6.2 CRITICAL FLUTTER SPEED 



For typical flutter to be possible , there must exist one or more 

 values of the speed S at which a steady vibration of the foil and beam 

 is possible in spite of existing damping actions. The lowest such speed 

 is the critical flutter speed, which is the item of principal practical 

 interest. 



To seek a critical flutter speed for the foil-beam system by the 

 usual method, assiime that in Equations [51a, b] v and 8 are complex 



functions of the time proportional to e (i = >^-l). Then v = iuv, 



p loot 



V = - to V, etc. , and, after canceling e , the remaining equations are 



linear in v and 0. Nonzero values of v or 6 are possible only if the 



determinant of the coefficients of v and 6 in these equations vajiishes ; 



that is, if 



[-t/m + D"^S2k^ + ia)(c-i_ + BS)] [-oo^Ig + °"^^i^2 " ^^^ ^ ^'^^^2 "*" \^^^ 

 - (-oj^hm - D"-^a k k^ - BS^ - iwCS) (-cj^hm - D'-^a^-^k^k^ + iuLBS) = 



The real and imaginary parts of this equation must hold separately. The 



-2 

 imaginary equation may be divided by iw if w ^ 0, and the D term that 



occurs in it may be simplified by means of Equation [50c], thus: 



50 



