Correlation of Analytical & Experimental Elastic Mode Shapes for a
Transcript of Correlation of Analytical & Experimental Elastic Mode Shapes for a
MSC Software Confidential MSC Software Confidential
Correlation of Analytical & Experimental Elastic Mode
Shapes for a Small Aspect Ratio Wing Using Modal
Descrambling
2012 Regional User Conference
Presented By: James Senter
May 8, 2013
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• The goal of this effort is to identify a method by which the “art”
of naming modes can be replaced by a more scientific approach.
• Mode identification is especially difficult for full FEM’s and highly
coupled modes.
• Using Modal Descrambling and the Modal Assurance Criterion,
an approach is proposed by which the scrambled modes of a
given structure are reduced to a subset of simpler “pure” modes.
Introduction
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• Modal descrambling is the process by which a complex mode is
deconstructed into 5 simpler elementary modes
– Pure Bending
– Pure Torsion
– Pure Control Surface Rotation
– Pure Tab Rotation
– Pure Elastic Streamwise Camber Deformation
Modal Descrambling
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• Conducted a small scale GVT of a rectangular steel plate
– A36 steel
– 12” x 24”
– 3/16” thick
• Measured response at 77 total measurement locations
• First 3 bending, torsion and camber modes were measured
Ground Vibration Test
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Ground Vibration Test, continued
Experimental 1st Bending, 2-View Experimental 1st Torsion, 2-View
Experimental 1st Camber, 2-View
Experimental 1st Bending, 2-View Experimental 1st Torsion, 2-View
Experimental 1st Camber, 2-View
Experimental 1st Bending, 2-View Experimental 1st Torsion, 2-View
Experimental 1st Camber, 2-View
1st Bending
1st Torsion
1st Camber
FRF - Reference 6Z, Response 6Z FRF - Reference 39Z, Response 39Z
FRF - Reference 6Z, Response 6Z FRF - Reference 39Z, Response 39Z
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• FEM created in MSC.Nastran of an identical plate
• Study of mesh density performed to determine converged mesh
• CQUAD elements used to model plate
• Final set of modes shows excellent agreement with test
Analysis Model
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• Each scrambled mode for both test and analysis were
descrambled into 3 primary components: bending, torsion and
elastic streamwise camber
– Control surface and tab not present
• Analytical modes demonstrate perfect symmetry about two axes
• Experimental modes display very small non-symmetries
Structural Motion Transfer
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Mode 1 – Experimental vs. Analytical
Experimental1st Bending – 65.9 Hz
Analytical1st Bending – 66.2 Hz
Scrambled Mode
DescrambledBending
DescrambledTorsion
DescrambledCamber
=
+
+
=
+
+
=
+
+
Scale 1.017
Scale 0.002
Scale -0.019
Scale 1.052
Scale 0.000
Scale -0.052
Scale 1.000
Scale 1.000
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Mode 2 – Experimental vs. Analytical
Experimental1st Torsion – 81.1 Hz
Analytical1st Torsion – 82.9 Hz
Scrambled Mode
DescrambledBending
DescrambledTorsion
DescrambledCamber
=
+
+
=
+
+
=
+
+
Scale -0.643
Scale 1.632
Scale 0.000
Scale 1.001
Scale1.000
Scale 1.000
Scale 0.011
Scale -0.001
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Mode 3 – Experimental vs. Analytical
Experimental2nd Torsion – 176.0 Hz
Analytical2nd Torsion – 180.7 Hz
Scrambled Mode
DescrambledBending
DescrambledTorsion
DescrambledCamber
=
+
+
=
+
+
=
+
+
Scale -0.509
Scale 1.590
Scale 0.000
Scale 1.005
Scale 1.000
Scale 1.000
Scale -0.081
Scale -0.005
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Mode 4 – Experimental vs. Analytical
Experimental2nd Bending – 179.3 Hz
Analytical2nd Bending – 182.4 Hz
Scrambled Mode
DescrambledBending
DescrambledTorsion
DescrambledCamber
=
+
+
=
+
+
=
+
+
Scale 1.190
Scale 0.002
Scale 1.333
Scale 0.000
Scale 1.000
Scale 1.000
Scale -0.193
Scale -0.333
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Mode 5 – Experimental vs. Analytical
