholar 

  17. F. Solaas and O. M. Faltinsen, “Combined numerical and analytical solutions for sloshing in two-dimensional tanks of general shape,” J. Ship. Res., 41, 118-129 (1997).

    Google Scholar 

  18. F. Welt and V. I. Modi, “Vibration damping through liquid sloshing. Part 1 — A nonlinear analysis,” ASME, Trans. J. Vibr. Acoust., 114, 10-16 (1992).

    Google Scholar 

  19. F. Welt and V. I. Modi, “Vibration damping through liquid sloshing. Part 2 — Experimental results,” ASME, Trans. J. Vibr. Acoust., 114, 17-23 (1992).

    Google Scholar 

  20. G. N. Mikishev and B. I. Rabinovich, Dynamics of a Solid with Cavities Partially Filled with Liquid [in Russian], Mashinostroenie, Moscow (1968).

    Google Scholar 

  21. S. F. Feshchenko, I. A. Lukovskii, B. I. Rabinovich, et al., Methods for Determination of Associated Masses in Movable Cavities [in Russian], Naukova Dumka, Kiev (1969).

    Google Scholar 

  22. O. S. Limarchenko, “Variational statement of the problem of motion of a reservoir with liquid,” Dokl. Akad Nauk Ukr.SSR, Ser. A, No. 904-908 (1978).

  23. G. S. Narimanov, “On the motion of a vessel partially filled with liquid with regard for the motion of the liquid,” Prikl. Mat. Mekh., 21, No. 4, 513-524 (1957).

    Google Scholar 

  24. I. A. Lukovskii and A. N. Timokha, “A nonlinear theory of sloshing in movable cavities: classical and nonclassical problems,” in: Problems of Analytic Mechanics and Its Applications [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1999), pp. 169-200.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    O. V. Solodun

Authors
  1. O. V. Solodun
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Solodun, O.V. Investigation of Forced Oscillations in Circular Cylindrical Vessels Separated by Diametrical Barriers. Nonlinear Oscillations 5, 83–98 (2002). https://doi.org/10.1023/A:1014661129140

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014661129140

Keywords

Search

Navigation