Besch and Liu 



due to circulatory flow was varied by inserting steady values of lift 

 slope Cn and aerodynamic center a c obtained by a separate cal- 

 culation. This approach was originated by Yates Q4] . The noncircu- 

 latory terms were varied by inclusion of a multiplicative factor p. 

 The factor permitted reducing the magnitude of the noncirculatory 

 loading below that associated with two-dimensional flow. This modi- 

 fication was introduced by the authors |_15j > m accordance with a 

 suggestion by Yates [_1 6 J . Spanwise distributions for p will be dis- 

 cussed later. 



The given expressions correspond to two-dimensional hydro - 

 dynamic loading when a lift slope of 2 it , an aerodynamic center lo- 

 cation at quarter chord, and a noncirculatory modification factor of 

 unity are used. Three-dimensional loading requires that appropriate 

 spanwise distributions of these quantities be used. In a number of 

 flutter calculations presented later, the effects of three-dimensional 

 flow were studied by varying the above quantities but keeping all span- 

 wise values equal. 



Spanwise distributions of lift slope and aerodynamic center 

 were obtained from lifting surface theory [_1 7j . The distributions 

 were calculated using a uniform angle of attack along the span of the 

 strut, and an antisymmetric loading boundary condition at the free 

 surface. 



Two different distributions of noncirculatory modification fac- 

 tor were used, one for low frequencies and one for high frequencies 

 Q. 5 J . At low frequencies, the factor consisted of the three-dimension- 

 al added mass of the strut, expressed as a fraction of the two- 

 dimensional added mass, outboard of the spanwise position being con- 

 sidered. The free surface was treated as a reflecting plane. At high 

 frequencies, the spanwise distribution of added mass on a surface- 

 piercing strut decreases to zero at the free surface. This condition 

 was approximated by assuming the midspan of the submerged portion 

 of the strut to be a reflecting plane and using the low frequency dis- 

 tribution on either side. 



Values of the nondimensional frequency, £ u /g , were used to 

 distinguish between low frequency and high frequency conditions, 

 indicating that the generation of gravity waves was involved in the 

 boundary condition. The low frequency condition exists for values of 

 It o> /g of 1 or less, while high frequency loading corresponds to 

 values of x-w^/g of 10 or greater. 



354 



