Perturbation Solution of Dynamic Stability Derivatives over Pointed Bodies of Revolution

Abstract

Fig. 3 Natural frequencies for the rst bending and torsional modes against xa for selected values of frequency ratio v h /va for c = a) 0.4 and b) 20.4.and va are uncoupled fundamental bending and torsional natural frequencies that are both independent of x a and c, whereas the plotted graphs shown by solid and dashed lines represent fundamental bending and torsional coupled natural frequencies, respectively. It is clear from Fig. 3a that as the negative x a increases, the frequency difference between the two vibrational modes of interest increases and as a consequence utter speed also increases, thus reinforcing the importance of modal coupling in such studies. 10 In contrast, when negative c (c = 20.4 in this case) is present together with negative x a (see Fig. 3b), frequency convergence occurs between the two modes of interest, and as a result the utter speed reduces. The preceding frequency phenomenon was also noticed by Weisshaar and Foist, 7 but not from an aeroelastic point of view, so that its effect on utter behavior was not reported.From the preceding results, it can be concluded that the wash-out behavior of a composite wing can be useful in increasing its utter speed when the mass axis is well behind the shear center of the wing cross section as opposed to the corresponding case when the wing exhibits wash-in behavior. The investigation has also revealed that for certain combinations of positive c and negative x a , the utter speed is unaffected by changes in the frequency ratio vh/va.