×

Efficient modal dynamic analysis of flexible beam-fluid systems. (English) Zbl 1428.74065

Summary: This paper proposes an efficient simplified method to determine the modal dynamic and earthquake response of coupled flexible beam-fluid systems and to evaluate their natural vibration frequencies. The methodology developed extends available analytical solutions for mode shapes and natural vibration frequencies of slender beams with various boundary conditions to include the effects of fluid-structure interaction. The proposed method is developed for various beam boundary conditions considering lateral interaction with one or two semi-infinite fluid domains. Numerical examples are provided to illustrate the application of the proposed method, and the obtained results confirm the importance of accounting for fluid-structure interaction effects. We show that the developed procedure yields excellent results when compared to more advanced coupled fluid-structure finite element solutions, independently of the number of included modes, beam boundary conditions, and number of interacting fluid domains. The proposed simplified method can be easily implemented in day-to-day engineering practice, as it constitutes an efficient alternative solution considering the fluid-structure modeling complexities and related high expertise generally involved when using advanced finite elements.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics

Software:

Matlab; mctoolbox
Full Text: DOI

References:

[1] Westergaard, H. M., Water pressures on dams during earthquakes, Trans. ASCE, 98, 418-472 (1933)
[2] Jacobsen, L. S., Impulsive hydrodynamics of fluid inside a cylindrical tank and of fluid surrounding a cylindrical pier, Bull. Seismol. Soc. Am., 39, 189-1949 (1949)
[6] Chopra, A. K., Earthquake behavior of reservoir-dam systems, J. Eng. Mech. Div. ASCE, 94, EM6, 1475-1500 (1968)
[7] Chopra, A. K., Earthquake response of concrete gravity dams, J. Eng. Mech. Div. ASCE, 96, EM4, 443-454 (1970)
[10] Liaw, C. Y.; Chopra, A. K., Dynamics of towers surrounded by water, Int. J. Earthquake Eng. Struct. Dyn., 3, 1, 33-49 (1974)
[11] Tanaka, Y.; Hudspeth, R. T., Restoring forces on vertical circular cylinders forced by earthquakes, Int. J. Earthquake Eng. Struct. Dyn., 16, 1, 99-119 (1988)
[12] Han, R. P.S.; Xu, H., Simple and accurate added mass model for hydrodynamic fluid-structure interaction analysis, J. Franklin Inst., 333B, 6, 929-945 (1996) · Zbl 0865.73038
[13] Nagaya, K., Transient response in flexure to general uni-directional loads of variable cross-section beam with concentrated tip inertias immersed in a fluid, J. Sound Vib., 99, 3, 361-378 (1985) · Zbl 0585.73099
[14] Uscilowska, A.; Kolodziej, J. A., Free vibration of immersed column carrying a tip mass, J. Sound Vib., 216, 147-157 (1998) · Zbl 1235.70057
[15] Oz, H. R., Natural frequencies of an immersed beam carrying a tip mass with rotatory inertia, J. Sound Vib., 266, 1099-1108 (2003)
[16] Wu, J. S.; Hsu, S.-H., A unified approach for the free vibration analysis of an elastically supported immersed uniform beam carrying an eccentric tip mass with rotary inertia, J. Sound Vib., 291, 1122-1147 (2006)
[17] Wu, J. S.; Chen, K.-W., An alternative approach to the structural motion analysis of wedge-beam offshore structures supporting a load, Ocean Eng., 30, 1791-1806 (2003)
[18] Chang, J. Y.; Liu, W. H., Some studies on the natural frequencies of immersed restrained column, J. Sound Vib., 130, 3, 516-524 (1989)
[19] Nagaya, K.; Hai, Y., Seismic response of underwater members of variable cross section, J. Sound Vib., 103, 119-138 (1985)
[20] Xing, J. T.; Price, W. G.; Pomfret, M. J.; Yam, L. H., Natural vibration of a beam-water interaction system, J. Sound Vib., 199, 491-512 (1997)
[21] Zhao, S.; Xing, J. T.; Price, W. G., Natural vibration of a flexible beam-water coupled system with a concentrated mass attached at the free end of the beam, Proc. Inst. Mech. Eng. Part M J. Eng. Marit. Environ., 216, 2, 145-154 (2002)
[22] Xing, J. T., Natural vibration of two-dimensional slender structure-water interaction systems subject to Sommerfeld radiation condition, J. Sound Vib., 308, 67-79 (2007)
[23] Nasserzare, J.; Lei, Y.; Eskandari-Shiri, S., Computation of natural frequencies and mode shapes of arch dams as an inverse problem, Adv. Eng. Software, 31, 11, 827-836 (2000)
[24] de Souza, S. M.; Pedroso, L. J., Study of flexible wall acoustic cavities using beam finite element, (da Costa Mattos, H. S.; Alves, Marcflio, Mechanics of Solids in Brazil (2009), Brazilian Society of Mechanical Sciences and Engineering), 223-237
[26] Bouaanani, N.; Lu, F. Y., Assessment of potential-based fluid finite elements for seismic analysis of dam-reservoir systems, J. Comput. Struct., 87, 206-224 (2009)
[27] Miquel, B.; Bouaanani, N., Simplified evaluation of the vibration period and seismic response of gravity dam-water systems, J. Eng. Struct., 32, 2488-2502 (2010)
[28] Young, D.; Felgar, R. P., Tables of characteristic functions representing normal modes of vibration of a beam, (Engineering Research Series No. 44 (1949), Bureau of Engineering Research: Bureau of Engineering Research Austin, Texas)
[29] Chang, T.; Craig, R. R., Normal modes of uniform beams, J. Eng. Mech. Div., EM4, 95, 1027-1031 (1969)
[30] Blevins, R. D., Formulas for Natural Frequency and Mode Shape (1984), Kriger publishing Company: Kriger publishing Company Florida, pp. 296-297
[31] Tang, Y., Numerical evaluation of uniform beam modes, J. Eng. Mech., 129, 1475-1477 (2003)
[32] Higham, N. J., Accuracy and Stability of Numerical Algorithms (2002), SIAM · Zbl 1011.65010
[35] Everstine, G. C., A symmetric potential formulation for fluid-structure interaction, J. Sound Vib., 79, 157-160 (1981)
[36] Olson, L. G.; Bathe, K. J., Analysis of fluid-structure interactions: a direct symmetric coupled formulation based on the fluid velocity potential, Comput. Struct., 21, 21-32 (1985) · Zbl 0568.73088
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.