7. TWO SIMPLE CASES OF FLUTTER 



The mathematical theory of flutter is so complicated in realistic 



cases that it is not easy to form intmtive ideas of the flutter process. 



For this reason a certain interest may attach to simple cases that are 



easily understood. It apprears that typical flutter can occur only if at 



least two degrees of freedom are coupled together; and commonly, but not 



always, there is a difference of phase between the two motions. 



Two relatively simple examples are described in detail. Although the 



theory given here might conceivably be roughly applicable to some actual 



problem, the principal aim in devising these cases has been to make them 



simple. 



In both cases a rigid foil is assumed to be immersed in a uniform 



streajn, and for the lift F on the foil the simple steady-motion approxi- 



mation is used: 



F = - BSv + BS^e 

 L 



In steady motion , is conveniently assumed to represent merely a small 

 inclination of the foil to the approaching stream and v, a slow 

 perpendicular velocity of translation. This formula is known to pro-vide 

 a fair approximation also when 6 varies slowly, as is assumed here. Then 

 must represent rotation about an axis parallel to the foil and perpen- 

 dicular to the stream, while v may be regarded as denoting a displacement 

 of a line on the foil located at the axis of rotation, v being 



* In Appendix H of Reference k, it is shown that the effect of the term 

 is relatively small if — is small. Hence, the 6 term is dropped here. 



71 



