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Research Papers

Damage Localization by Isolating the Part of the Response Due to the Damage Only

[+] Author and Article Information
Akash Dixit

e-mail: wilkn@yahoo.com

Sathya Hanagud

Professor
Daniel Guggenheim School
of Aerospace Engineering,
Georgia Institute Of Technology,
Atlanta, GA30332

1Corresponding author.

Manuscript received February 24, 2011; final manuscript received June 29, 2012; accepted manuscript posted July 6, 2012; published online October 31, 2012. Assoc. Editor: Wei-Chau Xie.

J. Appl. Mech 80(1), 011015 (Oct 31, 2012) (8 pages) Paper No: JAM-11-1062; doi: 10.1115/1.4007080 History: Received February 24, 2011; Revised June 29, 2012; Accepted July 06, 2012

A new physical parameter is presented and it is applied to damage detection to address the two main challenges in the field of vibration-based structural health monitoring: the sensitivity of detection and the requirement of data of the baseline state. The parameter is also shown to be not affected by noise in the detection ambience. Assuming the damaged structure to be a linear system, its response can be expressed as the summation of the responses due to the undamaged and the damaged part. If the part of the response due to the damage is isolated, it forms what can be regarded as the damage signature. In this paper, the occurrence of damage signature is investigated when the damaged structure is excited at one of its natural frequencies, and it is called partial-mode contribution. The existence of damage signature as partial-mode contribution is first verified using an analytical derivation. Thereupon, its existence is ascertained using finite element models and by doing experiments. The limits of size of the damage that can be determined using the method are also investigated.

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Figures

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Fig. 1

Experimental setup

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Fig. 2

Frequency response function

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Fig. 3

Normalized mode shapes of clamped-free beam: experimental damaged beam (dotted line), experimental data curve-fitted using undamaged beam modes (dashed line), analytical undamaged beam (solid line), analytical damaged beam (dot-dashed line)

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Fig. 4

Normalized curvature shapes of clamped free beam: experimental undamaged beam (dotted line), experimental damaged (dashed line), analytical undamaged (solid line), analytical damaged (dot-dashed line)

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Fig. 5

Normalized difference between normalized mode shapes of clamped free damaged and undamaged beams: experimental-analytical (solid line), experimental-experimental (dotted line), analytical-analytical (dashed line)

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Fig. 6

Normalized difference between normalized curvature shapes of damaged and undamaged clamped-free beam: experimental-analytical (solid line), experimental-experimental (dotted line), analytical-analytical (dashed line)

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Fig. 7

Normalized damage signature (partial-mode contribution): experimental displacement mode (solid line), experimental curvature mode (dashed line), analytical displacement mode (dot-dashed line), analytical curvature mode (dotted line)

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Fig. 8

Damage signature of normalized modes and curvatures: mode 1 (continuous line), mode 2 (dashed line)

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Fig. 10

Normalized partial-mode contribution, mode shape (continuous lines) and curvature shape (dashed lines); ζd = 0.35, ɛ = 0.1, ΔLz = 0.01, first twelve modes considered

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Fig. 9

Normalized difference between damaged and undamaged beam mode shape (continuous lines) and curvature shape (dashed lines) ζd = 0.35, ɛ = 0.1, ΔLz = 0.01

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Fig. 11

Normalized difference between damaged and undamaged beam mode shape (continuous lines) and curvature shape (dashed lines); ζd = 0.5, ɛ = 0.1, ΔLz = 0.01

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Fig. 12

Normalized partial-mode contribution, mode shape (continuous lines) and curvature shape (dashed lines); ζd = 0.5, ɛ = 0.1, ΔLz = 0.01; first twelve modes considered

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Fig. 13

Normalized difference between damaged and undamaged beam mode shape (continuous lines) and curvature shape (dashed lines); ζd = 0.7, ɛ = 0.1, ΔLz = 0.01

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Fig. 14

Normalized partial-mode contribution, mode shape (continuous lines) and curvature shape (dashed lines); ζd = 0.7, ɛ = 0.1, ΔLz = 0.01; first twelve modes considered

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Fig. 15

Normalized difference between damaged and undamaged beam mode shape (continuous lines) and curvature shape (dashed lines); ζd = 0.35, ɛ = 0.01, ΔLz = 0.01

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Fig. 16

Normalized difference between damaged and undamaged beam mode shape (continuous lines) and curvature shape (dashed lines); ζd = 0.35, ɛ = 0.4, ΔLz = 0.01

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Fig. 17

Normalized partial-mode contribution, mode shape (continuous lines) and curvature shape (dashed lines); ζd = 0.35, ɛ = 0.01, 0.4, ΔLz = 0.01; first twelve modes considered

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Fig. 18

Normalized difference between damaged and undamaged beam mode shape (continuous lines) and curvature shape (dashed lines); ζd = 0.35, ɛ = 0.1, ΔLz = 0.001

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Fig. 19

Normalized difference between damaged and undamaged beam mode shape (continuous lines) and curvature shape (dashed lines); ζd = 0.35, ɛ = 0.1, ΔLz = 0.1

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Fig. 20

Normalized partial-mode contribution, mode shape (continuous lines) and curvature shape (dashed lines); ζd = 0.35, ɛ = 0.1, ΔLz = 0.001, 0.1; first twelve modes considered

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