OSV: 1300 Flutter Analysis of an AGARD 445.6 Wing
Flutter analysis of an AGARD 445.6 wing model is performed using the PK method.
The results are validated against experimental data from a NASA technical memorandum^{1}.
Model Files
Benchmark Model
 Dimension
 Value (m)
 Span
 0.762
 Root Chord Length
 0.5587
 Tip Chord Length
 0.3682
 E1
 3.151E+09
 E2
 4.162E+08
 NU12
 0.31
 G12
 4.392E+08
 RHO
 381.980
Comparison of Normal Modes
Reference results^{1}  






Mode 1  F = 9.5992 Hx  Mode 2  F = 38.1650 Hz  Mode 3  F = 48.3482 Hz  Mode 4  F = 91.5448 Hz 
Results from OptiStruct  






Mode 1  F = 9.4589 Hz  Mode 2  F = 39.5289 Hz  Mode 3  F = 49.2213 Hz  Mode 4  F = 94.8019 Hz 
Flutter Analysis
Comparison of Flutter Speed Coefficient
The flutter speed coefficient $\left(\frac{v}{{b}_{s}{\omega}_{\alpha}\sqrt{\overline{\mu}}}\right)$ is calculated from OptiStruct and plotted against M and compared against the reference plot from Figure 16(a) on page 66^{1}.
 $v$
 Flutter velocity
 ${b}_{s}$
 Streamwise semi chord length at wing root = $\frac{0.5587}{2}$ m
 ${\omega}_{\alpha}$
 Natural circular frequency of the first uncoupled torsional mode $=2\pi f=2\pi (39.5289)$ rad/s (This is the 2^{nd} normal mode for this wing)
 $\overline{\mu}$
 Mass ratio
Comparison of Flutter Frequency Ratio
The flutter frequency ratio $\left(\frac{\omega}{{\omega}_{\alpha}}\right)$ is calculated from OptiStruct and plotted against M. This is compared against the reference plot from Figure 16(b) on page 67^{1}.
Observations
 The flutter speed coefficient and flutter frequency ratio from OptiStruct are in close agreement with the experimental reference data.
 The current support of OptiStruct Aeroelastic Analysis is limited to Subsonic flow (M < 1.0) and hence the simulations were not performed beyond M = 0.9. The support for supersonic regime is planned for a future release and Figure 5 and Figure 6 will be updated with the pertinent data points in this regime.
 In realistic conditions, for M ~ 0.75 and above, local pockets of supersonic flow could occur around the structure. This intermediate regime is denoted as transonic.
 In the flutter speed coefficient versus M plot, the experimental reference data shows a reduction in flutter speed coefficient around M = 1.0 and this is called the transonic dip.
 OptiStruct flutter analysis is capable of capturing the descent of this dip.