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Offshore and Structural Mechanics

A Study of the Roll Motion by Means of a Free Decay Test

[+] Author and Article Information
Hamid Zeraatgar1

Department of Marine Technology, Amirkabir University of Technology, 424 Hafez Avenue, P.O. Box 15875-4413, Tehran, Iranhamidz@aut.ac.ir

Mohsen Asghari

Department of Marine Technology, Amirkabir University of Technology, 424 Hafez Avenue, P.O. Box 15875-4413, Tehran, Iranmohs.asghari@gmail.com

Firooz Bakhtiari-Nejad

Department of Mechanical Engineering, Amirkabir University of Technology, 424 Hafez Avenue, P.O. Box 15875-4413, Tehran, Iranbaktiari@aut.ac.ir

1

Corresponding author.

J. Offshore Mech. Arct. Eng 132(3), 031303 (May 04, 2010) (8 pages) doi:10.1115/1.4000393 History: Received February 02, 2008; Revised June 09, 2009; Published May 04, 2010; Online May 04, 2010

In this study, a method for the extraction of damping by tracing free roll decay is presented. For this purpose, in calm waters, a bulk carrier model is given a large initial roll angle and then released. Consequently, the roll motion is recorded. Restoring coefficients and virtual moments of inertia for the model are determined by means of an inclining test and recording the damped period, respectively. The linear damping coefficient is evaluated by using the damping ratio. Four different forms of combinations of restoring moment and damping coefficient are assumed in order to determine the nonlinear form of the roll motion. These equations are numerically solved for various damping coefficients and results are compared with the experimental data. By virtue of this comparison, the damping coefficients are determined for each case. It may be concluded that the use of the nonlinear restoring moment, which is an odd polynomial of the fifth order, and the cubic form for the nonlinear damping moment best fits the roll behavior for the ship model. The amount of energy dissipated by the damping moments is also calculated in the time domain. The energy method also confirms that the nonlinear form of restoring force in conjunction with the cubic form of the damping force is the best solution of the roll motion for small to large angles.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Test facilities composed of (1) wave damper, (2) sliding system, (3) rollmeter, (4) laser pointer, (5) laser beam projection, (6) heeling system, (7) draft mark, and (8) ballasting system

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Figure 2

The roll tank composed of (1) wave damper, (2) sliding system, (4) laser pointer, and (6) heeling system (dimensions are in mm)

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Figure 3

Body lines of the model

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Figure 4

Restoring moment of the model

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Figure 5

The equivalent linear damping ratio as a function of the oscillation number

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Figure 6

Identification of the damping ratio

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Figure 7

Identification of the nonlinear damping coefficient (cubic nonlinear damping+linear restoring moment)

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Figure 8

Identification of the nonlinear damping coefficient (quadratic nonlinear damping+linear restoring moment)

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Figure 9

Identification of the nonlinear damping coefficient (cubic nonlinear damping+fifth order restoring moment)

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Figure 10

Identification of the nonlinear damping coefficient (quadratic nonlinear damping+fifth order restoring moment)

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Figure 11

Modeling of the roll motion with linear restoring and linear damping

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Figure 12

Linear and nonlinear losses of the model, where W0 is the total damped energy, which is equal to the initial total mechanical energy

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Figure 13

Percentage of the total nonlinear damped energy with respect to the total damped energy

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