Determination of normal frequencies and modes of liquid sloshing in reservoir with variable bottom

A problem about normal oscillations of ideal homogeneous liquid, which partially fills a reservoir with vertical walls, but with variable (inclined) bottom, is under consideration. A numerical implementation of the Ritz method was developed, and by partial example, which corresponds to a plane inclined bottom, the results of numerical realization are shown. We determined frequencies and normal modes of liquid oscillations as well as errors of satisfaction of the non-flowing boundary condition at the bottom. The results showed that the wave profiles for different directions of liquid oscillations differ. The magnitude of errors makes it possible to use the determined normal modes as coordinate functions for solving the nonlinear problem of liquid sloshing in such types of reservoirs.