AAE 556 Aeroelasticity Lecture 14 Aeroelastic tailoring 14-1 Purdue Aeroelasticity... Aeroelastic tailoring benefitsPurdue Aeroelasticity 14-2... Flexural axis β Definition - a line locu
Trang 1AAE 556 Aeroelasticity Lecture 14
Aeroelastic tailoring
14-1
Purdue Aeroelasticity
Trang 2Aeroelastic tailoring benefits
Purdue Aeroelasticity
14-2
Trang 3Purdue Aeroelasticity
14-3
Apparatus-stiffness tailoring model
θ
K 1
view A-A (looking inboard toward root)
d sin γ f cosγ
Mθ
δ 2 δ 1
φ
view B-B (looking upstream,chordwise)
d cos γ
K 2 K 1
wing
Mφ
f sin γ
view B-B (looking upstream,
chordwise)
Trang 4Stiffness tailoring model
y
V
V cos Λ Λ
φ
θ
γ
K1
f
c
B
B
A A
γ
Purdue Aeroelasticity
=
+
−
−
+
=
θ
φ θ
φ θ
φ
θ φ
θ
φ
θ
φ γ γ
γ γ
γ γ
γ
γ θ
φ
M
M K
K K
K
K K
K
K
2 2
cos sin
cos sin
) (
cos sin
) (
sin
cos ]
[
Trang 5Flexural axis
β
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
−
=
o
o
Px
Py M
M
θ
φ
xo
yo
−
o
o y
x
1 tan
β
Purdue Aeroelasticity
Λ
Trang 6Purdue Aeroelasticity
14-6
Structural angular displacements
θ φ
cos sin
sin cos2 K 2 y o K K x o
K K
K
P
− +
+
=
[( ) sin γ cos γ ( cos2 γ sin2 γ )]
θ φ
K K
x y
K
K K
K
P
o
−
−
=
Solve for the flexural axis coordinates by setting the chordwise elastic angle of attack to zero
0 tan Λ =
−
θE
Trang 7Purdue Aeroelasticity
14-7
Flexural axis with cross-coupling
stiffnesses
0
−
θE
P
K y K x K y K x
K Kθ φ
tan tan
o o
Trang 8Purdue Aeroelasticity
14-8
Plug expressions for stiffness terms to
get the flexural axis position
o
x y
β = − ÷
Λ
− +
+
Λ +
+
−
=
−
tan cos
sin ) (
sin cos
tan )
sin cos
( cos
sin )
(
2 2
2 2
γ γ
γ γ
γ γ
γ γ
θ φ
θ φ
φ θ
θ
φ
K K
K K
K K
K
K y
x
o o
φ
θ
K
K
R =
Λ
− +
−
−
Λ
−
− +
−
=
−
=
tan cos
sin ) 1
( sin
) 1
( 1
tan ] cos
) 1
( 1 [ cos
sin ) 1
(
2
γ γ
γ
γ γ
γ β
R R
R
R y
x
o o
Trang 9Purdue Aeroelasticity
14-9
example
90 75 60 45 30 15 0 -15 -30 -45 -60 -75 -90 -90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90
flexural axis angle vs.
struct ural principal axis angle
structural sweep angle (degrees)
30 deg.
sweepback
30 deg.
sweepforward
15 deg.
sweepback
zero sweep
15 deg.
sweepforward
When wing is sweptforward increase
divergence speed
by moving the β
axis forward (plus)
γ
β
forward
aft/back
forward aft/back
Wash-out laminate Increase divergence
Wash-in laminate Increase lift
Trang 10Purdue Aeroelasticity
14-10
Divergence
y
V
V cos Λ Λ
φ
θ
γ
K 1
K 2 d f
c
B B
A A
γ
q D =
Kθ Sea o
cos2Λ (1−R)
2 tanΛ − b
2e
sin2γ + 1 −Rb
2e tanΛ
+(R−1) 1 + 2e b tanΛ sin2γ
φ
θ
K
K
R =
(1 − R)
2 tanΛCR − b
2e
sin 2γ + 1 − Rb
2e tanΛCR
Get rid of divergence
ΛCR = tan−1
1 + b
2e
(R− 1)
2 sin 2γ +(R− 1)sin2 γ
R b
2e + (R −1)
2 sin2γ − b
2e (R − 1)sin2γ
Trang 11Purdue Aeroelasticity
14-11
Example (page 171)
b
-30 -20 -10 0 10 20 30 40
structural orientation angle, γ (degrees)
ΛC
0 30 60 90 -90 -60 -30
b/c=6 e/c=0.3
e/c=0.1
5.71deg
divergence impossible
1 3
K R
K
θ φ
= =
γ
Wash-out laminate Increase divergence
Wash-in laminate Increase lift
Wash-in laminate Increase lift
Wash-out laminate Increase divergence
Trang 12Purdue Aeroelasticity
14-12
Wings with sweep angles above the curves shown
will not diverge.
K R
K
θ φ
=
6 0.1
b c e c
=
=