search for a useable S, however, is about as complicated. 



o 

 A useful minimum for u) can be obtained from Equation [6Ua] provided 



2 

 the coefficients of S and S are not negative, namely: 



i c c [m'I'e - (h'm* ) 



.™n2i-l 



Otherwise, the determination of a minimum o) is more complicated. 



In Section 3 it was remarked that the approximate values of a , a , 



FF 11' 12 



a , and a^^ are the same as the values for a slender uniform rigid rod of 

 length £ and mass \il forced at one end. For the rod, a = a^^ . Thus the 

 equations derived here for q2. << 1 are applicable also to a foil attached 

 at one end of such a rod. 



It is interesting also that the equations still hold if )l = 0, which 

 corresponds to removal of the beam altogether. Thus the foil may exhibit 

 flutter all by itself. Usually, any low- frequency harmonic vibration of 

 the foil that can occur with the beam attached can also occur without the 

 beam, and at the same to and S, provided the mass of the foil is increased 



from m to m' and its moment of inertia from Iq to I'n, and provided h is 



1 ? 

 changed to a value h' such that h'm = hm + — yJl . 



6.6 SIMILITUDE 



An interesting question is the relative influence of the various 

 parameters of the foil-beam system upon the cricitcal flutter speed. 

 Relevant foil parameters are m, I , h, and L; the lift constants B, C, 

 and E^ (or the foil constants pl^, b, and e); and c, and Cp . Also, 

 there are the attachment elasticities k-, and kp. The influence of the 



6h 



