M Moment due to shear warping of beam 



M Total moment on hydrofoil about axis of rotation 



e 



m, m Effective mass of foil and of a rigid body, respectively 

 (including virtual mass due to surrounding fluid) 



^1' 



Shear force on beam taken positive with F and Y 



Equals {>i^) ^^\ qVvTTJ^ ; ^VTT^- 



EI 

 respectively 



S Uniform speed of stream of fluid; sinh q^l 



S Critical flutter speed 

 c 



s Sin q f. 

 t Time 



V Displacement of beam, positive in same direction as F; 

 similar displacement of foil at axis of rotation 



V Equals v at x = 0, or at line of attachment of foil 



X, y Rectangular coordinates with x axis always parallel to 

 the beam axis and y along a perpendicular principal 

 axis 



y When vibrations are due to bending flexibility only, 

 (KAG =°°) y is the equivalent rotation of a cross 

 section of the beam about an axis perpendicular to the 

 xy-plane due to bending and rigid-body motion; positive 

 in direction of positive -^L- 



dx 



For a vibrating beam with finite bending and shear 

 flexibility, y is no longer the slope of the beajn but 

 represents an equivalent rotation of the cross section 

 about an axis perpendicular to the xy-plane. For the 

 meaning of equivalent rotation, see Appendix A and 

 Equation [A27] of Reference 11 



< Bending strain; a number allowing for effect of varia- 

 tion in E or shape of cross section 



i Specific gravity of fluid 



