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Research Papers

Structural Intensity Modeling and Simulations for Damage Detection

[+] Author and Article Information
Micah R. Shepherd, Stephen C. Conlon, Stephen A. Hambric

Applied Research Laboratory,  The Pennsylvania State University, P.O. Box 30,State College, PA 16804

Fabio Semperlotti

Department of Aerospace and Mechanical Engineering,  University of Notre Dame, Notre Dame, IN 46556

J. Vib. Acoust 134(5), 051004 (Jun 05, 2012) (10 pages) doi:10.1115/1.4006376 History: Received January 25, 2011; Revised January 06, 2012; Published June 04, 2012; Online June 05, 2012

Structural health monitoring (SHM) techniques have previously been proposed based on structural intensity (SI) due to its sensitivity to changes in boundary and loading conditions, and impedance, as well as to various damage mechanisms. In this paper, computational techniques for SI-based SHM are presented. Finite element solvers combined with SI equations can yield intensity maps over structures to determine characteristic changes in power flow due to damage. Numerical techniques for structural surface intensity (SSI) are also introduced using two alternative methods: A time domain approach that directly uses SSI equations that are valid at the surface of any elastic solid, and a frequency domain technique, which computes SI for very thin plate elements located at the surface of the structure. Advanced contact features such as nonlinearity can also be included in the model to increase the damage detection sensitivity. A plate model is used to illustrate these capabilities using SSI maps at nonlinear harmonics (NSSI). The results show both improved damage sensitivity and more global detection capabilities in a NSSI-based SHM system. A complex structure is also included to show global and local changes in SSI due simulated damage scenario. The techniques developed can be applied to general SI/SSI assessments and the design of SI-based SHM systems.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of the cross section of an elastic body. The structural intensity normal to the z-plane will be zero at the surface.

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Figure 2

Intensity distributions through the thickness h for several wave types including an arbitrary coupled wave. SI points in a different direction than SSI for all wave types except purely longitudinal.

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Figure 3

FE model of beam with an arrow indicating the location and direction of the harmonic drive. The opposite end of the beam has several dampers to dissipate energy.

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Figure 4

Comparison of SSI (dB re 1 W/m2 ) on the top surface of beam driven at 100 Hz. SSI was estimated using (a) SI in the top solid element, (b) SI in a 3 mm aluminum top layer, (c) SI in 25 μm polymide top layer, and (d) using Eqs. 6,7 directly. SSI magnitude and phase match very well for cases (c) and (d), suggesting that the aluminum top layer is not thin enough to accurately represent intensity at the surface.

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Figure 5

SSI magnitude and phase integrated over width for using (a) SI in the top solid element, (b) SI in a 3 mm aluminum top layer, (c) SI in 25 μm polymide top layer and (d) using Eqs. 6,7 directly. Method (c) approximates SSI with the least error in magnitude and phase.

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Figure 6

To model crack contact, a bilinear stiffness model was used. The stiffness (k) at a node will change depending on whether the crack is “open” or “closed.”

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Figure 7

Schematic of plate with crack modeled as bilinear stiffness. The star represents the crack location, the circle represents the drive location (in the x direction) and the triangle represents the damper location (in x and y directions).

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Figure 8

Time domain SSI map of the nondamaged plate driven at 100 Hz with unit vectors indicating the power flow direction and color/shading indicating the intensity magnitude in dB re 1 W/m2

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Figure 9

Change in SSI magnitude (in dB) due to the introduction of a linear crack through the thickness, for an in-plane (x) drive at 100 Hz. SSI changes are largest at elements immediately surrounding the damage. The maximum change in SSI away from the damage magnitude is less than 1 dB indicating that the linear crack has very little global effect on the intensity.

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Figure 10

Change in SSI magnitude due to the introduction of a bilinear crack through the thickness, for an in-plane (x) drive at 100 Hz. Small SSI changes are detected at the damage as well as at other locations away from the damage. This is due to slight changes in both the local and the global power flow. The maximum change near the crack and away from the crack is 2.0 dB.

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Figure 11

Decibel change in SSI magnitude from the healthy to bilinear crack plate at (a) 200 Hz (2 × drive frequency), (b) 400 Hz (4 × drive), (c) 600 Hz (6 × drive), and (d) 800 Hz (8 × drive). The changes at even harmonics of the drive frequency show large changes near the damage as well as significant changes over other areas of the plate, while the change at the drive frequency (100 Hz) and other frequencies are close to zero (not shown).

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Figure 12

Mean change in element SSI magnitude for the bilinear stiffness damage shown with 95% bounds at 100 Hz (drive frequency) and its harmonics. The mean change for the drive frequency and all other frequencies are near zero, whereas the mean change for the even harmonics between −4 and −6 dB. The even harmonics also have much larger 95% bounds showing the global nature of the nonlinear scattering.

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Figure 13

(a) Expanded CAD drawing of mockup transmission frame and (b) finite element model of the frame structure. A time harmonic drive was located perpendicular to the shorter flange and response points are indicated by stars.

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Figure 14

Frequency response functions at four locations on the transmission frame for a normal drive along the flange (see Fig. 1 for drive and response locations). The operating deflection shape is shown at 327 Hz and 2500 Hz.

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Figure 15

Transmission frame SSI for a drive at (a) 327 Hz and (b) 2.5 kHz. Only surface elements are shown.

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Figure 16

Decibel change in SSI at (a) 327 Hz and (b) 2.5 kHz for a simulated rivet failure in the strap. The change in intensity for case (a) is global suggesting that sensor location could detect damage equally on almost any location on the structure. The change in intensity for case (b) is strongest in the leg opposite the drive. The best sensor locations for this frequency would then be on the leg opposite the driven leg. Only surface elements are shown.

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