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Research Papers

Identification of Cracks in Beams With Auxiliary Mass Spatial Probing by Stationary Wavelet Transform

[+] Author and Article Information
Shuncong Zhong

Dynamics and Aeroelasticity Research Group, School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester M13 9PL, United Kingdom

S. Olutunde Oyadiji

Dynamics and Aeroelasticity Research Group, School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester M13 9PL, United Kingdoms.o.oyadiji@manchester.ac.uk

J. Vib. Acoust 130(4), 041001 (May 22, 2008) (14 pages) doi:10.1115/1.2891242 History: Received March 09, 2006; Revised July 16, 2007; Published May 22, 2008

This paper proposes a new approach based on auxiliary mass spatial probing by stationary wavelet transform (SWT) to provide a method for crack detection in beamlike structure. SWT can provide accurate estimation of the variances at each scale and facilitate the identification of salient features in a signal. The natural frequencies of a damaged beam with a traversing auxiliary mass change due to the change in flexibility and inertia of the beam as the auxiliary mass is traversed along the beam. Therefore, the auxiliary mass can enhance the effects of the crack on the dynamics of the beam and, therefore, facilitate the identification and location of damage in the beam. That is, the auxiliary mass can be used to probe the dynamic characteristic of the beam by traversing the mass from one end of the beam to the other. However, it is difficult to locate the crack directly from the graphical plot of the natural frequency versus axial location of auxiliary mass. This curve of the natural frequencies can be decomposed by SWT into a smooth, low order curve, called approximation coefficient, and a wavy, high order curve called the detail coefficient, which includes crack information that is useful for damage detection. The modal responses of the damaged simply supported beams with auxiliary mass used are computed using the finite element method (FEM). Sixty-four cases are studied using FEM and SWT. The efficiency and practicability of the proposed method is illustrated via experimental testing. The effects of crack depth, crack location, auxiliary mass, and spatial probing interval are investigated. From the simulated and experimental results, the efficiency of the proposed method is demonstrated.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Model of a cracked simply supported beam with auxiliary mass

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Figure 2

The first four natural frequency curves of the cracked beam (hc=2.5mm) with an auxiliary mass traversing along the beam (m=2kg): (a) first natural frequency curve, (b) second natural frequency curve, (c) third natural frequency curve, and (d) fourth natural frequency curve

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Figure 3

SWT decomposition of the first natural frequency curve of a cracked beam (hc=10mm) with an auxiliary mass (m=1kg) of spatial probing interval si=25mm: (a) first natural frequency curve, (b) SWT approximation coefficient of the first natural frequency curve, (c) SWT detail coefficient of the first natural frequency curve, and (d) denoised detail coefficient of the first natural frequency curve

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Figure 4

SWT decomposition of the first two natural frequency curves of a cracked beam (lc=0.4m) with different crack depths and an auxiliary mass (m=2kg) of spatial probing interval si=25mm: (——) hc=2.5mm, (- - - -) hc=5mm, (⋯⋯) hc=7.5mm, (-⋅-⋅-⋅), hc=10mm; (a1) first natural frequency curves, (a2) SWT detail coefficient of the first natural frequency curves, (a3) zoom curves of SWT detail coefficient of the first natural frequency curves in the cracked area, (b1) second natural frequency curves, (b2) SWT detail coefficient of the second natural frequency curves, and (b3) zoom curves of SWT detail coefficient of the second natural frequency curves in the cracked area

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Figure 5

Denoised SWT detail coefficient of the first two natural frequency curves of a cracked beam (lc=0.4m) with different crack depths and an auxiliary mass (m=2kg) of spatial probing interval si=25mm: (——) hc=2.5mm, (- - - -) hc=5mm, (⋯⋯) hc=7.5mm, (-⋅-⋅-⋅) hc=10mm; (a1) denoised detail coefficients of the first natural frequency curves, (a2) zoomed curves of the denoised detail coefficients of the first natural frequency curves in the cracked area, (b1) denoised detail coefficients of the second natural frequency curves, and (b2) zoomed curves of the denoised detail coefficients of the second natural frequency curves in the cracked area

