Besoh and Liu 



calculations should be performed with both two-dimensional and three- 

 dimensional loading so that all potential instabilities will be discovered. 



III. 4. Torsional Flutter 



The calculated hydroelastic modes of torsion-type struts 

 exhibit more simple behavior than those of bending-type struts. Only 

 one mode is unstable. It is the mode with the second-lowest frequency, 

 and therefore with a predominantly first torsion mode shape, at zero 

 speed. Low damping is predicted in this mode at all speeds below 

 flutter, in contrast to the high damping predicted in the bending flutter 

 mode. Observed characteristics of torsional flutter correlate well 

 with the characteristics of this hydroelastic mode. A mode analogous 

 to the new mode previously described appears for some torsion-type 

 struts, but it is stable throughout the speed range of interest. Three- 

 dimensional loading modifications have very little effect on the quali- 

 tative characteristics of the hydroelastic modes of torsion-type struts, 

 but do change the predicted flutter speeds. 



Predicted torsional flutter speeds ranged from 59 percent 

 conservative to 36 percent nonconservative when three-dimensional 

 loading was used. The predicted flutter speeds were nonconservative 

 for struts with extremely heavy pods, and became increasingly con- 

 servative as the struts decreased in mass ratio and approached the 

 bending flutter region. 



As an example of hydroelastic modes for torsion-type struts, 

 the modes for Model 2T of Reference 4 are shown in Figure 11. The 

 structural characteristics of Model 2T are identical to those of Model 2 

 except for the addition of a long, slender pod to the strut tip. The pod 

 is described in the Appendix. The damping ratio includes the value of 

 structural damping measured at zero speed. One value of damping 

 ratio and frequency was reported in Reference 4, and the others were 

 measured at NSRDC by deflecting the strut with an attached line and 

 cutting it during the test runs. A flutter speed of 18. 1 knots was 

 obtained at NSRDC, and a frequency of 6. 4 Hz was observed at that 

 speed. The vibration mode shape prior to and at flutter was predomi- 

 nantly first torsion. 



Flutter is predicted to occur in mode 2 at 14. 1 knots when 

 two-dimensional loading is used. This prediction is conservative by 

 22 percent. The calculated damping values are lower than the expe- 

 rimental values, but show a similar variation with speed. Frequencies 

 of the hydroelastic modes remain relatively constant as a function of 

 speed, and agree well with available data. The mode shape of the un- 

 stable mode, mode 2, changes from first torsion to first bending prior 



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