Figure 4.6 Comparison between p and k methods of flutter analysis for a twin-jet transport airplane.

From Hassig (1971) Fig. 1, used by permission.

Hassig applied the p and k methods of flutter analysis to a realistic aircraft configuration. By incorporating the same unsteady aerodynamic representation in each analysis he was able to make a valid comparison of the results. His observations are typified by Fig. 4.6 (which is his Fig. 1). It can be noted from this figure that not only is the modal coupling wrongly predicted by the k method, but, more important, the wrong mode is predicted to become unstable. The only consistently valid result between the two analyses is that of the flutter speed for which g ā€” y ā€” 0. In spite of the inconsistent modal coupling exhibited by the k method, it does permit the use of simple harmonic modeling of the unsteady aerodynamic terms. As previously mentioned the accuracy of simple harmonic airload predictions far exceeds the accuracy of airload predictions for transient motions. It is for this reason that a compromise between the two models has been suggested.

The pā€”k method is such a compromise. It is based on conducting a p method type of analysis with the restriction that the unsteady aerodynamics matrix is for simple harmonic motion. Using an estimated value of k in computing [A(z &)], one finds the flutter determinant to be

Given a set of initial guesses for k, say ktl ā€” ho>, j U for the z'th root, this equation can be solved for p. This typically yields a set of complex conjugate pairs of roots, the number of which corresponds to the number of degrees of freedom in the structural model. For one of the roots, denoting the initial solution as p2[M]+^-[M][w2]-Poo[A(ik) = 0.

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