Document Type: Research Paper

Authors

1 mechanical engineering department, faculty of engineering, university of Kurdistan,

2 civil engineering department, faculty of engineering, university of kurdistan, sanandaj, iran

Abstract

Water storage tanks are amongst the essential infrastructures, and the study of their natural frequencies plays a pivotal role in predicting and detecting dynamic behavior. Therefore, it helps to the uninterrupted operation of an industrial plant and the use of tank water in emergencies. This paper has studied the influence of different shell materials including steel, aluminum, and laminated composites with three types of different fiber orientations, on the natural frequencies of thin-walled aboveground water storage tanks that have pinned boundary conditions at the base. Models investigated in this paper, either the roof is without an internal support structure or else a group of columns and radial beams are used for supporting it. These huge tanks had the height to diameter ratio 0.4, and a water surface at 90% of the height of the tank's cylinder. The thicknesses of the cylindrical shells are tapered. The tanks without internal support included the vibrations that affect the cylinder mode shapes or the roof mode shapes or simultaneously both the cylinder and roof mode shapes. On the other hand, the mode shapes of the tanks with internal support affect predominantly only the cylinder. Among the studied tanks, the third type of composite tanks had the highest rigidity, and the first type of composite tanks had the lowest rigidity. The natural frequencies related to the first modes of vibrations for cylinder and roof shells with a wide range of circumferential wave numbers (n) and an axial half-wave (m) are studied.

Graphical Abstract

Keywords

Main Subjects

[1] T. Mazuch, J. Horacek, J. Trnka, J. Vesely, "Natural modes and frequencies of a thin clamped-free steel cylindrical tank partially filled with water: FEM and Measurement", Journal of Sound and Vibration, Vol. 193, No.3, pp. 669-690, (1996).

[2] RK Gupta, "Free vibrations of partially filled cylindrical tanks",Engineering Structures, Vol. 17, No.3, pp. 221-230, (1995).

[3] Han RPS, Liu JD, "Free vibration analysis of a fluid-loaded variable thickness cylindrical tank", Journal of Sound and Vibration, Vol. 176, No.2, pp. 235-253, (1994).

[4] Goncalves PB, Ramos NRSS, "Free vibration analysis of cylindrical tanks partially filled with liquid", Journal of Sound and Vibration, Vol. 195, No.3, pp. 429-444, (1996).

[5] Haroun MA, Tayel MA, "Asymmetrical vibrations of tanks-analytical", Journal of Engineering Mechanics, Vol. 111, No.3, pp. 346-358, (1985).

[6] Amabili M, "Shell plate interaction in the free vibrations of circular cylindrical tanks partially filled with a liquid: The artificial spring method", Journal of Sound and Vibration, Vol. 199, No.3, pp. 431-452, (1997).

[7] Amabili M, Paidoussis MP, Lakis AA, "Vibrations of partially filled cylindrical tanks with ring stiffeners and flexible bottom", Journal of Sound and Vibration, Vol. 213, No.2, pp. 259-299, (1998).

[8] Haroun MA, Housner GW, "Earthquake response of deformable liquid storage tanks", J. Appl. Mech. Trans ASME, Vol. 48, No.2, pp. 411-418, (1981).

[9] Veletsos AS, Tang Y, Tang HT, "Dynamic-response of flexibly supported liquid storage tanks", J. Struct. Eng. ASCE, Vol. 118, No.1, pp. 264-283, (1992).

[10] Virella JC, Luis A, Godoy, Luis ES, "Fundamental modes of tank-liquid systems under horizontal motions", Engineering Structures, Vol. 28, No.10, pp. 1450-1461, (2006).

[11] Virella JC, Godoy LA, Suarez LE, "Influence of the roof on the natural periods of empty tanks", Engineering Structures, Vol. 25, No.7, pp. 877-887, (2003).

[12] Malhotra PK, Thomas W, Martin W, "Simple procedure for seismic analysis of liquid-storage tanks", Structural Engineering International, Vol. 10, pp. 197-201, (2000).

[13] Balendra T, Ang KK, Pramasivam P, Lee SL, "Free vibration analysis of cylindrical liquid storage tanks", Journal of computers and structures, Int. J. Mech. Sci, Vol. 24, No. 1, pp. 47-59, (1982).

