Skip to main content
SpringerLink
Log in

Motion of a Solid Body with a Cavity Containing a Multilayer Ideal Fluid*

  • Published:
International Applied Mechanics Aims and scope

The motion of a solid body with a cavity containing a heavy multilayer ideal incompressible fluid is considered using a linear problem statement. An algorithm for obtaining a system of ordinary differential equations describing the forced vibrations of the multilayer fluid in the solid body moving in a certain way is given. Using a cylindrical cavity of arbitrary cross-section as an example, this system of equations is analyzed in the cases of complete and partial filling of the cavity, translational vertical and horizontal displacements of the body, vibrations of the body as a physical pendulum. It is shown that in the case of a cavity in the form of a rectangular parallelepiped when the perturbing force acts horizontally parallel to its lateral sides, the waves are excited on the free and inner surfaces of the multilayer fluid, which are asymmetric about the symmetry planes of the rectangular parallelepiped. If the cavity is axisymmetric, then only one-node vibrations of the free and inner surfaces are excited. The frequency equation of free oscillations of multilayer fluid is analyzed for a number of partial cases: full and partial filling of the cavity, infinitely high depths of filling, two-layer and three-layer fluids. For identical layers of the fluid (constant depth of filling of layers and constant ratio of the densities of the layers) the analytical solution of the frequency equation is obtained and analyzed.

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. K. Win and A. N. Temnov, “Oscillations of immiscible fluids in a stationary cylindrical vessel and their mechanical analogs,” Vesn. MGTU im. Baumana, Ser. Estest. Nauki, No. 3, 57–69 (2016).

  2. K. K. Win and A. N. Temnov, “Experimental and theoretical study of vibrations of a rigid body with a layered fluid,” Inzh. Zh.: Nauka i Innov., MGTU im. Baumana, Elektr. Zhurn., No. 4, 1–13 (2018).

  3. V. S. Gontkevich, “Natural vibrations of a stratified fluid in vessels,” Izv. AN SSSR, Mekh. Zhydk. i Gaza, No. 1, 147–152 (1973).

  4. Yu. N. Kononov, “Oscillation of a physical pendulum with a multilayer ideal fluid,” Mat. Probl. Mekh. Obch. Mat., Zb. Prats., Inst. Mat. NAN Ukr., 12(5), 73–89 (2015).

  5. N. D. Kopachevskii, “Vibrations of immiscible fluids,” Zh. Vych. Mat. Mat. Fiz., 13, No. 5, 1249–1263 (1973).

    MathSciNet  Google Scholar 

  6. N. D. Kopachevskii and D. O. Tsvetkov, “Vibrations of a stratified fluid,” Sovr. Mat., Fund. Napr., No. 29, 103–130 (2008).

  7. G. N. Mikishev and B. I. Rabinovich, Dynamics of a Rigid Body with Cavities Partially Filled with a Fluid [in Russian], Mashinostroenie, Moscow (1968).

  8. N. N. Moiseev, “The problem of the motion of a rigid body containing fluid masses with a free surface,” Mat. Sborn., 32(74), No. 1, 61–96 (1953).

  9. N. N. Moiseev, “The problem of small vibrations of an open vessel with a fluid under an elastic force,” Ukr. Mat. Zhurn., Vol. 4, No. 2, 168–173 (1952).

    Google Scholar 

  10. N. N. Moiseev and A. A. Petrov, Numerical Methods for Calculating the Natural Frequencies of Vibrations of a Limited Volume of Fluid, Izd. VTs AN SSSR, Moscow (1966).

  11. M. Amaouche and B. Meziani, “Coupled frequencies of a rectangular hydroelastic system with two fluids,” Meccanica, No. 47, 71–83 (2012).

  12. H. A. Ardakani, T. J. Bridges, and M. R. Turner, “Dynamic coupling between horizontal vessel motion and two-layer shallow-water sloshing,” J. Fluids Struct., No. 59, 432–460 (2015).

  13. V. I. Bukreev, I. V. Sturova, and A. V. Chebotnikov, “Seiche oscillations in a reservoir filled with a double-layer fluid,” Fluid Dynam., 49, No. 3, 395–402 (2014).

