See Figure 1 which shows the wind-tunnel model of a flexible uniform wing. The wing

has the span of ' and the chord of c. The torsional stiffness of the wing is constant and

is represented by GJ, and the sectional lift-curve slope is also constant and is denoted

by a.

The wing is clamped at y = 0 and is supported at y = ' by a torsional spring of the

stiffness K, which is attached to the airfoil shear centre. Assume that the aerodynamic

center is located at the quarter-chord from the leading edge. Also, both the shear center and the centre of gravity for all airfoil sections along the wing are located at the

mid-chord. As seen in the figure, y-axis represents the elastic axis of the wing which

is actually the loci of the shear centres.

(a) Obtain the general expression (i.e. parametric form) for the static elastic twist, (y),

of the wing.

(b) Obtain the divergence dynamic pressure, qD, for the following values of K'=GJ, and

using (preferably) MATLAB, plot the variation of qD as a function of K'=GJ. Assume c =

0.1m, ' = 2 m, a = 2 rad-1, and GJ = 23 Nm2; K'=GJ = 0, 0.1, 1, 10, 100, 1000, 1.

(c) Plot the distribution of along the span for K'=GJ = 0.1 and K'=GJ = 100 at 25%

of their corresponding qD. Assume r = 3 and cmac = -0.1.