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Research Papers

Damage Identification of Beams Using a Continuously Scanning Laser Doppler Vibrometer System

[+] Author and Article Information
Da-Ming Chen

Department of Mechanical Engineering,
University of Maryland, Baltimore County,
1000 Hilltop Circle,
Baltimore, MD 21250
e-mail: damingc1@umbc.edu

Y. F. Xu

Department of Mechanical Engineering,
University of Maryland, Baltimore County,
1000 Hilltop Circle,
Baltimore, MD 21250
e-mail: yxu2@umbc.edu

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,
1000 Hilltop Circle,
Baltimore, MD 21250
e-mail: wzhu@umbc.edu

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 6, 2015; final manuscript received May 3, 2016; published online June 17, 2016. Assoc. Editor: Patrick S. Keogh.

J. Vib. Acoust 138(5), 051011 (Jun 17, 2016) (16 pages) Paper No: VIB-15-1418; doi: 10.1115/1.4033639 History: Received October 06, 2015; Revised May 03, 2016

A continuously scanning laser Doppler vibrometer (CSLDV) system is capable of rapidly obtaining spatially dense operating deflection shapes (ODSs) by continuously sweeping a laser spot from the system over a structure surface. This paper presents a new damage identification methodology for beams that uses their ODSs under sinusoidal excitation obtained by a CSLDV system, where baseline information of associated undamaged beams is not needed. A curvature damage index (CDI) is proposed to identify damage near a region with high values of the CDI at an excitation frequency. The CDI uses the difference between curvatures of ODSs (CODSs) associated with ODSs that are obtained by two different CSLDV measurement methods, i.e., demodulation and polynomial methods; the former provides rapid and spatially dense ODSs of beams, and the latter provides ODSs that can be considered as those of associated undamaged beams. Phase variables are introduced to the two methods for damage identification purposes. Effects of the order in the polynomial method on qualities of ODSs and CODSs are investigated. A convergence index and a criterion are proposed to determine a proper order in the polynomial method. Effects of scan and sampling frequencies of a CSLDV system on qualities of ODSs and CODSs from the two measurement methods are investigated. The proposed damage identification methodology was experimentally validated on a beam with damage in the form of machined thickness reduction. The damage and its region were successfully identified in neighborhoods of prominent peaks of CDIs at different excitation frequencies.

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References

Figures

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Fig. 1

(a) ODS of a beam with damage in the form of thickness reduction (damaged), that of an undamaged beam (undamaged) and that from a polynomial fit (polynomial); (b) CODSs associated with the ODSs in (a); (c) the CDI using the difference between the CODSs of the damaged and undamaged beams; and (d) the CDI using the difference between the CODS of the damaged beam and that from the polynomial fit. Locations of damage ends are indicated by two vertical dashed lines.

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Fig. 2

The CSLDV system developed

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Fig. 3

(a) Dimensions of a damaged aluminum beam with a region of machined thickness reduction, (b) the region of machined thickness reduction, (c) the beam with its left end clamped by a bench vice and its right end connected to a shaker, and (d) the experimental setup for ODS measurements of the beam

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Fig. 4

(a) CSLDV velocity output of a beam at a sinusoidal excitation frequency of 111 Hz and the X-mirror feedback signal with a triangular input signal, (b) in-phase and quadrature ODS components from the demodulation method with θ = 0 deg, and (c) in-phase and quadrature ODS components from the demodulation method with the optimal θ = 61.74 deg

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Fig. 5

(a) CSLDV velocity output of a beam at a sinusoidal excitation frequency of 111 Hz, and the X-mirror feedback signal with a sinusoidal input signal; (b) in-phase and quadrature ODS components from the polynomial method with γ = 0 deg; and (c) in-phase and quadrature ODS components from the polynomial method with the optimal γ = 62.56 deg

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Fig. 6

Comparison between ODSs from the demodulation method and the polynomial method with m = 5

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Fig. 7

(a) ODSs from the polynomial method with m ranging from two to seven and (b) CODSs from the polynomial method with m ranging from two to nine

