normal frequencies and modes

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 oscilla