Fluid Dynamics

, Volume 4, Issue 6, pp 74–81 | Cite as

Nonsmall liquid oscillations in moving vessels

  • I. G. Gataullin
  • V. I. Stolbetsov
Article

Abstract

The system of approximate nonlinear equations describing liquid oscillations in axisymmetric vessels is constructed. The equations are obtained for the case in which two coordinates belonging to the family of generalized coordinates characterizing the liquid motion are not small. This family is selected so that from the resulting nonlinear equations we can obtain as a particular case the nonlinear equations of [1–3], which are valid for the class of cylindrical vessels, and the requirements are satisfied that the resulting nonlinear equations correspond to the widely adopted linearized equations of liquid oscillations [4–6], Nonlinear equations are obtained which describe liquid oscillations in arbitrary vessels of rotation with radial baffles.

Keywords

Linearize Equation Nonlinear Equation Liquid Motion Cylindrical Vessel Liquid Oscillation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. S. Narimanov, “The motion of a vessel partially filled with a liquid with account for nonsmall motion of the latter”, PMM, vol. 21, no. 4, 1957.Google Scholar
  2. 2.
    G. S. Narimanov, “Liquid oscillations in moving vessels”, Izv. AN SSSR, OTN, no. 10, 1957.Google Scholar
  3. 3.
    V. I. Stolbetsov, “The equations of nonlinear oscillations of a vessel partially filled with a liquid”, Izv. AN SSSR, MZhG [Fluid Dynamics], vol. 3, no. 2, 1969.Google Scholar
  4. 4.
    N. N. Moiseev, “Motion of a rigid body containing liquid masses having a free surface”, Matem sb., no. 32, issue 1, 1953.Google Scholar
  5. 5.
    G. S. Narimanov, “The motion of a rigid body whose cavity is partly filled with liquid”, PMM, vol. 20, no. 1, 1956.Google Scholar
  6. 6.
    D. E. Okhotsimskii, “The theory of motion of a body with cavities partly filled with a liquid”, PMM, vol. 20, no. 1, 1956.Google Scholar
  7. 7.
    V. I. Stolbetsov, “Nonsmall liquid oscillations in a right circular cylinder”, Izv. AN SSSR, MZhG [Fluid Dynamics], vol. 2, no. 2, 1967.Google Scholar
  8. 8.
    V. I. Smirnov, Course in Higher Mathematics, Vol. 5 [in Russian], Gostekhizdat, Moscow-Leningrad, 1947.Google Scholar
  9. 9.
    V. I. Stolbetsov and V. M. Fishkis, “A mechanical model of a liquid performing nonsmall oscillations in a spherical vessel”, Izv. AN SSSR, MZhG [Fluid Dynamics], vol. 3, no. 5, 1968.Google Scholar

Copyright information

© Consultants Bureau 1972

Authors and Affiliations

  • I. G. Gataullin
    • 1
  • V. I. Stolbetsov
    • 1
  1. 1.Moscow

Personalised recommendations