Key Parameters and Results

The scripts were run with specific values to demonstrate their functionality. Below are some of the key results and the values used for the calculations.

• model1_2_3.m - Model 1 (Quasi-Static) For the quasi-static model, the following critical speeds were computed:

  • Divergence speed: 59.15 m/s

  • Flutter speed: 21.35 m/s

The output plots for this model, and the flutter_real_discrete.m and flutter_real.m scripts, show the real part of the eigenvalues (damping) versus the airspeed. The point where the real part of an eigenvalue crosses the zero line from negative to positive indicates the onset of instability (flutter).

• flutter_real.m (Goland Wing) This script, when run with a sweep angle of 30 degrees and the specified Goland wing parameters, produced a flutter speed of approximately 420.1 m/s.

• flutter_real_discrete.m (Discrete Airfoil) Using the parameters specified in the script, the flutter speed was found to be approximately 23.9 m/s.

The flutter_real_discrete.m and flutter_real.m scripts both implement fully unsteady loads based on the Theodorsen theory and use a method similar to the V-g method for solving the aeroelastic equations.

• amplitude_vs_U.m (Time-Domain Response) This script was used to simulate the oscillatory response at three different airspeeds, demonstrating the change in system stability:

  • U = 5 m/s: The response shows a stable, damped oscillation.

  • U = 15 m/s: The oscillations are still damped but take longer to die out, indicating reduced stability.

  • U = 30 m/s: The response becomes unstable, with the amplitude of oscillation growing rapidly, confirming that the system is operating past its flutter speed.

Parametric Studies

In addition to the primary analysis, several parametric studies were conducted to understand the impact of various design parameters on the aeroelastic behavior of the wing. These studies include:

• Variation of Reversal Dynamic Pressure with Mach Number: A study on how the dynamic pressure at which aileron reversal occurs changes with increasing Mach number.

• Lift Effectiveness with Different Sweep Angles: An analysis of the effect of wing sweep on the lift effectiveness, demonstrating how sweep can alter the aeroelastic behavior.

• Divergence Speed vs. Sweep Angles for Varying Mach Number: A comprehensive study that plots the divergence speed against the wing sweep angle, showing how this relationship is influenced by different flight Mach numbers.

Getting Started

To run these scripts, you will need a MATLAB environment.

1. Clone this repository to your local machine.

2. Open the desired MATLAB script (.m file) in the MATLAB editor.

3. Modify the parameters in the "USER INPUT" or "Wing Parameters" sections of the script as needed.

4. Run the script. The output will include command-line messages and plots showing the frequency and damping as a function of airspeed.

Note: This project was developed as a self-study exercise in May 2025. The models and approximations used are for educational purposes.