1. Ifthelastmodeofthebasisusedtobuildthetransformationmatrix(adoptedtoconvertthereducedorder aero matrix to the full order one) is replaced by the quantity xpert−xα=0the improvement is significant. With just three modes the displacements are very well captured. There is no practical numerical difference between the 4 methods used to build the transformation matrix. If the basis of modes is not modified (i.e. the last mode is not replaced with the quantity xpert−xα=0) then the convergence is very slow (results omitted for brevity). This is not surprising, since a set of cantilevered modes cannot capture a rigid body pitch motion well. If the basis is modified then with just 5 modes the convergence is excellent (figures 6-7)
2. ζi=0:03 is considered. It can be seen that the LCO frequency is not affected much, while the LCO speed is closer to the experimental value. The modal convergence of the approximation (tip displacement) is demonstrated in figures 16 and 17: with 5 modes the convergence is practically achieved, as it was demonstrated for the steady case (figures 6-7). The convergence of the tip speed is shown in figures 18 and 19. Again, the convergence is achieved with just 5 modes.
3. = 14:01[Hz]. In figures 14-23 the “consistent” flutter speed is mentioned and comparison with the linear flutter speed and with the experimental value is made. We now clarify what this terminology means. The linear flutter speed VlinearF
4. 1Boyd, W.N. “Effect of chordwise forces and deformations and deformations due to steady lift on wing flutter”, AIAA Paper 1979-794.