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Technical Brief

Structural Damage Detection Using Slopes of Longitudinal Vibration Shapes

[+] Author and Article Information
W. Xu

Department of Mechanical Engineering,
University of Maryland, Baltimore County,
Baltimore, MD 21250;
Department of Engineering Mechanics,
Hohai University,
Nanjing 210098, China
e-mail: xuwei2007hohai@hhu.edu.cn

W. D. Zhu

Professor
Fellow ASME
Division of Dynamics and Control,
School of Astronautics,
Harbin Institute of Technology,
P.O. Box 137,
Harbin 150001, China;
Department of Mechanical Engineering,
University of Maryland, Baltimore County,
Baltimore, MD 21250
e-mail: wzhu@umbc.edu

S. A. Smith

Department of Mechanical Engineering,
University of Maryland, Baltimore County,
Baltimore, MD 21250
e-mail: ssmith11@umbc.edu

M. S. Cao

Professor
Mem. ASME
Department of Engineering Mechanics,
Hohai University,
Nanjing 210098, China
e-mail: cmszhy@hhu.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 13, 2014; final manuscript received September 18, 2015; published online March 18, 2016. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 138(3), 034501 (Mar 18, 2016) (10 pages) Paper No: VIB-14-1389; doi: 10.1115/1.4031996 History: Received October 13, 2014; Revised September 18, 2015

While structural damage detection based on flexural vibration shapes, such as mode shapes and steady-state response shapes under harmonic excitation, has been well developed, little attention is paid to that based on longitudinal vibration shapes that also contain damage information. This study originally formulates a slope vibration shape (SVS) for damage detection in bars using longitudinal vibration shapes. To enhance noise robustness of the method, an SVS is transformed to a multiscale slope vibration shape (MSVS) in a multiscale domain using wavelet transform, which has explicit physical implication, high damage sensitivity, and noise robustness. These advantages are demonstrated in numerical cases of damaged bars, and results show that MSVSs can be used for identifying and locating damage in a noisy environment. A three-dimensional (3D) scanning laser vibrometer (SLV) is used to measure the longitudinal steady-state response shape of an aluminum bar with damage due to reduced cross-sectional dimensions under harmonic excitation, and results show that the method can successfully identify and locate the damage. Slopes of longitudinal vibration shapes are shown to be suitable for damage detection in bars and have potential for applications in noisy environments.

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Figures

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Fig. 1

The first three normalized longitudinal mode shapes with unit maximum values: (a) the first mode shape, (b) the second mode shape, and (c) the third mode shape

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Fig. 3

The first three longitudinal mode shapes in a noisy environment: (a) the first mode shape, (b) the second mode shape, and (c) the third mode shape

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Fig. 4

Slopes of the first three longitudinal mode shapes in a noisy environment: (a) the first mode shape, (b) the second mode shape, and (c) the third mode shape

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Fig. 2

Slopes of the first three longitudinal mode shapes: (a) the first mode shape, (b) the second mode shape, and (c) the third mode shape

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Fig. 6

Two longitudinal steady-state response shapes under harmonic excitation with a unit amplitude at (a) 4900 Hz and (b) 15,000 Hz

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Fig. 7

Slopes of the two longitudinal steady-state response shapes under harmonic excitation with a unit amplitude at (a) 4900 Hz and (b) 15,000 Hz

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Fig. 8

Two longitudinal steady-state response shapes under harmonic excitation with a unit amplitude at (a) 4900 Hz and (b) 15,000 Hz in a noisy environment

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Fig. 9

Slopes of the two longitudinal steady-state response shapes under harmonic excitation with a unit amplitude at (a) 4900 Hz and (b) 15,000 Hz in a noisy environment

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Fig. 5

Multiscale slopes of the first three longitudinal mode shapes and their top views: ((a) and (d)) the first mode shape, ((b) and (e)) the second mode shape, and ((c) and (f)) the third mode shape. Dashed lines in (d)–(f) correspond to actual locations of two edges of the damaged section.

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Fig. 11

Experimental setup: (a) an aluminum bar with damage due to reduced cross-sectional dimensions and an electromagnetic shaker and (b) the 3D SLV

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Fig. 12

An expanded view of damage in the bar due to reduced cross-sectional dimensions with a laser beam spot on it

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Fig. 13

Real part of the longitudinal ODS under harmonic excitation at 4900 Hz

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Fig. 14

Slope of the real part of the longitudinal ODS under harmonic excitation at 4900 Hz

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Fig. 15

(a) Multiscale slope of the real part of the longitudinal ODS under harmonic excitation at 4900 Hz and (b) its top view; dashed lines in (b) correspond to actual locations of two edges of the damaged section

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Fig. 10

Multiscale slopes of the two longitudinal steady-state response shapes under harmonic excitation with a unit amplitude at (a) 4900 Hz and (b) 15,000 Hz and ((c) and (d)) their respective top views; dashed lines in (c) and (d) correspond to actual locations of two edges of the damaged section

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