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TECHNICAL PAPERS

Coupled Bending-Torsional Vibration of a Cracked Hollow Beam Model in Water and Identification of Cracking

[+] Author and Article Information
Xinfeng Yang, A. S. Swamidas, R. Seshadri

Faculty of Engineering and Applied Science,  Memorial University of Newfoundland, St. John’s, NF, A1B 3X5 Canada

I. Datta

 Spar International Inc., 11757 Katy Freeway, Suite 500, Houston, Texas 77079-1725, USA

J. Vib. Acoust 127(6), 575-587 (Sep 08, 2004) (13 pages) doi:10.1115/1.1888587 History: Received August 16, 2000; Revised September 08, 2004

The coupled flexural-torsional vibration equations of a floating beam model, considering added fluid masses, are developed. The beam has varying bending stiffness, varying torsional stiffness and varying mass distribution; frequencies and mode shapes are calculated using Galerkin’s method. Stiffness for the cracked beam (backbone) has been calculated using an energy procedure. Experimental values have been compared with the results of theoretical predictions and the agreement between the two found to be good. The frequency contour method has been used to identify the crack.`

Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 2

Backbone of ship model

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Figure 3

Arrangement for torsional vibration tests

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Figure 4

Frequency response function for excitation near the center of the floating body, and the response at the forward end of the body

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Figure 5

Added mass of a two-dimensional body (15-16)

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Figure 6

Cross section of backbone at a point, considering added mass

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Figure 7

Mode shapes for horizontal displacement of the uncracked floating body (v=horizontal displacement)

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Figure 8

Mode shapes for torsional rotation of the uncracked floating body (θ=torsional angle)

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Figure 9

A crack of length (2a) located at one flank of the hollow backbone beam

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Figure 10

Mode shapes for the vertical displacement of the uncracked floating body

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Figure 11

Mode shapes from tests on the uncracked floating body

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Figure 12

Normalized flexural-torsional frequencies against crack length ratio for a crack located at c∕l=0.5 (a=crack half-length, l=span length of the lexan box beam, f=frequency for uncracked beam, fc=frequency for cracked beam)

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Figure 13

Normalized flexural-tosional frequencies against crack length ratio for a crack located at c∕l=0.75 (a=crack half-length, l=span length of the lexan box beam, f=frequency for uncracked beam, fc=frequency for cracked beam)

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Figure 14

Normalized flexural-torsional frequency against crack location ratio [nondimensional crack depth=a∕(b+h)=0.08] [a=crack half-length, l=span length of the lexan box beam, b=depth of the lexan box beam (for horizontal bending), h=width of the lexan box beam (for horizontal bending), f=frequency for uncracked beam, fc=frequency for cracked beam]

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Figure 15

Normalized flexural-torsional frequency against crack location ratio [nondimensional crack depth=a∕(b+h)=0.20] (a=crack half-length, l=span length of the lexan box beam, b=depth of the lexan box beam, h=width of the lexan box beam, f=frequency for uncracked beam, fc=frequency for cracked beam)

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Figure 16

Normalized flexural-torsional frequency against crack location ratio [nondimensional crack depth=a∕(b+h)=0.40] (a=crack half-length, l=span length of the lexan box beam, b=depth of the lexan box beam, h=width of the lexan box beam, f=frequency for uncracked beam, fc=frequency for cracked beam)

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Figure 17

Normalized flexural-torsional frequency against normalized crack length and crack location ratios

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Figure 18

Three frequency contours for the first four modes of flexural-torsional displacements

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Figure 19

Crack identification by intersection of three contours for the first, third, and fourth modes (frequency ratios for the three modes are 0.9816, 0.9786, and 0.9922). Deduction: a∕(b+h)=0.20, c∕l=0.5

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Figure 20

Crack identification by intersection of three contours for the first, second, and third modes (frequency ratios for the three modes are 0.9848, 0.9756 and 0.9820). Deduction: a∕(b+h)=0.24, c∕l=0.20.

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