An Approximate Analytical Solution of Sloshing Frequencies for a Liquid in Various Shape Aqueducts

Yuchun Li,Zhuang Wang

doi:10.1155/2014/672648

Abstract

An approximate analytical solution of sloshing frequencies for a liquid in the various shape aqueducts is formulated by using the Ritz method. The present approximate method is, respectively, applied to find the sloshing frequencies of the liquid in rectangular, trapezoid, oval, circular, U-shaped tanks (aqueducts), and various shape tuned liquid dampers (TLD). The first three antisymmetric and symmetric frequencies by the present approach are within 5% accuracy compared to the other analytical, numerical, and experimental values. The approximate solutions of this paper for the various shape aqueducts are acceptable to the engineering applications.

Highlights

Sloshing is a common physical phenomenon which occurs in moving tanks with contained liquid masses, such as liquid cargo carriers, rockets, aircrafts, and the seismically excited storage tanks, dams, reactors, and nuclear vessels
The purpose of this paper is to provide a simple and quick method to evaluate the sloshing frequencies of a liquid in the various shape aqueducts
1.0257 1.0279 1.0558 frequencies in the rectangular tanks by Antisymmetric frequencies Finite element (ANSYS) Code and the exact solution [3] were compared with each other, and the results showed the two solutions have a good agreement

Summary

Introduction

Sloshing is a common physical phenomenon which occurs in moving tanks with contained liquid masses, such as liquid cargo carriers, rockets, aircrafts, and the seismically excited storage tanks, dams, reactors, and nuclear vessels. On the basis of the small displacement assumption, the irrotational fluid can be modeled by a degenerate solid finite element [12, 13] with no shear resistance. This displacement-based finite element formulation, which had been introduced into the commercial ANSYS Code [14], was usually used for simulating the sloshing problems [15, 16] in certain engineering fields. The sloshing frequencies of a liquid in an arbitrarysection aqueduct can be accurately extracted by the above mentioned methods. The purpose of this paper is to provide a simple and quick method to evaluate the sloshing frequencies of a liquid in the various shape aqueducts

Basic Equations of Two-Dimensional Free Sloshing

Approximate Analytical Solution

Numerical Examples

Findings

Conclusion