AAE 556 Aeroelasticity Lecture 11 Swept wing aeroelasticity Reading Sections 3.1 through Purdue Aeroelasticity

Flying door wing structure idealization with uniformly distributed aerodynamic loads springs resist upward and downward motion 2 Purdue Aeroelasticity

Static equilibrium equations 3 Purdue Aeroelasticity

Computed deflections bending slope twist angle 4 Purdue Aeroelasticity

5 example Sweepback = 5.72 o

Purdue Aeroelasticity 6 Compute the determinant (  ) of the aeroelastic stiffness matrix

Purdue Aeroelasticity 7 Divergence condition Only one divergence q for a 2 DOF system so that

Purdue Aeroelasticity 8 Eliminate divergence? Just sweep the wing aft Set denominator equal to zero No divergence if

Purdue Aeroelasticity 9 example Torsional stiffening is a good thing

Compute lift on the flexible wing (lift effectiveness) Substitute for the angles  and  10 Purdue Aeroelasticity

Flexible wing lift intermediate result 11 Purdue Aeroelasticity

Final result lift effectiveness definition 12 Purdue Aeroelasticity

Compute aeroelastic features of an example wing let 13 Purdue Aeroelasticity

Lift effectiveness vs. q So what? What are the consequences? 14 Purdue Aeroelasticity

15 Flexural axis (FA) concept an attempt to explain aeroelastic effects FA Definition - a line (locus of points) along which the streamwise (or chordwise) angle of attack does not change when a discrete load is applied there (and the air is off). xoxo yoyo  upward load minus plus

Purdue Aeroelasticity 16 What is the difference between flexural axis and elastic axis?   flexural axis x y upward load The air is off!!!

Purdue Aeroelasticity 17 Flexural axis concept an attempt to explain aeroelastic effects xoxo yoyo  

Purdue Aeroelasticity 18 Step #1 Compute angular displacements

Purdue Aeroelasticity 19 Use flexural axis definition This result always gives us a flexural axis location forward of the usual elastic axis. Increased wing sweepback rotates the flexural axis further forward and opens up the distance between aero loads and the hypothetical flexural axis

Purdue Aeroelasticity 20 example

Purdue Aeroelasticity 21 Summary  A load placed at the flexural axis creates no streamwise angle of attack at that section  the flexural axis position depends on the stiffness ratio and the sweep angle  the flexural axis and the elastic axis coincide when there is no wing sweep  the flexural axis is upstream for a swept back wing and downstream for a swept forward wing