Free vibrations of liquid in a tank with a partition

Abstract

I The article presents an analytical solution to the problem of small oscillations of a liquid in a rigid tank with an elastic baffle. This mechanical system is a model for various oil tankers. The frequency transcendental equation of the problem is obtained in closed form under certain assumptions, the left side of which is a meromorphic function with an infinite number of simple poles. This result is achieved by expanding the homogeneous solution into a series in terms of the eigenfunctions of the Laplace equation in a rectangular coordinate system.