1. Purdue Aeroelasticity
AAE 556 Aeroelasticity
The final blow
Final exam
Monday May 3
1-3 p.m.
ARMS 1021
Purdue Aeroelasticity

2. Purdue Aeroelasticity
What’s on the test?
Instructions  
This test consists of 50 problems and is closed book, closed notes.
Please attach this cover sheet to your solution worksheets. Put your name or initials on each sheet of paper handed in.
Purdue Aeroelasticity

3. Purdue Aeroelasticity
An example
A two degree of freedom system has displacement degrees of freedom w and z. The force in the w direction is proportional to z.
When the system is oscillating harmonically, the displacement w and the force are drawn in a complex plane in the figures shown to the right.
Which of the two situations, (A) or (B), will be associated with an oscillatory instability?
Explain your answer.
Purdue Aeroelasticity

4. Purdue Aeroelasticity
Another example
A single-degree-of-freedom airfoil with a small viscous damper, with damping constant Cv, attached to the trailing edge of the airfoil is made to oscillate harmonically by adjusting the sign and size of Cv. The equation of motion for the airfoil in an incompressible flow is found to be:
where
Purdue Aeroelasticity

5. Purdue Aeroelasticity
Problem
Outline (describe) an iterative computational scheme to find the flutter speed and flutter frequency of this single degree of freedom airfoil when the actual viscous damping is known to be . Note that since we have not given actual parameters such as “a” you can’t do many computations.
Draw figures to support your numerical approach. Be sure to explain how and when you will be able to tell when instability occurs. Equations and diagram(s) are, as usual, always helpful.
Purdue Aeroelasticity

6. Purdue Aeroelasticity
More stuff
Any problem from Test 1
Formulating Lagrange’s equations
Finding dynamic and static instabilities
Mode shapes
Rayleigh-Ritz
Purdue Aeroelasticity