Flutter of Flexible Hydrofoil Struts 



groups. The higher flutter speeds correspond to strut models which 

 are geometrically larger by a factor of approximately 4 than strut 

 models represented in the lower group. Within each group, the flutter 

 speeds are sensitive to mass ratio and a sweep parameter k . The 

 sweep paremeter \_5, 6J combines sweep angle and unswept aspect 

 ratio into a single parameter. Numerical values of k are given for 

 the data points in Figure 4. For similar size models, the data can be 

 fairly consistently divided into families based on similar values of k 

 as shown. An increase in sweep angle therefore increases the flutter 

 speed, while an increase in aspect ratio decreases the flutter speed. 

 Lines of constant k value approach zero as mass ratio decreases in 

 a manner which could be approximated by a square root dependence on 

 mass ratio, a relation which has previously been observed [_3j for low 

 mass ratio struts. Similar trends have been predicted in the lower 

 mass ratio region when sweep angle was included in the analysis 

 |_6, 7, 8j . Groups of different sized models can be correlated by di- 

 mensional analysis. It has been shown ^9 J that the flutter speeds are 

 related according to the square root of bending or torsional stiffness. 



Torsional Flutter Region 



Generalized mass ratio for torsional motion can be represent- 

 ed by the ratio of the total moment of inertia of a strut and the added 

 moment of inertia of the submerged portion of the strut. In the present 

 work, rotation was assumed to occur about the elastic axis of the 

 strut. The resulting torsional mass ratio may be written 



^torsion 



1 a 



*pb 4 (l/8 + a 2 )i+I* ^ 



Available flutter speeds for torsion-type struts are plotted as 

 a function of torsional mass ratio in Figure 5. A substantial amount 

 of data is shown which was obtained at NSRDC and has not been pre- 

 viously published. All strut models in this group had pods and were 

 similar in size to the struts described in Reference 4. A complete 

 description of this data will be published in the near future. 



As shown in Figure 5, torsional flutter has been obtained at 

 values of torsional mass ratio between 0. 61 and 6. 2 . Flutter speeds 

 generally decrease as mass ratio increases. The wide variation in 

 flutter speed results at least in part from wide variation in strut 

 characteristics. In an attempt to adjust flutter speeds for differences 

 in geometric size and torsional frequency, the data has been replotted 



349 