[14] Lam KY, Loy CT, "Influence of boundary conditions and fibre orientation on the natural frequencies of thin orthotropic laminated cylindrical shells", Composite Structures, Vol. 31, No. 1, pp. 21-30, (1995).

[15] Lam KY, Loy CT, "Influence of boundary conditions for a thin-laminated cylindrical shell", Composite Structures, Vol. 41, No. 3-4, pp. 215-228, (1998).

[16] Gunawan H, Mikami TJ, Kanie T, Sato SM, "Free vibration of fluid-filled cylindrical shells on elastic foundations", Thin Wall Struct, Vol. 43, No. 11, pp. 1746-1762, (2005).

[17] Mohamad SQ, Rani WS, Wenchao W, "Recent research advances on the dynamic analysis of composite shells: 2000-2009", Composite Structures, Vol. 93, No. 1, pp. 14-31, (2010).  

[18] Mohamad SQ, "Recent research advances in the dynamic behavior of shells: part I, laminated composite shells", Applied Mechanics Reviews, Vol. 55, No. 4, pp. 325-350, (2002).

[19] Mohamad SQ, Recent research advances in the dynamic behavior of shells, part2: Homogeneousshells, Applied Mechanics Reviews , Vol. 55, No. 5, pp. 415-434, (2002).

[20] Loptin, AV, Morozov EV, "Fundamental frequency of the laminated composite cylindrical shell with clamped edges", International Journal of Mechanical Sciences, Vol. 92, pp. 35-43, (2015).

[21] Liu B, Xing YF, Mohamad QS, Ferreira, AJM, "Exact characteristic equations for free vibrations of thin orthotropic circular cylindrical shells", Composite Structures,  Vol. 94, No. 2, pp. 484-493, (2012).

[22] Guoyong J, Xiang X, Yuquan Y, Shi SX, Zhigang, "Free vibration analysis of composite laminated cylindrical shells using the Haar wavelet method", Composite Structures, Vol. 109, pp. 169-177, (2014).

[23] Guoyong J, Xiang X, Yuquan Y, Shi SX, Zhigang L, "A numerical solution for vibration analysis of composite laminated conical, cylindrical shell and annular plate structures", Composite Structures, Vol. 111, pp. 20-30, (2014).

[24] Kumar, A., Sharma, K. & Dixit, A.R. "A review of the mechanical and thermal properties of graphene and its hybrid polymer nanocomposites for structural applications", J Mater Sci, Vol. 54, pp. 5992–6026 (2019).

[25] Kumar, A., Sharma, K. & Dixit, A.R. " Carbon nanotube- and graphene-reinforced multiphase polymeric composites: review on their properties and applications", J Mater Sci,Vol. 55, pp. 2682–2724 (2020).

[26] Simulia DC, "Abaqus Analysis User's Manual, Dassault Syst", Pawtucket, USA, (2016).

[27] Jack RV, "the behavior of shells composed of isotropic and composite materials", Kluwer Academic Publishers, Boston, (1993).

[28] Eurocode 8, "Design of Structures for Earthquake Resistance, Part 4: Silos, Tanks and Pipelines (BS EN 1998-4:2006)", European Committee for Standardization, Brussels, (2006).    

[29] IITK-GSDMA, "Guidelines for Seismic Design of Liquid Storage Tanks", Gujarat State Disaster Management Authority Gandh inagar, Kanpur, India, (2007).

[30] "Seismic design of storage tanks", New Zealand Society for Earthquake Engineering (NZSEE) Inc, Wellington, New Zealand, (2009).

[31] Amabili M, "Theory and experiments for large-amplitude vibrations of empty and fluid-filled circular cylindrical shells with imperfections", Journal of Sound and Vibration, Vol. 262, No. 4, pp. 921-975, (2003).

[32] Williston LW, Haroun MA, Proceedings of Fourth US National Conference on Earthquake Engineering, Palm Springs, CA, "Comparison of available analytical options for cylindrical storage tank response subjected to ground motion", Vol.3, pp. 207-216, (1990).

CAPTCHA Image