Structural dynamics are often an important consideration when evaluating system characteristics. A concern related to structural dynamics is the analysis of flutter for a flight vehicle. The instability associated with flutter can be quite sensitive to the structural dynamics; therefore, analysis of robustness with respect to error, or uncertainty, is becoming increasingly important for the flight test community. In particular, uncertainty models are needed for μ-method analysis as described in "Characterizing Worst-Case Flutter Margins From Flight Data'' (DRC-97-03), NASA Tech Briefs, Vol. 21, No. 4 (April 1997), page 62.

A method of determining optimal uncertainty descriptions for models of structural dynamics has been developed. This method results in the smallest uncertainty descriptions that are needed to account for data measured during ground vibration testing. Consequently, the resulting models generate least-conservative predictions of the flight conditions that are associated with flutter.

A ground vibration test is commonly performed as a pre-flight check that attempts to evaluate the quality of an analytical model. The basic concept is to excite the structural dynamics and measure responses at locations throughout the vehicle. The responses are then analyzed to estimate a set of modal properties such as natural frequencies and mode shapes. These modal properties are compared with the analytical model to determine the error and uncertainty in the model.

In reality, there are many estimates of modal properties that result from a ground vibration test. There may be hundreds of sensors that indicate slightly different estimates of natural frequencies. Also, the mode shapes are computed by a routine that interpolates responses from many sensors. Different interpolation schemes result in different estimates of modal properties.

The traditional method of analyzing test data is to generate modal properties that are a 2-norm minimization, or average, of a set of property estimates. The new method of analyzing test data is to use an ∞-norm minimization. The ∞-norm approach does not generate the optimal property; rather, it generates the optimal uncertainty set that is associated with the property. In this way, μ-method analysis of the resulting model generates least-conservative predictions of robust stability.

A wing testbed was used to demonstrate this concept. Ground vibration tests of the wing were performed to generate estimates of modal properties. The optimal properties and their associated errors were formulated using 1-norm, 2-norm, and ∞-norm analyses. Robust flutter speeds were computed for models with each set of optimal properties with respect to their associated errors. The results are given in Table 1. These results indicate that the highest, or least-conservative, flutter speed is computed for the model that uses modal properties and uncertainty from —-norm analysis.

This work was done by Starr Potter and Rick Lind of Dryden Flight Research Center. For more information, contact the Dryden Commercial Technology Office at (661) 276-3689.