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TECHNICAL PAPERS

Transmissibility as a Differential Indicator of Structural Damage

[+] Author and Article Information
Timothy J. Johnson, Douglas E. Adams

Purdue University, School of Mechanical Engineering, 1077 Ray W. Herrick Laboratories, West Lafayette, IN 47907-1077

J. Vib. Acoust 124(4), 634-641 (Sep 20, 2002) (8 pages) doi:10.1115/1.1500744 History: Received April 01, 2001; Revised April 01, 2002; Online September 20, 2002
Copyright © 2002 by ASME
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References

Cronkhite, J. D., and Gill, L., technical evaluators, “RTO MP-7,” 1998, RTO AVT Specialists’ Meeting on Exploitation of Structural Loads/Health Data for Reduced Life Cycle Costs, Brussels, Belgium.
Doebling, S. W., Farrar, C. R., Prime, M. B., and Shevitz, D. W., 1996, “Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in Their Vibration Characteristics: A Literature Review,” Los Alamos Report LA-13070-MS.
Zimmerman, D. C., Kaouk, M., and Simmermacher, T., 1995, “Structural Damage Detection Using Frequency Response Functions,” Proceedings of the International Modal Analysis Conference, pp. 179–184.
Schulz, M. J., Pai, P. F., and Abdelnaser, A. S., 1996, “Frequency Response Function Assignment Technique for Structural Damage Identification,” Proceedings of the International Modal Analysis Conference, pp. 105–111.
Schulz, M. J., Pai, P. F., Naser, A. S., Thyagarajan, S. K., Brannon, G. R., and Chung, J., 1997, “Locating Structural Damage Using Frequency Response Reference Functions and Curvatures,” Proceedings of the International Workshop on Structural Health Monitoring, pp. 690–701, F. K. Chang, ed., Stanford University, Technomic Publishing.
Schulz, M. J., Pai, P. F., Naser, A. S., Linville, M., and Chung, J., 1997, “Detecting Structural Damage Using Transmittance Functions,” Proceedings of the International Modal Analysis Conference, Orlando, FL, pp. 638–644.
Ribeiro,  A. M. R., Silva,  J. M. M., and Maia,  N. M. M., 2000, “On the Generalisation of the Transmissibility Concept,” January, Mech. Syst. Signal Process., 14(1), pp. 29–36.
Mottershead,  J. E., 2000, “On the Zeros of Structural Frequency Response Functions and Their Sensitivities,” January, Mech. Syst. Signal Process., 12(5), pp. 591–598.
Adams,  D. E., and Allemang,  R. J., 1999, “A New Derivation of the Frequency Response Function Matrix for Vibrating Nonlinear Systems,” J. Sound Vib., 227(5), pp. 1083–1108.
Adams,  D. E., and Allemang,  R. J., 1999, “Characterization of Nonlinear Vibrating Systems Using Internal Feedback and Frequency Response Modulation,” ASME J. Vibr. Acoust., 121(4), pp. 495–500.

Figures

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Damage with 10% reduction in K12 for a single input at degree-of-freedom 1 showing (top) H11(ω) frequency response function and (bottom) T21(ω) transmissibility function between degree-of-freedom pair (1,2)
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No damage with single input at degree-of-freedom 1 and transmissibility functions between degree-of-freedom pairs (1,2), (1,3), and (2,3)
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Two different damage (linear) levels between DOFs 1 and 2 with single input at DOF 1 and transmissibility functions between all DOF pairs (1,2), (1,3), and (2,3) showing sensitivity to 1% increase in damage
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No damage with input at DOF 3 and then DOF 2 with resultant transmissibility functions between all DOF pairs (1,2), (1,3), and (2,3)
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No damage with input at DOF 3 and then DOF 2 with resultant comparison of specific transmissibility function relations: X3(ω)/X2(ω) (input at DOF 3) and [X3(ω)]/[X1(ω)/X2(ω)/X1(ω)] (input at DOF 3/input at DOF 2)
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Experimental setup with actuators, sensors, and instrumentation
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Strain sensor array, piezo-actuators, and damage case near a “hot-spot”
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Contour plot showing damage in DOF pairs 1 and 3 as a function of frequency (damaged areas-black)
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Contour plots showing quantification of damage in DOF pairs 1 and 3 as a function of frequency: (Top) 1/3 inch cut, (Bottom) 2/3 inch cut
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General multiple-input multiple-output structural dynamic system with boundary conditions
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Three degree-of-freedom nonlinear system
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Damage between DOFs 1 and 2 with input at DOF 3 and then DOF 2 with resultant comparison of specific transmissibility function relations: X3(ω)/X2(ω) (input at DOF 3) and [X3(ω)/X1(ω)]/[X2(ω)/X1(ω)] (input at DOF 3/input at DOF 2)
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Two different damage (linear) levels between DOFs 1 and 2 with single input at DOF 2 and transmissibility functions between all DOF pairs (1,2), (1,3), and (2,3) showing sensitivity to 1% increase in damage in presence of 10% RMS noise on all responses
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No damage with input at DOF 1 for global change in stiffness due to environmental fluctuation with resultant transmissibility functions between all DOF pairs (1,2), (1,3), and (2,3) showing characteristic false positive indication of damage

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