Asymptotic Analysis of Sloshing in a Rectangular Tank

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.