Liquid vibrations in cylindrical tanks with flexible membranes

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 for-mulated for the velocity potential. To obtain boundary conditions on the liquid free surface, the mem-brane 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 ana-lytical solutions of two boundary value problems are obtained for unknown velocity potential and mem-brane 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 simula-tions, 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 dis-tance 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. (c) 2021 The Authors. Published by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Automated summary

This paper focuses on studying liquid vibrations in rigid circular cylindrical shells with internal flexible membranes. The incompressible and irrotational motion of fluid is considered, and boundary value problems for velocity potential are formulated to analyze the influence of membrane deflection and installation height on vibration frequencies. Both numerical and analytical methods are used to obtain solutions and evaluate the impact of various parameters on the system dynamics.