Influence of Fluid in Dynamic Calculation of Thin-Walled Cylindrical Tanks by Means of Calculating Added Masses of Fluid

• Published in: IOP conference series. Materials Science and Engineering 2020-02, Vol.753 (3), p.32051
• Main Authors: Leonenko, Yu S, Chemodurov, V T
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Cylindrical shells; Cylindrical tanks; Differential equations; Dynamic loads; Elastic shells; Exact solutions; Fluid flow; Fourier series; Free surfaces; Galerkin method; Incompressible flow; Incompressible fluids; Ordinary differential equations; Oscillation modes; Shallow water; Structural analysis
• ISSN: 1757-8981; 1757-899X
• DOI: 10.1088/1757-899X/753/3/032051

This paper presents the exact solution for the problem of the added masses of fluid, oscillating inside a cylindrical tank. A thin smooth cylindrical shell of finite length, filled with the ideal incompressible fluid that is subjected to transient dynamic load (it may be an earthquake, air explosion impact, etc.), is taken as a design model. In this case, the shell of a tank becomes a part of the oscillating process along with the fluid stored inside. The shell bending equation (stipulated by the membrane theory of shells) is taken as a design model for this case. In this equation, the shell deflection is expanded into Fourier series by oscillation modes, and the velocity potential takes the form of the Laplace's equation. Fluid's inertial reaction to the shell motion is covered by the shallow water theory, which is specified by the boundary free surface conditions and the influence of the tank hard bottom. These mathematical expressions of the shell response to the external transient impact are solved by the Bubnov-Galerkin method with the transformation of the initial relations into a system of ordinary differential equations, which include expressions for determining added masses of fluid by oscillation modes of the elastic shell.