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Fig. 8

Convergence index con(m) associated with ODSs from the polynomial method with m up to 14

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Fig. 9

ODSs of the damaged beam with different scan frequencies at excitation frequencies of (a) 111 Hz, (b) 335 Hz, (c) 688 Hz, and (d) 1193 Hz; all the ODSs were obtained by the demodulation method

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Fig. 10

CODSs of the damaged beam with different scan frequencies at excitation frequencies of (a) 111 Hz, (b) 335 Hz, (c) 688 Hz, and (d) 1193 Hz; all the ODSs associated with the CODSs were obtained by the demodulation method. Locations of damage ends are indicated by two vertical dashed lines.

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Fig. 11

(a) ODSs from the polynomial method with m = 5 with different scan frequencies at an excitation frequency of 111 Hz, (b) ODSs from the polynomial method with m = 7 with different scan frequencies at an excitation frequency of 335 Hz, (c) ODSs from the polynomial method with m = 8 with different scan frequencies at an excitation frequency of 688 Hz, and (d) ODSs from the polynomial method with m = 9 with different scan frequencies at an excitation frequency of 1193 Hz

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Fig. 12

(a) CODSs associated with the ODSs from the polynomial method with m = 5 with different scan frequencies at an excitation frequency of 111 Hz, (b) CODSs associated with the ODSs from the polynomial method with m = 7 with different scan frequencies at an excitation frequency of 335 Hz, (c) CODSs associated with the ODSs from the polynomial method with m = 8 with different scan frequencies at an excitation frequency of 688 Hz, and (d) CODSs associated with the ODSs from the polynomial method with m = 9 with different scan frequencies at an excitation frequency of 1193 Hz

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Fig. 13

Convergence indices con(m) associated with ODSs from the polynomial method with m up to 14 with a scan frequency of 0.2 Hz at excitation frequencies of (a) 111 Hz, (b) 335 Hz, (c) 688 Hz, and (d) 1193 Hz

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Fig. 14

ODSs of the damaged beam with different sampling frequencies at excitation frequencies of (a) 111 Hz, (b) 335 Hz, (c) 688 Hz, and (d) 1193 Hz; all the ODSs were obtained by the demodulation method

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Fig. 15

ODSs of the damaged beam with different sampling frequencies at excitation frequencies of (a) 111 Hz, (b) 335 Hz, (c) 688 Hz, and (d) 1193 Hz; all the ODSs were obtained by the polynomial method

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Fig. 16

CODSs of the damaged beam with different sampling frequencies at excitation frequencies of (a) 111 Hz, (b) 335 Hz, (c) 688 Hz, and (d) 1193 Hz; all the ODSs associated with the CODSs were obtained by the demodulation method. Locations of damage ends are indicated by two vertical dashed lines.

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Fig. 17

CODSs of the damaged beam with different sampling frequencies at excitation frequencies of (a) 111 Hz, (b) 335 Hz, (c) 688 Hz, and (d) 1193 Hz; all the ODSs associated with the CODSs were obtained by the polynomial method

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Fig. 18

Comparisons between CODSs from the demodulation and polynomial methods at excitation frequencies of (a) 111 Hz, (b) 335 Hz, (c) 688 Hz, and (d) 1193 Hz. Locations of damage ends are indicated by two vertical dashed lines.

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Fig. 19

CDIs at excitation frequencies of (a) 111 Hz, (b) 335 Hz, (c) 688 Hz, and (d) 1193 Hz. Locations of damage ends are indicated by two vertical dashed lines.

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Fig. 20

Comparisons between CODSs from the demodulation and polynomial methods when the beam was excited at frequencies of (a) 200 Hz and (b) 850 Hz. Locations of damage ends are indicated by two vertical dashed lines.

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Fig. 21

CDIs at excitation frequencies of (a) 200 Hz and (b) 850 Hz. Locations of damage ends are indicated by two vertical dashed lines.

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