Analytically approximate natural sloshing modes and frequencies in two-dimensional tanks

Analytical approaches to nonlinear and linear sloshing problems need to know approximate natural sloshing modes expressed by continuously-differentiable harmonic functions. A new method for constructing those approximate modes as well as for a fast computing of the corresponding natural sloshing frequencies is proposed in the two-dimensional case. The method facilities a parametric study of the natural sloshing frequencies in a prismatic tank associated with LNG (Liquefied Natural Gas) containers. The results are extensively compared with other approximate analytical solutions.