S ', and it may safely be assumed that the motion will then be harmonic. 



As S is increased above S , it is almost certain that the damping will be 



c 



negative, so that any vibration tends to build up. At one or more higher 

 sneeds , harmonic motion may again become possible; however, this is of 

 little practical interest. Thus S^ , the lowest value of S at which steady 

 harmonic motion can occur, constitutes the critical flutter speed that 

 must not be exceeded in practical operation. 



6.5 THREE SPECIAL CASES 



6.5.1 Damping Due to Lift Only (c = c = O) 



1/ c, = Co = 0, so that damping arises only from terms in F and Mg , 



then S may be canceled out of Equations [53b] and [53d] entirely because 



2 

 every term is then linear in S. Also, only the S term occurs now m 



Equation [53c] or [53a] but not in Equations [53b] and [53d]. These 



features open the way to the following simpler mode of solution: having 



2 



assumed a value of oi and calculated a , a , a , and a , calculate u 



from either [53b] or [53d]; if this value of w agrees with w as assumed, 

 then harmonic motion is possible at this w, provided S has a value that 



satisfies either Equations [53a] or [53c]. This value is easily found. 



2 

 If the two values of o) do not agree or if S turns out to be zero or 



negative, then the assumed w must be rejected. 



6.5.2 Foil Rigidly Mounted on the Beam 



The equations may be adapted to the assumption of rigid movmting by 

 letting k^ ->■ 0° and k2 -* "• Since s^/k^ = (l/ki) + a and s^/k^ = (l/k^) 

 + a22 and D/(k^k2) = (s;[_S2 - a3_2a23^k-Lk2 ) /(k-[^k2) , the following reduction 



60 



