A boundary element method and spectral analysis model for small-amplitude viscous fluid sloshing in couple with structural vibrations

A boundary element method (BEM) is presented for the coupled motion analysis of structural vibrations with small-amplitude fluid sloshing in two-dimensional space. The linearized Navier–Stokes equations are considered in the frequency domain and transformed into a Laplace equation and a Helmholtz equation with pure imaginary constant. An appropriate fundamental solution for the Helmholtz equation is provided. The conditions of zero stress are imposed on the free surface, and non-slip conditions of fluid particles are imposed on the walls of the container. For rigid motion models, the expressions for added mass and added damping to the structural motion equations are obtained. Numerical examples are presented.