The objectives of this paper are in studying the liquid vibrations in rigid circular cylindrical shells with internal flexible membranes or covered by membranes. The liquid in the container is supposed to be an ideal and incompressible one, and the fluid motion is irrotational. In above formulated suppositions the velocity potential is introduced; it satisfies the Laplace equation. The boundary value problem is formulated for the velocity potential. To obtain boundary conditions on the liquid free surface, the membrane deflection is considered, and the equality of normal components of liquid and membrane velocities is satisfied. The incompressible and inviscid liquid is supposed to perform irrotational motion in the fluid domain divided into two sub-domains by internal flexible membrane that is installed at the given height. For solutions of the problems both numerical and analytical methods are in use. The analytical solutions of two boundary value problems are obtained for unknown velocity potential and membrane deflection as the Fourier–Bessel series with coefficients depending on unknown frequency. Satisfying boundary conditions, we obtain the system of homogeneous algebraic equations. The condition of a non-trivial solution of this system gives the non-linear equation for evaluating the frequencies. The coupled membrane and liquid vibrations in cylindrical tanks are studied also by FEM and BEM methods. The comparison of results obtained using analytical approach with ones received with boundary and finite element method is provided. The main results are as follows. As follows from numerical simulations, if the membrane is installed inside the cylinder, then the most important parameter affecting the result, is the height of the membrane installation. If the membrane is installed at a considerable distance from the free surface, then the sloshing frequency practically does not change, and more precisely, it slightly increases. The dependencies of frequencies via the filling level are identified. The novelty of proposed approach consists in possibility to study the influence of elastic baffles and roofs in the liquid-filled tanks.

本文的目的是研究带有内部柔性膜或被膜覆盖的刚性圆柱壳中的液体振动。容器中的液体应该是理想的不可压缩的液体，流体运动是无旋的。在上述公式化假设中，引入了速度势；满足拉普拉斯方程。边界值问题是为速度势制定的。为了获得液体自由表面的边界条件，考虑了膜的偏转，并且满足液体法向分量和膜速度的相等性。不可压缩且无粘性的液体应该在流体域中进行无旋运动，流体域被安装在给定高度的内部柔性膜分为两个子域。对于这些问题的解决方案，数值方法和解析方法都在使用中。对于未知速度势和膜偏转，获得两个边界值问题的解析解，作为系数取决于未知频率的傅立叶-贝塞尔级数。满足边界条件，我们得到齐次代数方程组。该系统的非平凡解的条件给出了用于评估频率的非线性方程。圆柱罐中的耦合膜和液体振动也通过有限元法和边界元法进行了研究。提供了使用解析方法获得的结果与使用边界和有限元方法获得的结果的比较。主要结果如下。从数值模拟如下，如果膜安装在圆筒内，那么影响结果的最重要的参数是膜的安装高度。如果薄膜安装在离自由表面相当远的地方，那么晃动频率实际上不会改变，更准确地说，它会略微增加。通过填充水平识别频率的相关性。所提出方法的新颖之处在于可以研究充液罐中弹性挡板和顶部的影响。