1. Purdue Aeroelasticity
Models and concepts
How can I understand the problem? What is important and what is not?
How can I discover or identify the fundamental inter-relationships between phenomena?
How can I fix it?
Purdue Aeroelasticity

2. Purdue Aeroelasticity
Lecture 2 - summary
Aeroelasticity is concerned with interactions between aerodynamic forces and structural deformation – we need models to describe interactions and their effects
Features of good models - simple with results that are easy to interpret
Aeroelastic models include aerodynamic, inertial and structural features
Structural load/deformation model with bending and twist - unswept semi-monocoque wings
Aerodynamic fundamentals – relationship between aero loads and deformation
Aero/structural interaction analysis model
Models are limited but insightful
Purdue Aeroelasticity

3. Models – physical or mathematical? What do we want to learn?
Vehicle stability?
The origin of unusual features that have not been seen before?
How important is simplicity?
Purdue Aeroelasticity

4. Topology Optimization Structural Model Fidelity, Purdue Aeroelasticity
Design development uses models that increase in fidelity as more information and detail becomes available
AML
DRACO
OptiStruct
ASTROS
NASTRAN
Concepts
Innovation
TSO
FASTOP
FEM II
Layout
Sizing Optimization
A well-defined component
FEM I
Many choices
Topology Optimization
Load Paths
Structural Model Fidelity,
Cost to Change
Purdue Aeroelasticity

5. Modeling and information Features of good models
Look at how simple models are developed and how they can help us
Realistic predictions of physical phenomena
Identify and use significant problem parameters
Discover underlying causes of interactions
Minimal math complexity
Algebraic terms for effects (structures, aero..)
Manageability of math task and results
Ease of relating math to experimental results
Purdue Aeroelasticity

6. Low level degrees of freedom – a first step
lift, L
pitching
Moment
MAC
spring
force
Khh
torque
KTq
downward
displacement, h
Purdue Aeroelasticity

7. Purdue Aeroelasticity
What do you mean by “fundamental?” Aerodynamic models describe math relationships lift, pitching moment and angle of attack
lift and pitching moment co-efficients
angle of attack, a
Purdue Aeroelasticity

8. Terminology – airfoil center of pressure
Choose an origin (point “o” is usually at the leading edge)
locate a position x,
sum moments
center of pressure definition L x MO
Center of pressure
Purdue Aeroelasticity

9. We’ll use something called the aerodynamic center
Compute change in aero moment with respect to angle of attack L
xAC MO
Aero center
Aerodynamic center is at ¼ chord position for a 2D airfoil with incompressible flow
Purdue Aeroelasticity

10. Purdue Aeroelasticity
Wing twisting is important –we include it by using structural influence coefficients or stiffness
Going from the real world to the virtual world b h
Torque=T t
Boeing 727 wing box with torsional model outlined in red
Purdue Aeroelasticity

11. Features of the typical section aeroelastic model
lift
airspeed
Single degree of freedom
q, the structural twist angle
Structure resists twisting with an internal moment (torque) proportional to q Ms=KTq the more you twist the more the structure resists - linearly
Notice what this model does and does not do. It ignores the bending deflection and can't predict wing stress or twist anywhere on a real wing. It does approximate the interaction between airloads and the structural twist and point out how and where problems may occur. It is left to the reader how to relate the torsional spring to real life structural features and this is not easy to do. The model does give us a general idea about when we need to crank up the advanced analysis to analyze more accurately the load deflection interaction. It also identifies the importance of the offset between two reference points - the shear center and the aero center and shows us why we need to understand exactly the meaning of these two points.
We can't produce a number for the lift (like pounds) because the angle of attack including flexibility is an unknown in the beginning. The lift will depend on the angle of attack we input, but it also depends on how much the airfoil rotates because of flexibility. This is a statically indeterminate problem and requires that we write an equation for the relationship between loads and deflection.
The term KT is a “torsion spring constant” M q
Elastic axis – shear center?
Purdue Aeroelasticity

12. Purdue Aeroelasticity
Sum the torsional moments - write them in terms of torsional displacement, q
¼ chord
collect terms
Shear center
Stiffness is defined as the change in the generalized force (in this case the torque about the shear center) caused by a unit change in generalized displacement (in this case twist). The apparent torsional stiffness of the airfoil is the sum of the mechanical and aerodynamic stiffnesses. At dynamic pressures larger than the divergence dynamic pressure, the apparent torsional stiffness is negative, implying that any slight increase in angle of attack of the airfoil will cause it to twist without limit. As the aeroelastic torsional stiffness declines to zero.
Shear center offset
Purdue Aeroelasticity

13. Solution for twist angle q
Unless the aeroelastic torsional stiffness is positive, there can be no solution to the static equilibrium equation for this airfoil. A negative stiffness gives a negative twist angle for a positive angle of attack input, clearly an impossible answer.
What does this model tell us? Why is it useful? How can we add fidelity? Why would we want to?
The aeroelastic term qSeCLa/ KT appears. As qSeCLa/ KT approaches unity, q will approach infinity if the input angle of attack is constant.
A phenomenon called aeroelastic divergence will happen when the dynamic pressure, q , equals KT/SeCLa
Purdue Aeroelasticity

14. Purdue Aeroelasticity
Lift equation
Write this equation over a common denominator
Purdue Aeroelasticity

15. Lift expressed a different way
The aeroelastic parameter
Purdue Aeroelasticity

16. The final equation for lift
Purdue Aeroelasticity

17. Summary-what have we learned?
We have identified aerodynamic, structural and aeroelastic parameters that are important to aeroelasticity
Torsional stiffness
Lift curve slope
Elastic axis offset distance
Aeroelastic parameter depends upon structural stiffness, geometry and aerodynamic co-efficient
Purdue Aeroelasticity