6. FLUTTER OF A RIGID FOIL ATTACHED TO A UNIFORM BEAM 

 6.1 DERIVATION OF EQUATIONS OF MOTION 



A rigid foil attached to a uniform beam of length i will be considered 

 in this section. The foil is assumed to be equivalent to a straight flat 

 strip of rectangular shape, with length much greater than width, attached 

 to the beam so that its length is perpendicular to a principal plane of 

 the beam, with this plane being midway between the ends of the beam. In 

 the \mde fleeted position of foil and beam, the plane of the foil is 

 assumed to pa^s throu^ the principal axis of the beam. Elastic deflections 

 of foil and beam, where they are connected, will be allowed but the 

 affected part of the beam is assumed to be much smaller than the whole 

 beam. The relatively small part of the foil that lies within the beam may 

 be absent, being replaced perhaps by a throu^-shaft similar to the 

 mounting of a pair of diving planes. 



There is a certain axis of rotation lying in the plane of the foil and 



parallel to its length about which relative rotation of foil and beam 



evokes only elastic moments G acting on the beam and -G on the foil. Let 



6 denote a small angle of rotation of the foil about the axis , measured 



from zero when both foil and beam are in their neutral positions; in 



addition, the local part of the beam itself, due to vibration and aside 



from distortions of the attaching structure, may be rotated similarly 



through a small angle 6 . The positive directions are assumed the same for 

 o 



6, 9 , and G. The foil may also have a small translational displacement v 

 o 



perpendicular to its plane and the beam at the axis for 6 a small 



h3 



