CORRELATION OF ANALYTICAL AND EXPERIMENTAL ELASTIC MODE...

CORRELATION OF ANALYTICAL AND

EXPERIMENTAL ELASTIC MODE SHAPES FOR A

SMALL ASPECT RATIO WING USING MODAL

DESCRAMBLING

James Senter1, Evan Martin

1, Michael Rakieski

1 and Emil Suciu

1

1Loads & Dynamics Analyst , L-3 Communications Platform Integration

Division, 7500 Maehr Drive, Waco, Texas, 76715 USA

SUMMARY

The Modal Assurance Criterion is used to compare scrambled and descrambled

experimental and calculated mode shapes for a rectangular flat steel plate of

AR=2.

KEYWORDS

GVT, DLM, Modal Descrambling, Elastic Streamwise Camber Deformation,

MAC

CORRELATION OF ANALYTICAL AND EXPERIMENTAL ELASTIC

MODE SHAPES FOR A SMALL ASPECT RATIO WING USING

MODAL DESCRAMBLING

1: INTRODUCTION

The subject matter discussed in this paper is related to aircraft flutter analyses,

in particular the process of improving the analytical structural dynamic model

by comparing its results to the GVT results. The GVT results are available as

frequencies and mode shapes defined at specified points.

The user attempts to name or identify modes of vibration in order to understand

the physical problem. Some flutter analysts refer to the mode naming process

as an art. It can be argued that stick model modes can be consistently identified

by making use of the beam directional stiffness properties and the strain energy

summation method (Reference [1]). Full finite element structural dynamic

models do not easily lend themselves to such easily quantifiable processes as

shown in Reference [1] for stick models, therefore naming modes still remains

an art for such models. This is especially true for complicated modes such as

the mode shown in Figure 1 for a transport aircraft at the Doublet Lattice

Method (DLM, Reference [2]) aerodynamic surfaces.

Figure 1: Scrambled Mode Shape at the Aerodynamic Surfaces of Transport

Aircraft.

The mode shape shown in Figure 1, whether GVT-measured or calculated is

called “scrambled”, since it is a linear combination of 5 simpler and always the

same elementary modes: pure bending, pure torsion, pure control surface

rotation, pure tab rotation and pure elastic streamwise camber deformation

(Reference [3]). Any measured or calculated scrambled elastic mode of

vibration can be descrambled into the five elementary modes listed above. A

convenient way to do this is to transfer the structural motion to the DLM

aerodynamic surface and to perform the modal descrambling at this surface,

see Figure 2. So far, this method has only been used to correct unsteady

aerodynamic forces and moments for flutter analyses (Reference [4]).



MODAL DESCRAMBLING

Figure 2: Schematic of Descrambling Process of General Wing-Control Surface-

Tab Mode Shape at Any Strip of the DLM Aerodynamic Surface.

The modal descrambling process will be illustrated for a rectangular steel flat

plate wing of AR=2, shown in Figure 3. No control surface and tab are present.

Figure 3: Flat Plate Steel Wing of AR=2 to Be Analyzed and Tested.

For any scrambled mode of vibration, experimental or calculated, the Modal

Assurance Criterion (MAC, Reference [5]) comparison between the scrambled

mode and its descrambled modal components will provide a numerical

indicator which will help identify or name the mode: mostly bending or mostly

torsion or mostly camber. The existence of elastic streamwise camber

deformation especially as it occurs in real aircraft lifting surfaces is still

debated by a dwindling number of flutter analysts.

Pairs of scrambled or descrambled experimental vs. calculated mode shapes

can now be compared one-to-one, visually and numerically. The Modal

Assurance Criterion will be calculated for each corresponding pair of compared

modes, scrambled and descrambled.



MODAL DESCRAMBLING

This paper therefore has a triple purpose:

1. To improve the understanding of any lifting surface mode of vibration

by descrambling it into its simpler components and to obtain numerical

values of the degree of correlation between the scrambled mode and its

descrambled components; numerical guidance to aid in naming modes

will result.

2. To improve the process of correlating the analytical and experimental

modes of vibration of a lifting surface structure by obtaining numerical

values of the correlation between the corresponding pairs of scrambled

and descrambled experimental and calculated modes.