Experimental1st Camber – 264.5 Hz
Analytical1st Camber – 266.1 Hz
Scrambled Mode
DescrambledBending
DescrambledTorsion
DescrambledCamber
=
+
+
=
+
+
=
+
+
Scale -0.254
Scale -0.004
Scale -0.956
Scale 0.000
Scale 1.000
Scale 1.000
Scale 1.258
Scale 1.956
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• MAC calculated for scrambled and descrambled modes
• MAC provides an indication of participation of descrambled
modes as part of the overall scrambled mode
Modal Assurance Criterion
1 2 3 4 5
1 1
2 1
3 1
4 1
5 1
1-1 0.995
1-2 0.000
1-3 0.003
2-1 0.002
2-2 0.996
2-3 0.329
3-1 0.001
3-2 0.995
3-3 0.288
4-1 0.972
4-2 0.000
4-3 0.170
5-1 0.003
5-2 0.000
5-3 0.394
Scra
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Scrambled Mode Number
1 2 3 4 5
1 1
2 1
3 1
4 1
5 1
1-1 0.995
1-2 -
1-3 0.032
2-1 -
2-2 0.999
2-3 0.394
3-1 -
3-2 1.000
3-3 0.394
4-1 0.971
4-2 -
4-3 0.074
5-1 0.002
5-2 -
5-3 0.408
Scrambled Mode Number
Scra
mb
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Test Analysis
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• MAC also calculated for comparison of analytical and measured
modes, scrambled and descrambled
• Overall, modes show excellent agreement between test and
analysis
Modal Assurance Criterion
1 2 3 4 5 1-1 1-2 1-3 2-1 2-2 2-3 3-1 3-2 3-3 4-1 4-2 4-3 5-1 5-2 5-3
1 0.999 - - - - 0.996 - - 0.746 - - 0.368 - - - - - - - -
2 - 0.996 - - - - - - - 1.000 0.291 - - - - - - - - -
3 - - 0.998 - - - - - - - - - 0.998 0.264 - - - - - -
4 - - - 0.999 - - - - - - - - - - 0.971 - - - - -
5 - - - - 0.997 - - 0.399 - - - - - - - - - - - 0.404
1-1 0.994 - - - - 1.000 - - 0.778 - - 0.326 - - - - - - - -
1-2 - - - - - - - - - - - - - - - - - - - -
1-3 - - - - 0.369 - - 0.878 - - - 0.354 - - - - - 0.509 - 0.931
2-1 - - - - - - - - - - - - - - - - - - - -
2-2 - 0.996 - - - - - - - 1.000 0.287 - - - - - - - - -
2-3 - 0.405 - - - - - - - 0.386 0.446 - - - - - - - - -
3-1 - - - - - - - - - - - - - - - - - - - -
3-2 - - 0.996 - - - - - - - - - 1.000 - - - - - - -
3-3 - - 0.407 - - - - - - - - - 0.357 0.771 - - - - - -
4-1 - - - 0.972 - - - - - - - - - - 1.000 - - - - -
4-2 - - - - - - - - - - - - - - - - - - - -
4-3 - - - - - - - - - - - - - - - - 0.950 - - -
5-1 - - - - - - - 0.451 - - - 0.508 - - - - - 0.999 - 0.550
5-2 - - - - - - - - - - - - - - - - - - - -
5-3 - - - - 0.396 - - 0.889 - - - 0.272 - - - - - 0.545 - 0.998
An
alyt
ical
Mo
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Experimental Modes
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Naming Modes for a Steel Flat Plate of AR=2
and for a Steel Flat Plate of AR=0.5
AR = 0.5
AR = 2
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Naming Modes, continued
AR = 2 AR = 0.5
1st Bending 1st Camber
1st Torsion 1st Torsion
2nd Torsion 2nd Torsion
2nd Bending 2nd Camber
1st Camber 1st Bending
Wind Direction
Wind Direction
Wind Direction
Wind Direction
Wind Direction
Wind Direction
Wind Direction
Wind Direction
Wind Direction
Wind Direction
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• Comparison between experimental and analytical mode shapes,
scrambled and descrambled, is excellent
• If the MAC is calculated between a scrambled mode and its
descrambled components, a numerical guide arises which helps
with naming the mode, thus offering the possibility to augment
the mode naming art with something more precise.
• The visual and MAC comparisons between corresponding pairs
of scrambled and descrambled measured and analytical modes
offers the possibility to gage the analytical model and calculate
which descrambled component contributes the most to
disagreement, if any, between experiment and analysis.
Conclusions
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• Drawback of this correlation method: at least 2 to 3 times the
number of accelerometers as for a conventional GVT are
required ; not practical at present
• Until such time when the number of accelerometers used in a
GVT is no object, the practice of naming modes as an art form
will continue as such
Conclusions
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