Variational Solution of Fuel Sloshing Modes

Abstract : The problem of calculating the motion of an incompressible inviscid fluid with a free surface is formulated as a variational principle. The result is in the form of an expansion in powers of the wave height. The theory is specialized to the linear case where it is demonstrated that the variational principle is of the free boundary condition type. A procedure for calculating the natural frequencies and modes of the shallow and the deep tank by applying the Rayleigh-Ritz procedure to solution of the variational formulation is discussed. An approximate procedure for calculating the sloshing modes and frequencies of a tank of intermediate depth in terms of the solutions for shallow and deep tanks is suggested. The results of numerical calculations for conical tank are presented in the form of mode shape diagrams and frequency charts. (Author)