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Sloshing frequencies of longitudinal modes for a liquid contained in a trough

  • P. McIver (a1) and M. McIver (a1)

Abstract

The sloshing under gravity is considered for a liquid contained in a horizontal cylinder of uniform cross-section and symmetric about a vertical plane parallel to its generators. Much of the published work on this problem has been concerned with twodimensional, transverse oscillations of the fluid. Here, attention is paid to longitudinal modes with variation of the fluid motion along the cylinder. There are two known exact solutions for all modes; these are for cylinders whose cross-sections are either rectangular or triangular with a vertex semi-angle of ¼π. Numerical solutions are possible for an arbitrary geometry but few calculations are reported in the open literature. In the present work, some general aspects of the solutions for arbitrary geometries are investigated including the behaviour at low and high frequency of longitudinal modes. Further, simple methods are described for obtaining upper and lower bounds to the frequencies of both the lowest symmetric and lowest antisymmetric modes. Comparisons are made with numerical calculations from a boundary element method.

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References

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Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Courant, R. & Hilbert, D. 1953 Methods of Mathematical Physics, vol. 1. Interscience.
Davis, A. M. J. 1965 Two-dimensional oscillations in a canal of arbitrary cross-section. Proc. Camb. Phil. Soc. 61, 827846.
Davis, A. M. J. 1992 Discussion related to Watson and Evan: ‘Resonant frequencies of a fluid in containers with internal bodies’. J. Engng Math. 26, 445454.
Evans, D. V. & Linton, C. M. 1993 Sloshing frequencies. Q. J. Mech. Appl. Maths (to appear).
Evans, D. V. & Mciver, P. 1991 Trapped waves over symmetric thin bodies. J. Fluid Mech. 223, 509519.
Fox, D. W. & Kuttler, J. R. 1983 Sloshing frequencies. Z. Angew Math. Phys. 34, 668696
Isaacson, E. 1950 Water waves over a sloping beach. Commun. Pure Appl. Math. 3, 132.
Kobayashi, N., Mieda, T., Shibata, H. & Shinozaki, Y. 1989 A study of the liquid slosh response in horizontal cylindrical tanks. J. Pressure Vessel Technol. 111, 3238.
Lamb, H. 1932 Hydrodynamics, 6th Edn. Cambridge University Press.
McIver, P. 1989 Sloshing frequencies for cylindrical and spherical containers filled to an arbitrary depth. J. Fluid Mech. 201, 243257.
Mciver, P. & Smith, S. R. 1987 Free-surface oscillations of fluid in closed basins. J. Engng Math. 21, 139148.
Moiseev, N. N. & Petrov, A. A. 1966 The calculation of free oscillations of a liquid in a motionless container. Adv. Appl. Mech. 9, 91154.
Packham, B. A. 1980 Small-amplitude waves in a straight channel of uniform triangular crosssection. Q. J. Mech. Appl. Math. 33, 179187.
Peters, A. S. 1952 Water waves over sloping beaches and the solution of a mixed boundary value problem for ∇2ϕ-k2ϕ = 0 in a sector. Commun. Pure Appl. Maths 5, 87108.
Protter, M. H. & Weinberger, H. F. 1984 Maximum Principles In Differential Equations. Springer.
Shi, J. & Yih, C.-S. 1984 Waves in open channels. J. Engng Mech. 110, 847870.
Ursell, F. 1952 Edge waves on a sloping beach. Proc. R. Soc. Lond. A 214, 7997.
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Sloshing frequencies of longitudinal modes for a liquid contained in a trough

  • P. McIver (a1) and M. McIver (a1)

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