3. To somewhat curtail the poetic license we can take in identifying and

naming modes of vibration.

A better understanding of the mode shape (and implicitly of the structure of the

test article) will be achieved.

2: DETAILS OF THE GROUND VIBRATION TEST (GVT) AND

ANALYTICAL MODEL

a. Details of the GVT

A modal survey of a 12 inch by 24 inch steel plate was performed using impact

excitation. The plate was 3/16 inch thick and weighed 14.6 lbs. To properly

separate the elastic modes from the rigid body modes (to obtain nearly free-free

boundary conditions), the steel plate was placed on top of several layers of

bubble wrap and foam padding. For testing, the plate was divided into 7

chordwise and 11 spanwise test nodes for a total of 77 test nodes. Using the

roving accelerometer method of modal testing, 4 separate tests were performed

with the accelerometers moved to a different set of nodes for each test as

shown in Figure 4. Considerable care was exercised to avoid accepting FRFs

when double impact hammer strikes occurred.

The results were then combined into a single data set and modes were extracted

from the resulting Frequency Response Functions (FRF). To perform the test,

Smart Office version V4.1 B3096 CD8.01 by M+P International was used to

record measurement data and extract the modes of the plate. Six locations

were impacted for each test: at 3 corners, 1 location along both the short and

long edges, and in the center of the plate. These locations were chosen to

ensure that all flexible modes of the plate were adequately excited. The 1st

through 3rd bending, torsion and camber modes of the plate were successfully

measured. The highest rigid body mode was measured to be 14 Hz and the

first bending mode frequency was 65 Hz. With this significant separation, the



MODAL DESCRAMBLING

rigid and elastic modes do not interfere and provides better results for the

purposes of this effort. Figure 5 shows the FRFs for two different pairs of

excitation and response locations. In Figure 6, a sample of experimental mode

shapes as displayed with Smart Office software is shown. Note the presence of

elastic streamwise camber deformation visible in the scrambled bending and

torsion modes. This is due to the high degree of mass and stiffness coupling.

The verification of the modes identified in the modal survey test is discussed in

Section 3.

Figure 4: Modal Survey of Steel Plate.

Figure 5: Frequency Response Functions at Two Different Pairs of

Excitation/Response Points.

Test #1 Test #2

Test #3 Test #4

FRF - Reference 6Z, Response 6Z FRF - Reference 39Z, Response 39Z



MODAL DESCRAMBLING

Figure 6: A Sample of Experimental Mode Shapes at the GVT Accelerometer

Locations.

b. Details of the Analytical Model

Three different plate FEMs of varying plate finite element (CQUAD) densities

were created in MSC.PATRAN and analyzed with MSC Nastran SOL103 to

study the convergence of the normal modes solution. A test mesh consisting of

a 6 x10 element array was created with node locations coinciding with the

accelerometer placements on the test article. A coarser mesh and a finer mesh

were also created which consisted of a 4 x 6 and 12 x 20 element array,

respectively. The dimensions of each FEM were identical with the tested plate,

and the material properties of A36 steel were used to define the elements. The

free-free boundary condition was used for the normal modes solution. Table 1

shows the modes of each FEM compared to the modes identified in the modal

survey test. As the element density increased, the analytical frequencies began

to converge on the test frequencies. The fine mesh FEM showed the best

comparison to the test data with the percent differences of 3% or less and the

analytical results obtained with the fine mesh are considered to be converged.

The most dramatic convergence occurred for the camber mode. Figure 7

shows the 1st camber mode displacement of each mesh at the structural grid

points. Since the converged analytical modes compared so well to the test

modes, the free-free boundary condition was considered sufficient, and no

attempt was made to model the bubble wrap used to support the test article.

This confirms that the rigid and elastic modes are well separated and the rigid

body modes do not interfere with the elastic ones.

Table 1 shows that the converged MSC Nastran structural dynamic solution

with high-density mesh simulates the test results extremely closely. In Section

3 it will be shown that the visual and MAC comparison of the experimental and

Experimental 1st Bending, 2-View Experimental 1st Torsion, 2-View

Experimental 1st Camber, 2-View



MODAL DESCRAMBLING

analytical, scrambled and descrambled mode shapes is also very good. This is

due to the simple geometry and homogeneous properties of the plate. As

complexities are added eventually culminating in an aircraft structure, the

discrepancies between measured and analytical mode shapes will be larger.

