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Shock and Vibration
Volume 2014 (2014), Article ID 672648, 7 pages
Research Article

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

1Department of Hydraulic Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China
2Research Institute of Structural Engineering and Disaster Reduction, Tongji University, 1239 Siping Road, Shanghai 200092, China

Received 26 February 2013; Accepted 3 July 2013; Published 13 February 2014

Academic Editor: Ahmet S. Yigit

Copyright © 2014 Yuchun Li and Zhuang Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.