Calculation of Divergence dynamic Pressure

SonOfGod

Hello everyone,

I am revising for my final examination. I came across this simple problem which I can not solve. the problem is from a text book (Introduction to Structural Dynamics and Aeroelasticity
By Dewey H. Hodges, G. Alvin Pierce). It is the 7th question in the problem sets of the 3rd chapter. Here is the question:

======================================================================= ========================
Consider a torsionally elastic wind tunnel model of a uniform wing, the ends of which are rigidly fastened to the wind tunnel walls.
The model has a symmetric aerofoil section and the following characteristics:

Span = 0.9144 m
Chord = 0.1524 m
Torsional Rigidity GJ = 22.9677 Nm2
Lift curve slope =6.0 per radian

The aerodynamic centre may be taken as lying at the quarter-chord position measured from the leading edge of the wing.
The CG and the elastic axis are located at the mid-chord.

Calculate:

(i) The divergence dynamic pressure (Answer: 7781.86 N/m2)
(ii) The divergence speed at sea level (Answer: 112.69 m/s)
======================================================================= =======================

My attempt was to find it directly using the formula:

Divergence dynamic pressure = [GJ*(∏/2l)^2]/ eca

I have used the given values and taken "e" to be "0.25*c" (quarter chord).

My answer is not even close, its 1945.46 N/m2 :(

I can solve the second part of the question by equating 7781.86 with 0.5ρU^2. U is the speed that we need to find, and my answer matches.

Can anyone help ?


My exam is on 20th June, I hope someone who knows aeroelasticity (divergence) can help me out :)


Regards