Table 1: Analytical Modes Comparison to Test Data; Convergence of Analytical

Solution with Structural Mesh Density.

Figure 7: Analytical 1st Camber Mode of Plate with Varying Structural Mesh

Densities.

c. Structural Motion Transfer to the Aerodynamic Surfaces

and Modal Descrambling

The experimental mode shapes were obtained at 77 grid points, as previously

shown in Figure 6. An aerodynamic surface box arrangement of NSPAN=10



MODAL DESCRAMBLING

and NCHORD=6 for the steel flat plate wing was chosen so that the corners of

the boxes coincide with the accelerometer locations.

The measured mode shape displacements are then inputted into MSC Nastran

SOL145 at the specified corner grid points locations using the DMIG input

format for all the modes of interest. This structural motion is then transferred to

the DLM aerodynamic surface through the surface splining feature of SOL145.

The mode shapes at the aerodynamic set are then available for descrambling

and SOL145 is then stopped, since it is not expected that the flutter results for

this steel plate will bring any further enlightenment. After descrambling the

modes using a FORTRAN program, the descrambled displacements at the

centers of the aerodynamic boxes are plotted using MATLAB. A procedure to

display and animate the descrambled mode shapes using MSC PATRAN is in

work.

The analytical mode shapes obtained with the fine structural mesh are also

transferred to the same aerodynamic surface with NSPAN=10 and

NCHORD=6 using NASTRAN SOL145. The calculated mode shapes at the

centers of the aerodynamic boxes are now available for descrambling and for

graphical display at exactly the same locations as the measured modes.

3: COMPARISON OF THE GVT AND ANALYTICAL MODE

SHAPES

Figures 8 through 12 show the experimental and analytical scrambled and

descrambled plots of the first 5 mode shapes of the steel plate of AR=2 side-

by-side for easy visual comparison. The viewing angle and magnification

factors are the same for each corresponding pair of scrambled or descrambled

modes.

These comparisons are self-explanatory. The observation must be made that

the analytical results show perfect symmetry about 2 axes, while the

descrambled experimental results show the likely unavoidable extremely small

non-symmetries. These non-symmetries appear in the plots, but are very, very

small, as shown by the maximum normalized displacement accompanying each

plot.



MODAL DESCRAMBLING

Figure 8: Scrambled and Descrambled Experimental and Analytical 1st Bending

Modes.

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



MODAL DESCRAMBLING

Figure 9: Scrambled and Descrambled Experimental and Analytical 1st Torsion

Mode.

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



MODAL DESCRAMBLING

Figure 10: Scrambled and Descrambled Experimental and Analytical 2nd

Torsion

Mode.

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



MODAL DESCRAMBLING

Figure 11: Scrambled and Descrambled Experimental and Analytical 2nd

Bending

Mode.

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



MODAL DESCRAMBLING

Figure 12: Scrambled and Descrambled Experimental and Analytical 1st Camber

Mode.

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



MODAL DESCRAMBLING

The MAC was also calculated to compare the scrambled and descrambled

modes for both the analytical and experimental mode shapes. Those are shown

in Table 2 for the experimental modes and Table 3 for the analytical modes. In

each case, the numbering convention is X-1 for descrambled bending, X-2 for

descrambled torsion and X-3 for descrambled camber, X being the scrambled

mode number.

Table 2: MAC of Experimental

Scrambled and Descrambled

Modes

Table 3: MAC of Analytical

Scrambled and Descrambled

Modes

Note that the MAC comparison between the scrambled mode and its

descrambled components is a good indicator of the contribution of each

descrambled component to the scrambled mode. This numerical indicator can

be used to complement and augment the mode-naming process.

Table 4 shows the MAC comparison between corresponding pairs of scrambled

and descrambled experimental and analytical mode shapes. The comparison is

very good, confirming the visual agreement between these pairs of modes. All

values above 0.25 were plotted in Table 4 to provide some information on

commonality among experimental and analytical scrambled and descrambled

modes. It should be noted that at certain points along the diagonal, points that

would be expected to be 1 are not shown. This is due to the pure motions of

the analytical model which may have no bending or torsion component for a

given mode.

