FLUTTER

Write a computer program to solve the two-degree-of-freedom (pitch and plunge) problem using the p, k, and p − k methods, assuming Theodorsen unsteady aerodynamics for the k and p − k methods. For the Theodorsen aerodynamics, you should utilize the exact mathematical formulation for C(k).

Using this computer program, you should compute the flutter speed when a =  − 1 ⁄ 5, e =  − 1 ⁄ 10, μ = 20, r = 2 ⁄ 5, σ = 2 ⁄ 5.

Plot comparisons of the computed values of the damping and frequency as the reduced velocity changes.

Please refer to the Maple code link (Example 1).

Consider an incompressible, two-degree-of-freedom flutter problem in which a =  − 1 ⁄ 10, e =  − 1 ⁄ 15, μ = 25, r² = 7 ⁄ 25, σ = 2 ⁄ 5. Compute the flutter speed and the flutter frequency using the classical flutter approach. For the aerodynamic coefficients, use first the approximation of

Next, use the exact definition of the Theodorsen function, C(k). From an engineering viewpoint, discuss the differences in the results, in particular whether it is a good engineering approximation to use the approximate form of C(k). Plot the variation in the real and imaginary values of ω_θ ⁄ ω and C(k) terms with k.

Please refer to the Maple code link (Example 2).