OS-V: 1300 Flutter Analysis of an AGARD 445.6 Wing

The results are validated against experimental data from a NASA technical memorandum¹.

Model Files

Benchmark Model

Figure 1. AGARD 445.6 Wing Model

Comparison of Normal Modes

Mode shape and mode frequency comparisons are as follows. The results from OptiStruct are in agreement with the reference results¹.

Reference results1
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

From the .flt file of the first Mach number (M = 0.35) simulation, the flutter point (where damping changes sign) corresponding to the lowest mode is identified as the 2^nd mode with a velocity between 128.89 m/s to 131.12 m/s.

Note: By definition, instability (flutter or divergence) occurs when the damping values are zero. At this point, if the frequency is zero, then the instability is due to divergence. Otherwise, the instability is due to flutter.

Figure 2. Flutter Analysis Summary from .flt File

Plotting the v-g curve, the velocity at this flutter point is 129.417 m/s. This is the most critical flutter point that needs to be avoided for M = 0.35.

Figure 3. Identify Flutter Points. The flutter point corresponding to the lowest velocity is also visually identified.

Figure 4. Identify Frequency Value at Critical Flutter Point from v-f Curve

Plotting the v-f plot for the 1st mode (corresponding to the critical flutter point), the frequency value for 1^st mode at a velocity of 129.417 m/s is determined as 24.016 Hz. In the same way, the flutter speed and flutter frequency determination was repeated for M = {0.5, 0.7, 0.9}.

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 66¹.

(1)

$$\frac{v}{b_s{\omega }_{\alpha }\sqrt{\overline{\mu }}}$$

Figure 5. Flutter Speed Coefficient versus M Comparison Between Experimental Reference and OptiStruct Flutter Analysis

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 67¹.

(2)

$$\frac{\omega }{{\omega }_{\alpha }}$$

Figure 6. Flutter Frequency Ratio versus M Comparison Between Experimental Reference and OptiStruct Flutter Analysis

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.

Figure 7. Transonic Dip

Reference