4.2. PART2: FREQUENCYRESPONSE FUNCTION ESTIMATES FROM MEASUREDDATA 81
e cumulative coherences associated with nearly all response channels were close to unity
confirming extremely high-quality FRF estimates.
4.2.5 ILLUSTRATIVE EXAMPLE: WIRE ROPE MI/SO TEST DATA
ANALYSIS
Recalling the preliminary measured data analysis, summarized in Figure 4.5, the hypothe-
sized “algebraic” nonlinear system composed of measured time histories (applied force and
acceleration response) and synthesized “measured” time histories (cubed displacement and
velocityjvelocityj) depicted in Figure 4.10 was subjected to MI/SO analysis.
F
U
F(t)
(U(t))
3
U̇(t) ∙ |U̇(t)|
Ü(t)
H
1
H
2
H
3
Figure 4.10: Hypothesized MI/SO nonlinear system.
e cumulative coherence plot, shown in Figure 4.11 indicates that incorporation of the
two nonlinear terms produces a nearly unit value cumulative coherence (red curve), while the
ordinary coherence associated with a linear model (blue curve) indicates reduced coherence.
e results from Figure 4.11 provide clear evidence that the behavior of the wire rope
isolators is nonlinear. However, further definitive data analysis, described in Chapter 7, will
indicate that the nonlinear behavior is “hysteretic” rather than “algebraic” as currently hypoth-
esized. at being said, the present “algebraic” nonlinear model serves an important role as an
“intermediate” data analysis.
4.2.6 ILLUSTRATIVE EXAMPLE: ISS P5 MODAL TEST
e ISS P5 test article was excited with broadband random excitation forces at three separate
locations, MI/MO correlation and spectral analysis was preformed employing 1024 length win-
dows with 50% overlap processing. Cumulative coherences for all 261 TAM response channels
plus 3 drive point response channels were computed. MI/MO plots associated with the three
drive point FRFs (complete drive point FRF “matrix” as depicted for the ISPE in Figure 4.8 is
not provided here) are detailed in Figure 4.12.
82 4. MEASURED DATA ANALYSIS
File: WireNonR…MI/MO: Navg=29, df=0.488, MI/SO Cumulative Coherence
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Due to Force
Due to Force + U3Z
3
Due to Force + U3Z
3
+ V3Z*|V3Z|
Cumulative Coherence
10 15 20 25 30
Hz
35 40 5045
Figure 4.11: Hypothesized nonlinear system cumulative coherence.
Drive Point FRF “1” Drive Point FRF “25”
Drive Point FRF “38” ISS P5 Test Article Drive Points
X
Z
Y
38
25
1
CoherencePhaseMagnitudeCoherencePhaseMagnitude
CoherencePhaseMagnitude
1
0.5
0
200
0
-200
200
0
-200
10
-1
10
-2
10
-3
10
-4
10 15 20 25 30
Hz
35 40 5045
10 15 20 25 30
Hz
35 40 5045
10 15 20 25 30
Hz
35 40 5045
1
0.5
0
10
-1
10
-2
10
-3
10
-4
10 15 20 25 30
Hz
35 40 5045
10 15 20 25 30
Hz
35 40 5045
10 15 20 25 30
Hz
35 40 5045
10 15 20 25 30
Hz
35 40 5045
10 15 20 25 30
Hz
35 40 5045
10 15 20 25 30
Hz
35 40 5045
Figure 4.12: ISS P5 MI/MO FRF and cumulative coherence plots.
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