Flutter of Flexible Hydrofoil Struts 



Eigenvalues for selected speeds were obtained by a digital 

 computer calculation based on Muller's quadratic method Q. 3 J . 

 Flutter speeds were determined by interpolation among damping values 

 across the zero damping axis. Eigenvectors were also obtained, 

 giving the vibration mode shapes in standing -wave form. 



The most general form of strut motion is composed of travell- 

 ing waves as well as standing waves. Further calculations were there- 

 fore made to determine whether travelling -wave oscillations were 

 occurring. Travelling waves were found in connection with bending 

 motion and will be described later. 



III. 2. Hydrodynamic loading 



Hydrodynamic loading on discrete sections of the strut was 

 calculated with a strip theory. The theory was formulated to allow 

 spanwise variation of the loading so that the effects of three-dimen- 

 sional flow could be investigated. 



The lift and moment expressions used were 

 2 



■P. = p. 7rpb. 

 l l l 



h. - V 9. + V a. tan A + b.a. (G. + V -i. tan A ) 



n i n l 



ea ill n l 



ea 



-C n pV b. C(k) w. 

 iL . n i i 



a , l 



4 2 •• 



-M. = p. Trpb. (1/8 + a. ) (6. + V x. tan A ) 

 i 11 11 ni ea 



2 3 



+ p. Trpb. V (h. +V or. tan A )+ p.Trpb. a. (h. + V a. tan A ) 

 m. i n l ni ea i 111 ni ea 



2 2 

 p.7rpb. V (6. -a.b.-e. tan A ) 

 li n l ill ea 



+ 2ttpV b. 

 n i 



C(k) . C£ 



T P i 



(a. - a .) 

 1 c, 1 



2tt 



where 



w. = -h. + V 9. - V a. tan A + b 

 l l n l n l ea 



. ( °' 1 + a . - a. (9. + V , . 



l\27T C,l V 1 nl 



tan A ) 



ea 



In this formulation, spanwise loading variations were introduc 

 ed separately for circulatory and noncirculatory loading. The loading 



353 