    Article  Google Scholar 

  14. O. M. Faltinsen and A. N. Timokha, Sloshing, Cambridge University Press, Cambridge (2009).

  15. R. A. Ibrahim, “Recent advances in physics of fluid parametric sloshing and related problems,” J. Fluids Eng., No. 137, 1–52 (2015).

  16. R. A. Ibrahim, Liquid Sloshing Dynamics: Theory and Applications, Cambridge University Press, Cambridge (2005).

  17. D. A. Goncharov and A. A. Pozhalostin, “Symmetric vibrations of a liquid in a vessel with a separator and an elastic bottom,” IOP Conf. Ser.: J. Physics: Conf. Ser. 991 (012027), 1–5 (2018).

  18. Y. M. Kononov and Y. O. Dzhukha, “Vibrations of two-layer ideal liquid in a rigid cylindrical vessel with elastic bases,” J. Math. Sci., 246, No. 3, 365–383 (2020).

    Article  MathSciNet  Google Scholar 

  19. Y. M. Kononov, V. P. Shevchenko, and Y. O. Dzhukha, “Axially symmetric oscillations of elastic annular bases and a perfect two-layer liquid in a rigid annular cylindrical reservoir,” J. Math. Sci., 240, No. 1, 98–112 (2019).

    Article  MathSciNet  Google Scholar 

  20. H. Lamb, Hydrodynamics, Cambridge University Press, Cambridge (1945).

  21. M. La Rocca, G. Sciortino, C. Adduce, and M. A. Boniforti, “Experimental and theoretical investigation on the sloshing of a two-liquid system with free surface,” Phys. Fluids, 17 (062101), 1–17 (2005).

    MATH  Google Scholar 

  22. M. La Rocca, G. Sciortino, and M. A. Boniforti, “Interfacial gravity waves in two-fluid system,” Fluid Dynam. Res., No. 30, 31–66 (2002).

  23. B. Molin, F. Remy, C. Audiffren, R. Marcer, A. Ledoux, S. Helland, and M. Mottaghi, “Experimental and numerical study of liquid sloshing in a rectangular tank with three fluids,” in: Proc. 13 Int. Offshore and Polar Engineering Conf. www.isope.org, Greece, Rhodes, June 17–22 (2012).

  24. N. N. Moiseev and V. V. Rumyantsev, Dynamic Stability of Bodies Containing Fluid, Springer, Berlin (1968).

  25. A. D. Myskis, V. G. Babskii, N. D. Kopachevskii, L. A. Slobozhanin, and A. D. Tiuptsov, Low-Gravity Fluid Mechanics: Mathematical Theory of Capillary Phenomena, Springer, Berlin (1987).

  26. A. A. Pozhalostin and D. A. Goncharov, “Free axisymmetric oscillations of a two-layer liquid with an elastic separator between layers,” Russ. Aeronaut., 58, No. 1, 37–41 (2015).

    Article  Google Scholar 

  27. N. Vaziri, M. J. Chern, and A. G. L. Borthwick, “PSME model of parametric excitation of two-layer liquid in a tank,” Appl. Ocean Res., No. 43, 214–222 (2013).

  28. Z. Wang, L. Zou, and Z. Zong, “Threedimensional sloshing of stratified liquid in a cylindrical tank,” Ocean Eng., No. 119, 58–66 (2016).

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, 19 General Batyuk St., Sloviansk, Donetsk Oblast, 84116, Ukraine

    Yu. M. Kononov

Authors
  1. Yu. M. Kononov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. M. Kononov.

Additional information

*The research was partially sponsored by the program of fundamental research of the Ministry of Education and Science, project No. 0119U100042.

Translated from Prikladnaya Mekhanika, Vol. 57, No. 5, pp. 115–128, September–October 2021.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kononov, Y.M. Motion of a Solid Body with a Cavity Containing a Multilayer Ideal Fluid*. Int Appl Mech 57, 591–603 (2021). https://doi.org/10.1007/s10778-021-01109-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-021-01109-y

Keywords

Search

Navigation