Introduction aeroelasticity

Introduction
Aeroelasticity is the interaction between aerodynamic flows and elastic structures - such that the aerodynamic forces are dependent on the structural deformation, and the structural deformation is dependent on the aerodynamic forces. This interaction depends on the flexibility of the aerodynamic object.


 * Example: A flexible wing experiences an aerodynamic force and bends. The change in shape will cause the forces to also change. The change in forces will then cause a different deformation...

Specializations
Aeroelastic problems that also concern high-gain control systems belong to the field aeroservoelasticity.

Aeroelastic problems that also include thermal effects belong to the field aerothermoelasticity.

Problem Characteristics
Aeroelastic problems tend to belong to one of four types:
 * Instability Boundary Problems which find the threshold between stability and instability
 * Static Instability Boundary Problems which don't include inertial effects. These problems frequently concern "divergence"
 * Dynamic Instability Boundary Problems which include inertial effects, and frequently have oscillatory characteristics. These problems typically concern "flutter"
 * Response Problems which predict the response of a system to some input signal.
 * Static Response Problems which don't include inertial effects
 * Dynamic Response Problems which do include inertial effects.

Simplified Aeroelastic Problems
There exist some thought-experiments which are too simplified for real-world application, but demonstrate concepts.

Steady Aerodynamics
$$M_y$$ moment about the elastic axis (positive nose up)

$$M_{AC}$$ moment about the aerodynamic center (positive nose up)

$$C_{MAC}$$ coefficient of moment about the aerodynamic center

$$q$$ dynamic pressure

$$S$$ planform wing area

$$L$$ lift force (positive up)

$$C_L$$ lift coefficient

$$C_{L_0}$$ lift coefficient at 0 angle of attack

$$\alpha$$ angle of attack

$$e$$ distance from aerodynamic center to elastic axis (positive aft)

$$M_{AC}$$ moment about the aerodynamic center

From the parallel axis theorem, we know:

$$M_y = M_{AC} + Le $$

$$= C_{MAC}qS + C_L qSe $$

$$= C_{MAC_0}qS + \left(\Complex_{L_0} + \frac{\partial{C_L}}{\partial{\alpha}} \alpha\right) qSe $$