﻿ 移动容器中液体晃动的二种速度势描述及其等价性证明

# 移动容器中液体晃动的二种速度势描述及其等价性证明Two Velocity Potential Descriptions for Fluid Sloshing in Moving Tanks and Their Equivalence Proof

Abstract: In the existing literature, there were two different velocity potential functions being used in the different engineering disciplines for describing the motions of ideal fluid in the moving tanks. The resulting equations of motion were not identical. However, the two different velocity potentials were both called “velocity potential function” in the different engineering disciplines. It might result in a theoretical confusion in the interdisciplinary researches. This issue seemed not being clarified in the existing literatures. This paper will respectively propose the “absolute velocity potential” and the “relative velocity potential” to establish the motion equations of fluid, and prove the equivalence of the two descriptions. For the earthquake engineering, the “absolute velocity poten-tial” and “relative velocity potential” are respectively suitable for describing the motions of fluids subjected to velocity and acceleration (seismic) excitations.

[1] Dodge, F.T. (2000) The New “Dynamic Behavior of Liquids in Moving Containers”. Southwest Research Institute, San Antonio.

[2] Ibrahim, R.A. (2005) Liquid Sloshing Dynamics: Theory and Applications. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511536656

[3] Faltinsen, O.M. and Timokha, A.N. (2009) Sloshing. Cam-bridge University Press, Cambridge.

[4] Chen, W., Haroun, M.A. and Liu, F. (1996) Large Amplitude Liquid Sloshing in Seismically Excited Tanks. Earthquake Engineering and Structural Dynamics, 25, 653-669.
http://dx.doi.org/10.1002/(SICI)1096-9845(199607)25:7<653::AID-EQE513>3.0.CO;2-H

[5] Ikeda, T., Ibrahim, R.A., Harata, Y. and Kuriyama, T. (2012) Nonlinear Liquid Sloshing in a Square Tank Subjected to Obliquely Horizontal Excitation. Journal of Fluid Mechanics, 700, 304-328.
http://dx.doi.org/10.1017/jfm.2012.133

[6] Li, Y. and Wang, J. (2012) A Supplementary, Exact Solution of an Equivalent Mechanical Model for a Sloshing Fluid in a Rectangular Tank. Journal of Fluids and Structures, 31, 147-151.
http://dx.doi.org/10.1016/j.jfluidstructs.2012.02.012

[7] Li, Y., Di, Q. and Gong, Y. (2012) Equivalent Mechan-ical Models of Sloshing Fluid in Arbitrary-Section Aqueducts. Earthquake Engineering & Structural Dynamics, 41, 1069-1087.
http://dx.doi.org/10.1002/eqe.1173

[8] 王照林, 刘延柱. 充液系统动力学[M]. 北京: 科学出版社, 2002.

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