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



MODAL DESCRAMBLING

Table 4: MAC of pairs of Experimental and Analytical Scrambled and

Descrambled Modes

4: COMPARISON OF MODE SHAPES FOR A PLATE OF AR=2 AND

AR=0.5

Figure 13 shows the rectangular flat plate of AR=2 next to the plate of AR=0.5

with coordinate systems and arrow showing wind direction and reference axes.

Figure 13: Flat Plate Steel Wings of AR=2 and AR=0.5.

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

AR = 0.5

AR = 2



MODAL DESCRAMBLING

The plate of AR=0.5 is identical in every respect with the plate of AR=2 except

its orientation and the aerodynamic coordinate system. Figure 14 shows the

scrambled mode shapes of the two steel plates with the names assigned for

each.

Figure 14: Side-by-Side Comparison of the Scrambled Mode Shapes of Wing of

AR=2 and Wing of AR=0.5.

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



MODAL DESCRAMBLING

With respect to a coordinate system fixed at a corner of the plate of AR=2, the

modes of vibration of the plate are invariant with the location and angular

orientation of the plate in the global coordinate system. However, the steady

and unsteady aerodynamic forces on the wing of AR=0.5 will be very different

than the aerodynamic forces for the wing of AR=2. Due to the flutter analyst’s

need to understand the physical phenomenon, the modes are named quite

differently for the plate of AR=0.5 than for the plate of AR=2.

5: CONCLUSIONS

The structural dynamic characteristics of a flat steel plate of AR=2 of uniform

properties were tested using impact hammer excitation and Smart Office

software and also analyzed with MSC Nastran SOL103 and SOL145. The

experimental and the converged analytical frequencies and mode shapes were

compared. The comparison is very good due to the simple geometry and

homogeneous properties of the steel plate.

The experimental and analytical structural mode shapes were interpolated to

their respective aerodynamic surfaces having the same box arrangement. The

scrambled modal motions at the centers of the aerodynamic boxes were then

descrambled and the scrambled and descrambled mode shapes were then

compared.

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.

The drawback of this correlation method using descrambled modes is the fact

that for a real airplane, a minimum of 2 to 3 times the number of

accelerometers would be required for the average lifting surface as compared

to a conventional GVT in order to define the mode shape with the purpose of

properly descrambling it. Until it will be economical to routinely use such large

numbers of accelerometers, the practice of naming modes as an art form will

continue as such (see comparison between wing of AR=2 and wing of

AR=0.5).



MODAL DESCRAMBLING

6: ACKNOWLEDGEMENTS

The authors are indebted to Mr. John Corbett, who wrote the MATLAB mode

shape plotting procedure.

7: REFERENCES

1. Suciu, E., and Buck, J., “Postprocessor for Automatic Mode

Identification for MSC/NASTRAN Structural Dynamic Solutions with

Emphasis on Aircraft Flutter Applications”, presented at the 1998

MSC/NASTRAN America’s Users’ Conference, Los Angeles, CA,

October 5-8, 1998.

2. Rodden, W.P., and Johnson, E.H., “User’s Guide V68, MSC.Nastran

Aeroelastic Analysis”, The MacNeal-Schwendler Corporation, Los

Angeles, CA, 1994.

3. Panza, J.L., and Suciu, E., “A Closer Look at the Elastic Streamwise

Camber Deformation of Swept and Unswept Wings”, Presented at the

International Forum for Aeroelasticity and Structural Dynamics 2005 as

Paper No. IF-090, Munich, Germany, June 28 – July 1, 2005.

4. Suciu, E., Stathopoulos, N., Dickinson, M. and Glaser, J.,”The T-Tail

Flutter Mechanism Revisited”, Paper No. IFASD-2011-121, Presented at

the International Forum for Aeroelasticity and Structural Dynamics,

Paris, France, June 26-30, 2011.

5. Allemang, R.J., "The Modal Assurance Criterion (MAC): Twenty Years

of Use and Abuse", Presented at IMAC-XX: Conference & Exposition on

Structural Dynamics, 2002.

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