Flutter of Flexible Hydrofoil Struts 



to the predicted flutter inception, so that flutter is incorrectly predict- 

 ed to occur with a first bending mode shape. 



Slight changes occur in the hydroelastic modes when three- 

 dimensional loading modifications are included. The three-dimension- 

 al loading used for Model 2 was also used for Model 2T. The damping 

 of mode 2 increases, remaining below the experimental values for part 

 of the speed range below flutter inception but yielding a flutter speed of 

 18. 8 knots, which is very close to the experimental value but is slightly 

 nonconservative. The flutter mode shape is predicted to be predomi- 

 nantly first torsion, which is the mode shape that was observed. 



The good agreement between experimental and theoretical cha- 

 racteristics of mode 2 clearly establishes that the instability has been 

 correctly predicted. Identification of the unstable mode is easier than 

 for Model 2 because sufficient data are available and the modes are 

 unambiguous in predicting instability. 



The effects of independent variation of the loading modification 

 parameters on predicted flutter speeds for Model 2T are shown in 

 Figure 12. Equal values of loading were used at all spanwise stations. 

 The calculation is conservative and reasonably accurate using two- 

 dimensional loading, and is unaffected by loading modifications except 

 when lift slope is reduced below 70 percent of the two-dimensional 

 value. While the calculation is sensitive only to lift slope for the con- 

 ditions shown, strong interactions occur among the modifying para- 

 meters when they are varied simultaneously. This interaction is de- 

 monstrated by the 18. 8 knot flutter speed prediction obtained when 

 three-dimensional values are used for all modifying parameters. 



No mode corresponding to the new mode described for Model 2 

 appears in the speed range shown for Model 2T. Such a mode does 

 appear at higher speeds, however, but remains stable at all speeds 

 for which calculations were made. 



An indication of travelling wave motion was found in the flutter 

 mode of Model 2T. However, a discrepancy in calculated flutter speed 

 similar to that found for Model 2 prevents full confidence in the results. 

 The direct method of calculation yielded increasing and decreasing os- 

 cillations above and below a different flutter speed from that obtained 

 by eigenvalue calculation. Calculated mode shapes in bending and tor- 

 sion at flutter are shown in Figure 13 as functions of time. The bending 

 oscillations are travelling waves, while the torsional oscillations are 

 standing waves. Strut deflections due to torsion were approximately 

 twice as large as those due to bending. Therefore the flutter oscillat- 

 ions were predominantly standing waves, although travelling waves 



359 



