Flutter of Flexible Hydrofoil Struts 



values of mass ratio in the torsional flutter region. 



Strut submergence also affects the vibration mode shapes of 

 struts, and has a particularly large effect on the second bending mode. 

 As a result, a strut could change from a bending-type strut to a tor- 

 sion-type strut during changes in submergence. Because of the occur- 

 rence of minimum flutter speeds at different depths for different 

 modes, and the possibility of different flutter modes occuring at differ 

 ent depths, it is conceivable that a strut could undergo bending flutter 

 at one depth and torsional flutter at another depth. 



III. THEORETICAL FLUTTER CHARACTERISTICS 



The dual nature of experimental flutter results also appears 

 in theoretical results. Bending flutter and torsional flutter correspond 

 to instabilities in different hydroelastic modes. Transition from bend- 

 ing flutter to torsional flutter occurs when the torsional flutter mode 

 becomes less stable than the bending flutter mode. 



The frequency and mode shape characteristics of the hydro - 

 elastic modes involved in flutter are predicted accurately in the flutter 

 analysis. However, damping characteristics, and, consequently, 

 flutter speeds are not predicted accurately. In the bending flutter 

 region, flutter speed predictions are not usable because a second 

 mode is also predicted to be unstable which does not correspond to 

 experimental results. Flutter speed predictions in the torsional 

 flutter region correctly indicate the unstable mode but are generally 

 overconservative. Calculated hydroelastic modes of a strut with at- 

 tached foils indicate that the strut underwent torsional flutter at a 

 speed which was overconservatively predicted. 



III. 1. Flutter Theory 



Understanding of the differences between bending flutter and 

 torsional flutter requires consideration of the behavior of the hydro- 

 elastic modes [12_] , or resonances, of the strut systems over a wide 

 range of speeds, and not merely a calculation of each strut's speed 

 of neutral stability. This approach was in fact used in a paper [8j 

 presented at the Fourth Symposium on Naval Hydrodynamics. This 

 earlier paper described the hydroelastic modes of bending-type struts 

 only. The present paper extends the earlier results to include a des- 

 cription of the hydroelastic modes of torsion-type struts as well. 



Hydroelastic modes are the vibration modes of the strut-fluid 

 system and correspond to eigenvalues and eigenvectors of the velocity- 

 dependent equations of motion. The equations of motion were generated 



351 



