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Research Papers

Theoretical Modeling of TLD With Different Tank Geometries Using Linear Long Wave Theory

[+] Author and Article Information
X. Deng

 McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4L7, Canada

M. J. Tait1

Department of Civil Engineering, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4L7, Canadataitm@mcmaster.ca

1

Corresponding author.

J. Vib. Acoust 131(4), 041014 (Jul 14, 2009) (10 pages) doi:10.1115/1.3142873 History: Received June 21, 2007; Revised February 03, 2009; Published July 14, 2009

This study focuses on the modeling of tuned liquid dampers (TLDs) with triangular-bottom, sloped-bottom, parabolic-bottom, and flat-bottom tanks using the linear long wave theory. The energy dissipated by damping screens is modeled theoretically utilizing the method of virtual work. In this proposed model, only the fundamental sloshing mode is considered, and the assumption of small free surface fluid response amplitude is made. Subsequently, the equivalent mechanical properties including effective mass, natural frequency, and damping ratio of the TLDs, having different tank geometries, are compared. It is found that the normalized effective mass ratio values for a parabolic-bottom tank and a sloped-bottom tank with a sloping angle of 20 deg are larger than the normalized effective mass ratio values for triangular-bottom and flat-bottom tanks. An increase in the normalized effective mass ratio indicates that a greater portion of the water inside the tank participates in the sloshing motion. The derived equivalent mechanical models for the TLD tank geometries considered in this study can be used for the preliminary design of structural-TLD systems.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Equivalent mechanical model; (b) Cartesian coordinate attached to an arbitrary tank geometry

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Figure 2

Definition sketch for liquid sloshing in a triangular-bottom tank

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Figure 3

Definition sketch for liquid sloshing in a sloped-bottom tank

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Figure 4

Definition sketch for liquid sloshing in a parabolic-bottom tank

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Figure 5

Definition sketch for liquid sloshing in a flat-bottom tank

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Figure 6

Natural sloshing frequency in a sloped-bottom tank normalized by the natural sloshing frequency in a flat-bottom tank

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Figure 7

Natural sloshing frequency in a triangular-bottom tank

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Figure 8

Natural sloshing frequency in a sloped-bottom tank (s/L=0.6)

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Figure 9

Natural sloshing frequency in a parabolic-bottom tank

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Figure 10

Natural sloshing frequency in a flat-bottom tank

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Figure 11

Comparison of normalized natural sloshing frequency ratio for different tank geometries

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Figure 12

Influence of s/L0 on the normalized effective mass ratio for a sloped-bottom tank (h/L=0.1)

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Figure 13

Variation of normalized damping ratio with liquid depth ratio and normalized response amplitude for a triangular-bottom tank

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Figure 14

Variation of normalized damping ratio with liquid depth ratio and normalized response amplitude for a sloped-bottom tank

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Figure 15

Variation of normalized damping ratio with liquid depth ratio and normalized response amplitude for a parabolic-bottom tank

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Figure 16

Variation of normalized damping ratio with liquid depth ratio and normalized response amplitude for a flat-bottom tank

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Figure 17

Influence of s/L0 on the normalized damping ratio of a sloped-bottom tank (h/L=0.1)

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