Page 570 - Aircraft Stuctures for Engineering Student

13.3 Structural vibration 551

Substituting for 8 from Eq. (13.29) into Eq. (13.32) gives

Hence

sinX(s - sl) . 1
q{ (%+: 2) [r,e){l -cosx(z-s])) - cos As sin Xz

(13.33)

Therefore, aileron effectiveness (ps/ V)/< is given by

Integration of the right-hand side of the above equation gives

1 8cm.o
- e(acl/aa)
<
--
(13.34)
The aileron reversal speed occurs when the aileron effectiveness is zero. Thus, equat-
ing the numerator of Eq. (13.34) to zero, we obtain the transcendental equation
(%+: %) (COSXS - COSXS~) + cosXs = 0 (13.35)
a€

Alternative methods of obtaining divergence and control reversal speeds employ
matrix or energy procedures. Details of such treatments may be found in Ref. 3.

The remainder of this chapter is concerned with dynamic problems of aeroelasticity,
of whichflutter is of primary importance. Flutter has been defined as the dynamic
instability of an elastic body in an airstream and is produced by aerodynamic
forces which result from the deflection of the elastic body from its undeformed
state. The determination of critical or Jlutter speeds for the continuous structure of