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Research Papers: Flows in Complex Systems

Equivalent Linearized Mechanical Model for Tuned Liquid Dampers of Arbitrary Tank Shape

[+] Author and Article Information
J. S. Love1

Department of Civil Engineering,  McMaster University, 1280 Main St. W., Hamilton L8S 4L7, ON, Canadalovejs@mcmaster.ca

M. J. Tait

Department of Civil Engineering,  McMaster University, 1280 Main St. W., Hamilton L8S 4L7, ON, Canada

1

Corresponding author.

J. Fluids Eng 133(6), 061105 (Jun 17, 2011) (9 pages) doi:10.1115/1.4004080 History: Received October 30, 2009; Revised April 12, 2011; Published June 17, 2011; Online June 17, 2011

This paper presents a model to describe the behavior of sloshing in a general tank with a uniform fluid depth. An equivalent linearized mechanical model is developed for a tuned liquid damper (TLD) with arbitrary tank geometry. The finite element method is employed to determine the mode shapes of the sloshing fluid. In general, the mode shapes of arbitrary tanks will have response components in the x- and y-directions. The mode shapes enable the generalized properties of the sloshing fluid to be determined; these properties are subsequently used to establish equivalent mechanical properties. The nonlinear damping of slat-type damping screens is linearized, permitting it to be included in the model as amplitude-dependent viscous damping. The proposed model is in excellent agreement with existing linearized models for the special cases of rectangular and circular tanks. Sinusoidal shake table tests are conducted on tanks with chamfers placed in selected corners. In the literature, no experimental testing has focused on tanks of arbitrary shape with a constant fluid depth. The proposed model is in good agreement with the experimental results for the mode dominated by motion in the direction of excitation. However, the model is found to underestimate the response of the mode which is dominated by motion perpendicular to the excitation direction. The linearized mechanical model developed can serve as a useful preliminary TLD design tool.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Coordinate system of arbitrary tank with uniform depth

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Figure 2

(a) TLD tank under base excitation (b) equivalent mechanical model representation

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Figure 3

Comparison of existing and proposed model normalized fluid response for (a) rectangular and (b) circular tank

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Figure 4

Schematic of arbitrary TLD tank tested (dimensions in mm)

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Figure 5

Shake table experimental apparatus

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Figure 6

Normalized fundamental mode shapes (top: x-dominated mode; bottom: y-dominated mode) for (a) tank0a (b) tank2a (c) tank4a

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Figure 7

Loss coefficient, Cl , as a function of the Keulegan-Carpenter (KC) number

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Figure 8

Normalized wave heights (Λ = 0.003) (a) tank0a, (b) tank2a, (c) tank4a

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Figure 9

Normalized sloshing force in the x-direction (Λ = 0.003) (a) tank0a, (b) tank2a, (c) tank4a

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Figure 10

Normalized sloshing force in the y-direction (Λ = 0.003) (a) tank0a, (b) tank2a, (c) tank4a

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Figure 11

Normalized energy dissipation (Λ = 0.003) (a) tank0a, (b) tank2a, (c) tank4a

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