Analyzing Frequency of Conical (∆ shaped) Tanks
محورهای موضوعی : Engineering
1 - National Iranian Oil Company (NIOC), Iran
کلید واژه: Natural frequency, Finite Element Method, Conical shell, Modal characteristic, Apex angle,
چکیده مقاله :
A finite element analysis is presented for sloshing and impulsive motion of liquid-filled conical tanks during lateral anti-symmetric excitation. The performed analyses led to the development of a number of charts which can be used to identify the natural frequency, the mode shapes of conical tanks for both fundamental and the cos(θ)-modes of vibration. Conical tank geometry was described with several parameters namely, bottom radius( Rb) total height of liquid (h), angle of inclination of the tanks(θi), as variables. Numerical result of the free vibration was obtained for the cases of conical tanks with θi=0 and compared with existing experiments and other predicated results, showing a good agreement between the experiment and numerical results.
[1] Jacobson L.S., Ayre R.S., 1951, Hydrodynamic experiments with rigid cylindrical tanks subjected to transient motion, Bulletin of the Seismological Society of America 41: 15-35.
[2] Graham E.W., Rodriguez A. M., 1979, The characteristics of fuel motion which affect airplane dynamics, Journal of Applied Mechanics 19(3): 381-388.
[3] Abramson H.N, 1966, The Dynamic Behavior of Liquid in Moving Containers with Applications to Space Vehicle Technology, NASA SP-106, National Aeronautic and Space Administration, Washington.
[4] Feschenko S. F., Lukovsky I. A., Rabinovich B. I., Dokuchaev L. V, 1969, The methods for determining the added fluid masses in mobile cavities Kiev, Naukova Dumka 250: 13.
[5] Dokuchaev L. V, 1964, On the solution of a boundary value problem on the sloshing of a liquid in conical cavities, Applied Mathematics and Mechanics 28: 151-154.
[6] Abramson H. N., 1968, NASA Space Vehicle Design Criteria (Structures), NASA SP-8009 Propellant Slosh Loads, Washington.
[7] Mikishev G. N., Dorozhkin N. Y, 1961, An experimental investigation of free oscillations of a liquid in containers, Izvestiya Akademii Nauk SSSr, Otdelenie Tekhnicheskikh Nauk, Mekhanika, Mashinostroenie 4: 48-53.
[8] Bauer H. F, 1982, Sloshing in conical tanks, Acta Mechanica 43(3-4): 185-200.
[9] Bauer H. F., Eidel W, 1988, Non–linear liquid motion in conical container, Acta Mechanica 73 (1-4): 11-31.
[10] Lukovsky I. A., Bilyk A. N., 1985, Forced nonlinear oscillation of a liquid in moving axial-symmetric conical tanks in book: Numerical-Analytical Methods of Studying the Dynamics and Stability of Multidimensional Systems, Institute of Mathematics, Kiev.
[11] Schiffner K, 1983, A modified boundary element method for the three-dimensional problem of fluid oscillation, Proceedings of the Fifth International Conference Berlin, Hiroshima, Japan.
[12] Yamaki N., Tani J., Yamaji T., 1984, Free vibration of a clamped-clamped circular cylindrical shell partially filled with liquid, Journal of Sound Vibration 94: 531-550.
[13] Gupta R. K., Hutchinson G. L., 1988, Free vibration analysis of liquid storage tanks, Journal of Sound Vibration 122: 491-506.
[14] Mazuch T., Horacek J., Trnka J., Vesely J., 1996, Natural modes and frequencies of a thin clamped-free steel cylindrical storage tank partially filled with water, FEM and measurement, Journal of Sound and Vibration 193: 669-690.
[15] Han R. P. S., Liu J. D., 1994, Free vibration analysis of a fluid-loaded variable thickness cylindrical tank, Journal of Sound and Vibration 176: 235-253.
[16] Jeong K. H., Kim K. J., 1998, Free vibration of a circular cylindrical shell filled with bounded compressible fluid, Journal of Sound and Vibration 217: 197-221.
[17] Jeong K. H., Kim K. S., Park K. B., 1997, Natural frequency characteristics of a cylindrical tank filled with bounded compressible fluid, Journal of the Computational Structural Engineering Institute of Korea 10(4): 291-302.
[18] Dutta S., Mandal A., Dutta S.C., 2004, Soil structure interaction in dynamic behavior of elevated tanks with alternate frame staging configurations, Journal of Sound and Vibration 277: 825-853.
[19] Shrimali M.K., Jangid R.S., 2003, Earthquake response of isolated elevated liquid storage steel tanks, Journal of Constructional Steel Research 59: 1267-1288.
[20] Damatty El A.A., Sweedan A.M.I., 2006, Equivalent mechanical analog for dynamic analysis of pure conical tanks, Thin-Walled Structures 44: 429-440.
[21] Damatty El A., Korol R. M., Tang L. M., 2000, Analytical and experimental investigation of the dynamic response of liquid-filled conical tanks, Proceedings of the World Conference of Earthquake Engineering, New Zelan.
[22] Housner G.W., 1963, Dynamic behavior of water tanks, Bulletin of the Seismological Society of America 53:381-387.
[23] Haroun M.A., Housner G.W., 1981, Seismic design of liquid storage tanks, Proceeding of the Journal of Technical Councils, ASCE.
[24] Yih C.S., 1980, Stratified Flows, Academic Press Inc, New York.