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AAE 556

Aeroelasticity

Lecture 12

Swept wing aeroelasticity

The flexural axis concept

12-1Purdue Aeroelasticity

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Purdue Aeroelasticity 12-2

Swept wing static aeroelasticity

Reading Sections 3.1 through 3.6

i Goals Compute changes in aeroelastic loa on swept

wings ! lift effecti"eness

Explain effects using the flexural axis concept

A

#$

C

%

1

1

1

%section

1&1

sin

2

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Notes on Homework

handed back today

1' (ou must raw accurate) meaningful)

eciphera*le +ree #oy $iagrams ,+#$s-

2' (ou must ma.e your /0 neat an

organie

' (ou must clearly ientify your answers

3' (ou must chec. for imensional

compati*ility5' 4rering euations

Purdue Aeroelasticity 12-3

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Fridays Homework

roblem 3.3

Purdue Aeroelasticity 12-4

( ) ( ) tan0.75

tan2 2

K Q d e Q d ed c e

WQb QbbK

+ + = +

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7eminer & 0ing structure iealiation with

aeroynamic loas

82

81

f

%% cos

*

oC

C

springs resist upwar

an ownwar motion

12-5Purdue Aeroelasticity

tancos

on oLift L q cba

= = +

2cosnq q=

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Static e!uilibrium e!uations

= tant

( ) ( )

=

+

e

bQ

QeKQte

QbQtbK o

2cos

22

n lQ q Sc =

12-6Purdue Aeroelasticity

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"e#lections

+

=

eK

Kb

QK

Qb o

2

tan

1

cos2bending

slope

+

=

eb

K

KQK

Qe o

2

tan

1

cos

twistangle

12-7Purdue Aeroelasticity

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$i#t e##ecti%eness

+

== tancos

o

on SaqLLift

+

=

2tan1

cos

QbKeQKSaqL oon

Substitute for the angles and

12-8Purdue Aeroelasticity

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Fle&ible wing li#t

intermediate result

+= eKbK

KK

QqSaL oo

2

tan1

1

cos

2

tan

=bK

eK

KKQD

n lQ q Sc =

12-9Purdue Aeroelasticity

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Final result

cos

1

l o

D

qSc

L QQ

=

Lift on rigid surface

1

cos 1l oD

LqqSc

q

= lift effecti"eness

efinition

12-10Purdue Aeroelasticity

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'n e&ample wing

=

2

tan1cos

2

0

K

K

e

c

c

b

qqD

2/250 ftlbqo=

let

o

30=

6=c

b1.0=

c

e3=

K

K

12-11Purdue Aeroelasticity

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59992592991591995999'9

9'5

1'9

1'5

2'9

lift effecti"eness "s'ynamic pressure

ynamic pressure ,psf-

lifteffecti"eness unswept wing

i"ergence

9 egrees sweep

15 egrees sweep

unswept wing

$i#t e##ecti%eness %s. !

So what(

)hat are the

conse!uences(

12-12Purdue Aeroelasticity

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Purdue Aeroelasticity 12-13

Fle&ural a&is concept

an attempt to e&plain aeroelastic e##ects

Definition - the line along which the streamwise (or

chordwise) angle of attack does not change when a discrete

load is applied there.

xo

yo

0tan == E

upwar loa

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Purdue Aeroelasticity 12-14

Fle&ural a&is de#inition

)hy the con#using de#initions(

)hat is the di##erence between #le&ural a&is and elastic a&is(

flexuralaxis

xy

upwar

loa

The air is off

0tan == E

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Purdue Aeroelasticity 12-15

Fle&ural a&is concept

an attempt to e&plain aeroelastic e##ects

xo

yo

=

o

o

y

x1tan

0tan == E

=

M

M

K

K

0

0

=

o

o

Px

Py

M

M

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Purdue Aeroelasticity 12-16

Step *1

+ompute angular displacements

=

o

o

Px

Py

K

K

0

01

=

=

K

x

K

y

PxK

yK

KK

P

o

o

oo

o

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Purdue Aeroelasticity 12-17

,se #le&ural a&is de#inition

0tan! ==

K

y

K

xP ooE

0tan == E

tantan =

=

K

K

y

x

o

o

This result always gi"es us a flexural axis location forwar of

the usual elastic axis' :ncrease wing sweep*ac. rotates the

flexural axis further forwar an opens up the istance

*etween aero loas an the hypothetical flexural axis

=

=

K

x

K

y

PxK

yK

KK

P

o

o

oo

o

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Purdue Aeroelasticity 12-18

e&ample

2=

K

K

1=

K

K

3=

K

K

tantan =

=

K

K

y

x

o

o

K

K

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Purdue Aeroelasticity 12-19

Summary

i A loa place at the flexural axis creates no

streamwise angle of attac. at that section

i the flexural axis position epens on the

stiffness ratio an the sweep angle

i the flexural axis an the elastic axis coincie

when there is no wing sweep

i the flexural axis is upstream for a swept *ac.wing an ownstream for a swept forwar

wing