AAE352Lecture_14_Aeroelastic_tailoring in Aircarft

AAE 556 Aeroelasticity Lecture 14 Aeroelastic tailoring Aeroelastic tailoring benefits Apparatus-stiffness tailoring model δ2 d sinγ δ1 f cosγ Mθ θ K2 K1 V view A-A (looking inboard toward root) f sinγ d cosγ K2 Mφ wing φ K1 view B-B (looking upstream,chordwise) view B-B (looking upstream, chordwise) Stiffness tailoring model γ K1 V f γ d K2 Λ φ x B B 2 φ   K φ cos γ + K θ sin γ [ K ij ]  =  θ   ( K φ − K θ ) sin γ cos γ V cosΛ A b A θ c y ( K φ − K θ ) sin γ cos γ  φ   M φ  =  2   K φ sin γ + K θ cos γ  θ  M θ  Flexural axis Definition - a line (locus of points) along which the wing structure stream-wise angle of attack is zero when a discrete load is applied there – with the “wind” off Λ M φ   Pyo   =  M θ  − Pxo  −1  − xo  β = tan   yo β     yo xo Structural angular displacements due to upward load P at –xo,yo [( ) P φ= Kθ cos γ + Kφ sin γ ( yo ) + ( Kφ − Kθ )( xo ) sin γ cos γ K φ Kθ [ ] −P θ = ( Kφ − Kθ )( yo ) sin γ cos γ + ( xo ) ( Kφ cos γ + Kθ sin γ ) K φ Kθ Solve for the flexural axis coordinates by setting the chordwise elastic angle of attack to zero θ E = θ − φ tan Λ = ] Flexural axis with cross-coupling stiffnesses θ E = θ − φ tan Λ = P θE = = − K12 yo − K11 xo − ( K 22 yo + K12 xo ) tan Λ ) ( Kθ Kφ − xo K12 + K 22 tan Λ = yo K11 + K12 tan Λ Plug expressions for stiffness terms to get the flexural axis position 2 − xo ( K φ − Kθ ) sin γ cos γ + ( Kθ cos γ + K φ sin γ ) tan Λ = yo K φ cos γ + Kθ sin γ + ( K φ − Kθ ) sin γ cos γ tan Λ  xo  tan β =  − ÷  yo  Kθ R= Kφ − xo (1 − R) sin γ cos γ + [1 − (1 − R) cos γ ] tan Λ tan β = = yo − (1 − R) sin γ + (1 − R) sin γ cos γ tan Λ example 90 f lexural axis sweep (degrees) forward β 75 60 45 30 15 f lexural axis angle vs st ruct ural principal axis angle 15 deg sweepback zero sweep 30 deg sweepback Wash-out laminate Increase divergence Wash-in laminate Increase lift -15 -30 -45 -60 aft/back -90 -75 30 deg sweepforward -90 -75 -60 -45 -30 -15 15 deg sweepforward 15 30 45 60 75 90 st ruct ural sweep angle (degrees) aft/back γ forward When wing is sweptforward increase divergence speed by moving the β axis forward (plus) Divergence R= Kθ Kφ γ K1 V f Kθ Seao qD = b Rb b (1− R)     cos Λ  tanΛ −  sin2 γ + − tan Λ + (R − 1) + tan Λ sin γ        2e 2e 2e   γ d K2 V cosΛ Λ φ A x B b θ B Get rid of divergence (1 − R)  b Rb   + (R − 1) 1+ b tan Λ  sin2 γ = tan Λ − sin γ + 1− tan Λ CR CR CR    2e  2e  2e Λ CR   b (R − 1) sin 2γ + (R − 1)sin2 γ   1+ −1  = tan  b 2e(R −21) b R + sin2 γ − (R − 1)sin γ    2e 2e  A c y Example (page 171) Wash-in laminate Increase lift 30 Wash-out laminate Increase divergence e/c=0.3 20 (degrees) Wash-out laminate Increase divergence critical wing sweep angle,ΛCR 40 10 divergence impossible b/c=6 5.71deg -10 e/c=0.1 -20 Wash-in laminate Increase lift -30 -90 -60 -30 30 60 90 structural orientation angle, γ (degrees) b =6 c Kθ R= = Kφ γ Critical wing sweep angle vs structural angle γ Wings with sweep angles above the curves shown will not diverge Kθ R= Kφ b =6 c e = 0.1 c