Flutter of Flexible Hydro foil Struts 



III. 3. Bending Flutter 



The hydroelastic modes of several bending-type struts were 

 calculated. In general, two unstable modes were predicted for each 

 strut. One of the unstable modes showed fair correlation with ex- 

 perimental flutter occurrences, while the second unstable mode did 

 not correlate well with experimental results. It therefore appears 

 that one unstable mode corresponded to the experimentally observed 

 instabilities for all of the struts, while the other unstable mode was 

 incorrectly predicted to be unstable. The incorrect prediction was, 

 in fact, found to occur only for limited ranges of spanwise loading 

 inputs, suggesting that the prediction was caused by a slightly inac- 

 curate loading formulation in a highly sensitive calculation. 



The mode in which bending flutter occurred had a first bend- 

 ing mode shape, and had the lowest frequency among the existing 

 modes at the experimental flutter speed. At speeds below flutter, the 

 mode was highly damped. Its damping decreased rapidly in a short 

 speed interval prior to flutter. Values of damping were predicted 

 nonconservatively. 



These results will be illustrated by presenting detailed cha- 

 racteristics of the hydroelastic modes of a typical bending-type strut, 

 Model 2 of Reference 4. The structural characteristics and three- 

 dimensional loading parameters for Model 2 are given in the Appendix. 

 Several hydroelastic modes calculated for Model 2 are shown as 

 functions of speed in Figures 8 and 9. The damping ratio f was plott- 

 ed without structural damping because no experimental values were 

 available. Predominant mode shapes are indicated on the frequency 

 curves. Predicted instabilities must be compared with an experiment- 

 al flutter speed of 81 knots and a frequency of 4. 1 Hz at that speed. 

 The mode shape at flutter was observed to be predominantly first 

 bending in a motion picture of the experiment. 



Flutter is predicted to occur at 83 knots in the presence of 

 two-dimensional loading, as shown in Figure 8. The instability occurs 

 in a mode which first appears, fully damped, at a speed of 30 knots 

 and decreases in stability as speed increases until neutral stability is 

 reached at 83 knots. Although the unstable mode appears at a speed 

 near that at which mode 1 damps out, the two modes coexist over a 

 small speed range. Therefore the unstable mode is considered to be 

 a new mode rather than mode 1. The frequency and mode shape of the 

 new mode show good agreement with experiment. Mode 3 is stable 

 and increases in frequency as speed increases. 



The predicted instabilities are much different, and less 



355 



