Analytical and experimental study on natural sloshing frequencies in annular cylindrical tank with a bottom gap

- Journal title : Structural Engineering and Mechanics
- Volume 57, Issue 5, 2016, pp.877-895
- Publisher : Techno-Press
- DOI : 10.12989/sem.2016.57.5.877

Title & Authors

Analytical and experimental study on natural sloshing frequencies in annular cylindrical tank with a bottom gap

Lee, H.W.; Jeon, S.H.; Cho, J.R.; Seo, M.W.; Jeon, W.B.;

Lee, H.W.; Jeon, S.H.; Cho, J.R.; Seo, M.W.; Jeon, W.B.;

Abstract

This paper is concerned with the analytical derivation of natural sloshing frequencies of liquid in annular cylindrical tank and its verification by experiment. The whole liquid domain is divided into three simple sub-regions, and the region-wise linearized velocity potentials are derived by the separation of variables. Two sets of matrix equations for solving the natural sloshing frequencies are derived by enforcing the boundary conditions and the continuity conditions at the interfaces between sub-regions. In addition, the natural sloshing frequencies are measured by experiment and the numerical accuracy of the proposed analytical method is verified through the comparison between the analytical and experimental results. It is confirmed that the present analytical method provides the fundamental sloshing frequencies which are in an excellent agreement with the experiment. As well, the effects of the tank radial gap, the bottom flow gap and the liquid fill height on the fundamental sloshing frequency are parametrically investigated.

Keywords

liquid sloshing;annular cylindrical tank;natural frequency;three flow regions;linearized velocity potential;analytical derivation;experimental verification;

Language

English

References

1.

Akyildiz, A. (2012), "A numerical study of the effects of the vertical baffle on liquid sloshing in two-dimensional rectangular tank", J. Sound Vib., 331(1), 41-52.

2.

Amabili, M., Paidousis, M.P. and Lakis, A.A. (1998), "Vibrations of partially filled cylindrical tanks with ring-stiffners and flexible bottom", J. Sound Vib., 213(5), 259-299.

3.

Banerji, P. and Samanta, A. (2011), "Earthquake vibration control of structures using hybrid mass liquid damper", Eng. Struct., 33(4), 1291-1301.

4.

Baur, H.F. (1996), "Nonlinear mechanical model for the description of propellant sloshing", AIAA J., 4(9), 1662-1668.

5.

Bhargava, K., Ghosh, A.K. and Ramanujam, S. (2005), "Seismic response and failure modes for a water storage structure-A case study", Struct. Eng. Mech., 20(1), 1-20.

6.

Chakraborty, S., Debbarma, R. and Marano, G.C. (2012), "Performance of tuned liquid column dampers considering maximum liquid motion in seismic vibration control of structures", J. Sound Vib., 331(7), 1519-1531.

7.

Cho, J.R., Song, J.M. and Lee, J.K. (2001), "Finite element techniques for the free-vibration and seismic analysis of liquid-storage tanks", Finite Elem. Anal. Des., 37, 467-483.

8.

Cho, J.R. and Song, J.M. (2001), "Assessment of classical numerical models for the separate fluid-structure modal analysis", J. Sound Vib., 239(5), 995-1012.

9.

Cho, J.R., Kim, K.W., Lee, J.K., Park, T.H. and Lee, W.Y. (2002), "Axisymmetric modal analysis of liquid-storage tanks considering compressibility effects", Int. J. Numer. Meth. Eng., 55, 733-752.

10.

Cho, J.R., Lee, H.W. and Kim, K.W. (2002), "Free vibration analysis of baffled liquid-storage tanks by the structural-acoustic finite element formulation", J. Sound Vib., 258(5), 847-866

11.

Cho, J.R. and Lee, S.Y. (2003), "Dynamic analysis of baffled fuel-storage tanks using the ALE finite element method", Int. J. Numer. Meth. Fluid., 41, 185-208.

12.

Cho, J.R. and Lee, H.W. (2004), "Numerical study on liquid sloshing in baffled tank by nonlinear finite element method", Comput. Meth. Appl. Mech. Eng., 193, 2581-2598.

13.

Cho, J.R., Lee, H.W. and Ha, S.Y. (2005), "Finite element analysis of resonant sloshing response in 2-D baffled tank", J. Sound Vib., 288, 829-845.

14.

Colwell, S. and Basu, B. (2009), "Tuned liquid column dampers in offshore wind turbines for structural control", Eng. Struct., 31, 358-368.

15.

Dean, R.G. and Dalrymple, D. (1984), Water Wave Mechanics for Engineers and Scientists, 1st Edition, Prentice-Hall, New Jersey.

16.

Greenberg, M.D. (1987), Foundations of Applied Mathematics, Prentice-Hall, New Jersey.

17.

Ibrahim, R.A. (2005), Liquid Sloshing Dynamics, Theory and Applications, Cambridge University Press, New York.

18.

Jia, D., Agrawal, M., Wang, C., Shen, J. and Malachowski, J. (2015), "Fluid-structure interaction of liquid sloshing induced by vessel motion in floating LNG tank", ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering, OMAE2015-41463.

19.

Kim, H.J. and Adeli, A. (2005), "Hybrid control of irregular steel highrise building structures under seismic excitations", Int. J. Numer. Meth. Eng., 63(12), 1757-1774.

20.

Koh, C.G., Luo, M., Gao, M. and Bai, W. (2013), "Modeling of liquid sloshing with constrained floating baffle", Comput. Struct., 122, 270-279.

21.

Lee, H.H., Wong, S.H. and Lee, S.H. (2006), "Response mitigation on the offshore floating platform system with tuned liquid column damper", Ocean Eng., 33, 1118-1142.

22.

Love, J.S. and Tait, M.J. (2012), "A preliminary design for tuned liquid dampers conforming to space restrictions", Eng. Struct., 40, 187-197.

23.

Lukovsky, I., Ovchynnykov, D. and Timokha, A. (2012), "Asymptotic nonlinear multimodal modeling of liquid sloshing in an upright circular cylindrical tank. I. Modal equations", Nonlin. Oscillat., 14(4), 512-525.

24.

Morsy, H. (2010), "A numerical study of the performance of tuned liquid dampers", MD Thesis, MaMaster University, Hamilton, Canada.

25.

Moslemi, M., Kianoush, M.R. and Pogorzelski, W. (2011), "Seismic response of liquid-filled elevated tanks", Eng. Struct., 33(6), 2074-2084.

26.

Tait, M.J., Isyumov, N. and El Damatty, A.A. (2004), "The efficiency and robustness of a uni-directional tuned liquid damper and modeling with an equivalent TMD", Wind Struct., 7(4), 235-250.

27.

Tedesco, J.W., Kostem, C.N. and Kalnins, A. (1987), "Free vibration of cylindrical liquid storage tanks", Comput. Struct., 26(6), 957-964.

28.

Veletsos, A.S. and Yang, J.Y. (1976), "Dynamics of fixed-based liquid-storage tanks", Proceedings of US-Japan Seminar Earthquake Engineering Research, 317-341.