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Figure 6

SWT decomposition of the first two natural frequency curves of a cracked beam (lc=1.2m, center of the beam) with different crack depths and an auxiliary mass (m=2kg) of spatial probing interval si=25mm: (——) hc=2.5mm, (- - - -) hc=5mm, (⋯⋯) hc=7.5mm, (-⋅-⋅-⋅) hc=10mm; (a1) first natural frequency curves, (a2) SWT detail coefficient of the first natural frequency curves, (a3) zoom curves of SWT detail coefficient of the first natural frequency curves in the cracked area, (b1) second natural frequency curves, (b2) SWT detail coefficient of the second natural frequency curves, and (b3) zoomed curves of SWT detail coefficient of the second natural frequency curves in the cracked area

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Figure 7

Denoised SWT detail coefficient of the first two natural frequency curves of a cracked beam (lc=1.2m, center of the beam) with different crack depths and an auxiliary mass (m=2kg) of spatial probing interval si=25mm: (——) hc=2.5mm, (- - - -) hc=5mm, (⋯⋯) hc=7.5mm, (-⋅-⋅-⋅) hc=10mm; (a1) denoised detail coefficients of the first natural frequency curves, (a2) zoomed curves of the denoised detail coefficients of the first natural frequency curves in the cracked area, (b1) denoised detail coefficients of the second natural frequency curves, and (b2) zoomed curves of the denoised detail coefficients of the second natural frequency curves in the cracked area

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Figure 8

SWT decomposition of the first two natural frequency curves of a cracked beam (lc=0.4m, hc=5mm) with different auxiliary masses of spatial probing interval si=25mm: (——), m=1kg, (- - - -) m=2kg, (⋯⋯) m=4kg, (-⋅-⋅-⋅) m=8kg; (a1) first natural frequency curves, (a2) SWT detail coefficient of the first natural frequency curves, (a3) zoom curves of SWT detail coefficient of the first natural frequency curves in the cracked area, (b1) second natural frequency curves, (b2) SWT detail coefficient of the second natural frequency curves, and (b3) zoomed curves of SWT detail coefficient of the second natural frequency curves in the cracked area

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Figure 9

SWT decomposition of the first two natural frequency curves of a cracked beam (lc=0.4m) with different crack depths and an auxiliary mass (m=2kg) of spatial probing interval si=50mm: (——) hc=2.5mm, (- - - -) hc=5mm, (⋯⋯) hc=7.5mm, (-⋅-⋅-⋅) hc=10mm; (a1) first natural frequency curves, (a2) SWT detail coefficient of the first natural frequency curves, (a3) zoom curves of SWT detail coefficient of the first natural frequency curves in the cracked area, (b1) second natural frequency curves, (b2) SWT detail coefficient of the second natural frequency curves, and (b3) zoomed curves of SWT detail coefficient of the second natural frequency curves in the cracked area

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Figure 10

SWT decomposition of the first natural frequency curves of a cracked beam (lc=0.4m, hc=7.5mm) with an auxiliary mass (m=2kg) and the first mode shape of the same cracked beam without an auxiliary mass: (——) first natural frequency, (- - - -) first mode shape; (a1) SWT detail coefficient of the first natural frequency and mode shape curves (without added noise), (b1) denoised SWT detail coefficient of the first natural frequency and mode shape curves (without noise), (a2) SWT detail coefficient of the first natural frequency and mode shape curves (2% random noise added), and (b2) Denoised SWT detail coefficient of the first natural frequency and mode shape curves (2% random noise added)

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Figure 11

Experimental setup

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Figure 12

FRFs of a cracked aluminum beam (lc=0.4m, hc=5mm) with an auxiliary mass (m=4kg) located at different positions (lm) of the beam: (——) lm=0mm, (- - - -) lm=600mm, (⋯⋯) lm=1100mm

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Figure 13

SWT decomposition of the first two natural frequency curves of a cracked aluminum beam (lc=0.4m, hc=5mm) with an auxiliary mass (m=4kg) of spatial probing interval si=50mm: (a1) first natural frequency curve, (a2) SWT detail coefficient of the first natural frequency curve, (a3) denoised SWT detail coefficient of the first natural frequency curve, (b1) second natural frequency curve, (b2) SWT detail coefficient of the second natural frequency curve, and (b3) denoised SWT detail coefficient of the second natural frequency curve

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