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Dynamic coupling between shallow-water sloshing and horizontal vehicle motion

Published online by Cambridge University Press:  07 July 2010

HAMID ALEMI ARDAKANI  and
THOMAS J. BRIDGES
HAMID ALEMI ARDAKANI
Affiliation:
Department of Mathematics, University of Surrey, Guildford GU2 7XH, UK emails: [email protected] & [email protected]
THOMAS J. BRIDGES
Affiliation:
Department of Mathematics, University of Surrey, Guildford GU2 7XH, UK emails: [email protected] & [email protected]
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Abstract

The coupled motion between shallow-water sloshing in a moving vehicle and the vehicle dynamics is considered, with the vehicle dynamics restricted to horizontal motion. The paper is motivated by Cooker's experiments and theory for water waves in a suspended container. A new derivation of the coupled problem in the Eulerian fluid representation is given. However, it is found that transformation to a Lagrangian representation leads to a formulation which has nice properties for numerical simulation. In the Lagrangian representation, a simple and fast numerical algorithm with excellent energy conservation over long times, based on the Störmer–Verlet method, is implemented. Numerical simulations of the coupled dynamics in both the linear and non-linear case are presented.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 21 , Issue 6 , December 2010 , pp. 479 - 517
Copyright
Copyright © Cambridge University Press 2010

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References

[1]Alemi Ardakani, H. & Bridges, T. J. (2009a) Shallow-water sloshing in rotating vessels. Part 1: Two-dimensional flow field. URL: http://personal.maths.surrey.ac.uk/st/T.Bridges/SLOSH/Google Scholar
[2]Alemi Ardakani, H. & Bridges, T. J. (2009b) Dynamic coupling between shallow-water sloshing and a vehicle undergoing planar rigid-body motion. Technical Report, University of Surrey. URL: http://personal.maths.surrey.ac.uk/st/T.Bridges/SLOSH/CrossRefGoogle Scholar
[3]Alemi Ardakani, H. & Bridges, T. J. (2010) Symplecticity of the Störmer-Verlet algorithm for coupling between the shallow water equations and horizontal vehicle motion. Technical Report, University of Surrey. URL: http://personal.maths.surrey.ac.uk/st/T.Bridges/SLOSH/CrossRefGoogle Scholar
[4]aus der Wiesche, S. (2003) Computational slosh dynamics: Theory and industrial application. Comput. Mech. 30, 374–387.CrossRefGoogle Scholar
[5]Bridges, T. J. (2009) Wave breaking and the surface velocity field for three-dimensional water waves. Nonlinearity 22, 947–953.CrossRefGoogle Scholar
[6]Caglayan, I. & Storch, R. L. (1982) Stability of fishing vessels with water on deck: a review, J. Ship Res. 26, 106–116.Google Scholar
[7]Chester, W. (1968) Resonant oscillations of water waves. Part I. Theory. Proc. R. Soc. Lond. A 306, 5–22.Google Scholar
[8]Cooker, M. J. (1994) Water waves in a suspended container. Wave Motion 20, 385–395.CrossRefGoogle Scholar
[9]Cox, E. A., Gleeson, J. P. & Mortell, M. P. (2005) Nonlinear sloshing and passage through resonance in a shallow water tank. Z. Angew. Math. Phys. 56, 645–680.CrossRefGoogle Scholar
[10]Dubois, F., Petit, N. & Rouchon, P. (1999) Motion planning and nonlinear simulations for a tank containing fluid. In: European Control Conference, Karlsruhe, Germany, 6 pages.Google Scholar
[11]Feddema, J. T., Dohrmann, C. R., Parker, G. G., Robinett, R. D., Romero, V. J. & Schmitt, D. J. (1997) Control for slosh-free motion of an open container. IEEE Control Syst. Mag. 17, 29–36.Google Scholar
[12]Grundelius, M. & Bernhardsson, B. (1999) Control of liquid slosh in an industrial packaging machine. In: IEEE International Conference on Control Applications, Kohala Coast, Hawaii, 6 pages.Google Scholar
[13]Hairer, E., Lubich, C. & Wanner, G. (2003) Geometric numerical integration illustrated by the Störmer-Verlet method. Acta Numer. 12, 399–450.CrossRefGoogle Scholar
[14]Ibrahim, R. A. (2005) Liquid Sloshing Dynamics, Cambridge University Press.CrossRefGoogle Scholar
[15]Ikeda, T. & Nakagawa, N. (1997) Non-linear vibrations of a structure caused by water sloshing in a rectangular tank. J. Sound Vib. 201, 23–41.CrossRefGoogle Scholar
[16]Jones, A. F. & Hulme, A. (1987) The hydrodynamics of water on deck. J. Ship Res. 31, 125–135.CrossRefGoogle Scholar
[17]Johnson, R. S. (1997) A Modern Introduction to the Mathematical Theory of Water Waves, Cambridge University Press.CrossRefGoogle Scholar
[18]Leimkuhler, B. & Reich, S. (2004) Simulating Hamiltonian Dynamics, Cambridge University Press.Google Scholar
[19]Lui, P.-C. & Lou, Y. K. (1990) Dynamic coupling of a liquid-tank system under transient excitation. Ocean Eng. 17, 263–277.Google Scholar
[20]Marsden, J. E. & West, M. (2001) Discrete mechanics and variational integrators. Acta Numer. 10, 357–514.CrossRefGoogle Scholar
[21]Ockendon, J. R. & Ockendon, H. (1973) Resonant surface waves. J. Fluid Mech. 59, 397–413.CrossRefGoogle Scholar
[22]Ockendon, H., Ockendon, J. R. & Johnson, A. D. (1986) Resonant sloshing in shallow water. J. Fluid Mech. 167, 465–479.CrossRefGoogle Scholar
[23]Oliver, M., West, M. & Wulff, C. (2004) Approximate momentum conservation for spatial semidiscretizations of semilinear wave equations. Numer. Math. 97, 493–535.CrossRefGoogle Scholar
[24]Prieur, C. & de Halleux, J. (2004) Stabilization of a 1-D tank containing a fluid modeled by the shallow water equations. Syst. Control Lett. 52, 167–178.CrossRefGoogle Scholar
[25]Seymour, B. R. & Mortell, M. P. (1973) Nonlinear resonant oscillations in open tubes. J. Fluid Mech. 60, 733–749.CrossRefGoogle Scholar
[26]Tzamtzi, M. P. & Kouvakas, N. D. (2007) Sloshing control in tilting phases of the pouring process. Int. J. Math. Phys. Eng. Sci. 1, 175–182.Google Scholar
[27]Tzamtzi, M. P. & Koumboulis, F. N. (2008) Robustness of a robot control scheme for liquid transfer. In: Sobh, T., Elleithy, K., Mahmood, A. & Karim, M. A. (editors), Novel Algortithms and Techniques in Telecommunications, Automation and Industrial Electronics, Springer-Verlag, Dordrecht, The Netherlands, pp. 156–161.Google Scholar
[28]Verhagen, J. H. G. & van Wijngaarden, L. (1965) Non-linear oscillations of fluid in a container. J. Fluid Mech. 22, 737–751.CrossRefGoogle Scholar