**Figure 19.**

*V-f curve.*


#### **Table 5.**

*Comparison of flutter prediction.*

From the above table, the error is somewhat large in Case 1, because it is different for getting unsteady aerodynamic forces near transonic flight, and the other reason is not to consider the static pressure, which is caused by an initial angle and test points are much fewer.

In **Figure 20**, there is only two test points, which is connected to a straight line transcend the zero point, and makes us find the flutter speed. However, the other two colorful curves also go through the horizontal axis, which gets the different flutter speeds, greater than the former or less than it.

But in Case 2, in supersonic flight, the test result is in good agreement with all three methods, due to better optimization model and much more test points.

## **5. Conclusions**

From experimental mode data to mode verification, optimized FEM is much closer to the test rudder. Through flutter predictions, the predicated results are basically similar to the test data. We can draw some conclusions listed as follows:


*Verification and Validation of Supersonic Flutter of Rudder Model for Experiment DOI: http://dx.doi.org/10.5772/intechopen.98384*


## **6. Final remarks**

From the preceding discussions, an interesting phenomenon is observed, when we rotate the rudder axle for getting the diverse stiffness, the flutter speed is increased from 1.53 M to 2.51 M, but the structural weight or the rudder itself does not vary. Does it mean that the rudder itself can suppress flutter as the rudder is operated or controlled appropriately, and thereby, the flutter boundary is expanded?

Besides, V&V are tools for assessing the accuracy of the conceptual and computerized models. It can be extended to airworthiness certification of civil aircraft (see **Figure 21**).

From the above flowchart, if we modify the calculated model by test data, which ensures the analyzed precision, does it mean that analysis prediction could directly pass by Airworthiness Certification? Especially, for much of the Operational Reliability work, other highly nonlinear dynamic problems or very high frequency of acoustic ones, the assessment is so difficult, if it is not possible to copy in the experiment, that V&V became more associated with the issue of credibility, i.e., the quality, capability, or power to elicit belief, when we use the test to modify the model.

**Figure 21.** *V & V for airworthiness certification.*

### **Acknowledgements**

My deepest gratitude goes first and foremost to Mr. Erwin Johnson and Mr. Mohan Barbela, my previous coworkers in MSC, for their revisions of this paper. I would like to extend my heartfelt gratitude to MSC Software Corporation which has given me precious chances and experiences to improve my knowledge of FEM analysis.

This research work was financially supported by Shanghai Science and Technology Committee (Grant agreement No. 13QB1401500).
