Flutter of Flexible Hydrofoil Struts 



Calculations were performed by a digital computer program which 

 required that hydrodynamic force expressions be real. Because of 

 this restriction, the imaginary part of the Theodorsen circulation 

 function was omitted from the loading used. 



Unsatisfactory results were obtained from the direct method 

 of solution. The predicted flutter speed did not agree with that predict- 

 ed by the eigenvalue calculation. Furthermore, values of negative 

 damping above flutter inception were so large that no oscillation oc- 

 curred. As a result, the presence of travelling waves could not be 

 detected. The discrepancies between the two methods of solution may 

 have resulted from the difference in hydrodynamic loading used. It is 

 evident that further investigation of this method of calculation is re- 

 quired. 



The hydroelastic mode characteristics of Model 2 are typical 

 of three other bending -type struts that were analyzed. Flutter predic- 

 tions using two-dimensional loading were often fairly accurate. The 

 mode 3 instability appeared in two of the three additional calculations 

 using three-dimensional loading. The flutter inception speeds for the 

 new mode were again nonconservative, and less accurate than those 

 obtained using two-dimensional loading. Frequencies predicted for the 

 new mode agreed well with frequencies observed at flutter, while 

 those for mode 3 did not agree well. Frequency predictions were equal- 

 ly accurate for both types of loading. Predicted mode shapes for the 

 new mode were predominantly first bending. This agrees with mode 

 shapes observed for bending flutter. 



The damping behavior of the new mode as a function of speed 

 shows qualitative agreement with experimental results. In an expe- 

 riment performed at NSRDC, damping was found to be extremely high 

 for a bending -type strut at all speeds below flutter inception. At flutter 

 inception, damping decreased sufficiently to permit flow-excited os- 

 cillations of large amplitude. This behavior would be expected of an 

 instability occurring in the new mode, which decreases in damping 

 from a highly damped condition at intermediate speeds. 



In view of the more accurate frequency correlations of the new 

 mode, and its high damping characteristics at intermediate speeds, 

 it is concluded that bending flutter occurs in the mode designated as 

 the new mode. Measurements of damping of strut modes at various 

 speeds are needed to confirm this conclusion. The appearance of a 

 calculated instability in mode 3 is probably caused by extreme sen- 

 sitivity of the calculated damping to load variation. The present flutter 

 calculation can be used to indicate a possible occurrence of bending 

 flutter, but cannot be used for estimating flutter speeds. Design 



357 



