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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

Figures

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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 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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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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Strain sensor array, piezo-actuators, and damage case near a “hot-spot”
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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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Experimental setup with actuators, sensors, and instrumentation
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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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