Background Research

Goal

The goal of our project was to gain a better understanding of aeroelastic flutter. Aeroelastic flutter is a phenomenon when the flexibility of the structure of an aircraft coincides with aerodynamic forces to create oscillations. These oscillations build in amplitude and can result in a catastrophic failure of the airframe and loss of life [2].

Understanding the mechanics of these oscillations and developing a quantitative model is critical to the safe development of aircraft. According to [4], to decrease flutter, common design changes include: adding mass balances, stiffening the structure, and reducing the weight of control surfaces.

Model background

Flutter is a 2 DOF phenomenon, with degrees of freedom corresponding to the twist and bending of the wing. The frequencies of these two modes converge as the airspeed increases until they reach the same value. When the frequencies of the two modes converge to a single value, the modes build energy, and the amplitude increases until the structure fails, or higher order effects limit the amplitude [1].

The bending and twisting wing can be modeled as a discrete foil section with pitch (angular) and plunge (vertical translation) DOFs with a linear spring in plunge and a torsional spring in pitch. This results in a mathematical model that is a system of 2 second-order ODEs. See "Motion Model" for the detailed explanation of this model.

Experimental Setup Background

From the materials provided for this test, the two DOF can easily be seen as the pitch and plunge of an airfoil. The plunge occurs in the y-direction, controlled by a compound spring with an effective constant (compound spring is made of 5 springs of various constants). The pitch is controlled by a torsional spring, which is a 3cm rod that the airfoil is attached to. For the details of our experimental setup, see "How to Use a Wind Tunnel."

The goal of our mathematical model was to use a system of 2nd-order ODEs as a model for the physical vibration phenomena of an airfoil and to compare the model to our experimental data.

We also wanted to correlate flutter frequency to wind speed based on the experimental data, more specifically the FFT on the data. We found that as the airspeed increased, the real components of the eigenvalues for the pitch and plunge eigenmodes will converge to a single real value, after which point there is a single combined mode with negative net damping. The net damping can be negative because the energy is absorbed from the airflow by one mode to increase the amplitude of the other mode. This critical airspeed at which the real parts of the eigenvalues converge is the critical flutter speed. Because of the negative net damping, the amplitude of the oscillations increases until the structure reaches a non-linear elastic region (yield) and/or structural failure (which is correlated to yield).

For more information on our mathematical approach, please look at the derivation process shown on the "Motion Model" page.