Free Vibration Analysis of a Liquid in a Circular Cylindrical Rigid Tank Using the Hierarchical Finite Element Method

Sidi Mohammed Hamza Cherif,Mohammed Nabil Ouissi

doi:10.1590/1679-78251774

Sidi Mohammed Hamza Cherif, Mohammed Nabil Ouissi

Open Access

https://doi.org/10.1590/1679-78251774

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Abstract

A hierarchical finite element is developed for the free vibration analysis of a liquid in a rigid cylindrical tank with or without a free surface. It is a hierarchical quadrilateral element and has the advantage that the hierarchical mode number is allowed to vary independently of direction. Liquid behavior in tanks with large aspect ratios can therefore be solved very accurately by using a higher hierarchical mode number in the longer direction than in the shorter one. Furthermore, it is possible to idealize the liquid by using only one element. The solution can therefore be obtained to any desired degree of accuracy simply by increasing the hierarchical mode number. In this method, the liquid behavior is described by the displacements alone. The pressure and velocity potential are not considered as unknowns. The results are compared with other methods and show good agreement.

Highlights

There are many cases of fluid structure interaction, such as sloshing in liquid storage structures and dams, and vibration of components of a nuclear reactor in a fluid
Several methods based on the added mass approach for the analysis of the liquid storage structures were proposed (Housner, 1957, ASCE, 1986)
The hierarchical liquid finite element presented in this study is able to give accurate frequencies for liquids in axisymmetric cavities with or without free surface

Summary

Introduction

There are many cases of fluid structure interaction, such as sloshing in liquid storage structures and dams, and vibration of components of a nuclear reactor in a fluid. We must approach the solution by numerical methods based on the finite element method. In the added mass approach, a part of the mass of the fluid is added to the structural model along the interface between the two fields. This approach neglects the compressibility of the fluid. Several methods based on the added mass approach for the analysis of the liquid storage structures were proposed (Housner, 1957, ASCE, 1986)

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