Advertisement

Journal of Engineering Mathematics

, Volume 25, Issue 2, pp 115–135 | Cite as

Resonant frequencies of a fluid in containers with internal bodies

  • E. B. B. Watson
  • D. V. Evans
Article

Abstract

A number of problems are solved for the resonant frequencies of oscillation of a fluid in rectangular or circular containers having internal bodies such as surface or bottom-mounted vertical blocks or circular apertures in the top surface. The variation of these frequencies with the dimensions of the bodies is obtained. The method uses matched eigenfunction expansions and Galerkin expansions to derive explicit forms for the elementsSijof a 2×2 matrix required in the course of the solution. An approximate formula for an arbitrary-shaped body in a container which gives good agreement with the more accurate Galerkin approach is used to solve the resonant frequencies when the internal body is a submerged cylinder.

Keywords

Mathematical Modeling Resonant Frequency Industrial Mathematic Explicit Form Approximate Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Evans, D.V., The wide-spacing approximation applied to multiple scattering and sloshing problems.J. Fluid Mech. 210 (1989) 647–658.Google Scholar
  2. 2.
    Evans, D.V. and Linton, C.M., Active devices for the reduction of wave intensity.Applied Ocean Research 11 (1989) 26–32.Google Scholar
  3. 3.
    Evans, D.V. and McIver, P., Resonant frequencies in a container with a vertical baffle.J. Fluid Mech. 175 (1987) 295–307.Google Scholar
  4. 4.
    Fox, D.W. and Kuttler, J.R., Sloshing frequencies.J. Appl. Math. Phys. 34 (1983) 668–696.Google Scholar
  5. 5.
    Ghanimati, G.R. and Naghdi, P.M., Oscillation over basins of variable depth.J. Fluid Mech. 164 (1986) 359–381.Google Scholar
  6. 6.
    Jones, D.S.,The Theory of Electromagnetism, pp. 269–272. Pergamon Press (1964).Google Scholar
  7. 7.
    Linton, C.M., Wave reflection by submerged bodies in water of finite depth. Ph.D. Thesis, University of Bristol (1988).Google Scholar
  8. 8.
    Miles, J.W., Surface-wave scattering for a shelf.J. Fluid Mech. 28 (1967) 755–767.Google Scholar
  9. 9.
    Miles, J.W., On the eigenvalue problem for fluid sloshing in a half-space.Z. Angew Math. Phys. 23 (1972) 861–869.Google Scholar
  10. 10.
    Moiseev, N.N., Introduction to the theory of oscillation of liquid-containing bodies.Advances in Applied Mechanics 8 (1964) 233–289.Google Scholar
  11. 11.
    Moiseev, N.N. and Petrov, A.A., The calculation of free oscillations in a motionless container.Advances in Applied Mechanics 9 (1966) 91–154.Google Scholar
  12. 12.
    Newman, J.N., Interaction of waves with two-dimensional obstacles: a relation between the radiation and scattering problems.J. Fluid Mech. 71 (1975) 273–282.Google Scholar
  13. 13.
    Ohkusu, M., Hydrodynamic fores on multiple cylinders in waves.Proc. Int. Symp. Dyn. Marine Vehicles and Structures in Waves, London: Inst. Mech. Eng. (1970) 107–112.Google Scholar
  14. 14.
    Srokosz, M.A. and Evans, D.V., A theory for wave-power absorption by two independently oscillating bodies.J. Fluid Mech. 90 (1979) 337–362.Google Scholar
  15. 15.
    Yeung, R.W. and Wu, C.F., Nonlinear wave-body motion in a closed domain.Computers and Fluids 17 (1989) 351–370.Google Scholar

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • E. B. B. Watson
    • 1
  • D. V. Evans
    • 1
  1. 1.Department of MathematicsUniversity of BristolBristolUK

Personalised recommendations