An Asymptotic solution of liquid sloshing motion in a rectangular tank is presented based on the potential flow theory. A rectangular tank is excited harmonically, in the sway and heave modes. The Stokes perturbation theory is used to resolve the boundary value problem. The perturbed problem reduces to the non-homogeneous Mathieu's equation in the case of coupled harmonic excitations, which induces the sloshing motion subjected to parametric rolling of the tank. Lindstedt-Poincare’ method is used to determine the stable solution of the Mathieu's equation.
References
1.
DeanR.G. and DalrympleR.A., (1930) Water wave mechanics For Engineers and Scientists, Prentice, Inc, Englewood Cliffs, New Jersey.
2.
FaltinsenO.M. (1974) A nonlinear theory of sloshing n rectangular tanks, Journal of Ship Research, 18 (4) 224–241.
3.
IbrahimR.A., (2005), Liquid sloshing dynamics Theory and applications, Cambridge University Press.
4.
FrandsenJannette B., (2004). Sloshing motions in excited tanks, Journal of Computational physics, vol 196, and pp: 53–87.
5.
SriramV., (2008). Finite element simulation of Non linear free surface waves, Ph.D Thesis, I.I.T.Madras, India.
6.
FranceW.N.LevadouM.TreakleT.W.PaullingR.MichelR.K. and MooreC., (2001) An Investigation of Head-Sea Parametric Rolling and its Influence on Container Lashing Systems, SNAME Annual Meeting 2001Presentation.
7.
WuG.X.TaylorEatock R., (1994). Finite element analysis of two-dimensional non-linear transient water waves, Applied Ocean Research, vol 16, pp: 363–372.
8.
WuG.X. (2007). Second order resonance of Sloshing in a tank, Ocean Engineering, vol 34, 2345–2349.
