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

MSC Software Confidential

• 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


• 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


• 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


Ground Vibration Test, continued

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


• 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


• 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


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



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



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



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



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


• 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

mb

led

Mo

de

Nu

mb

erD

escr

amb

led

Mo

de

Nu

mb

er

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

led

Mo

de

Nu

mb

erD

escr

amb

led

Mo

de

Nu

mb

er

Test Analysis


• 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

des

Experimental Modes


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


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


• 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


• 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

Correlation of Analytical & Experimental Elastic Mode Shapes for a

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