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Sti
rlin
g
Sti
rlin
g D
ynam
ics
Dynam
ics
Pa
rtia
l W
ing
Pa
rtia
l W
ing
--Bo
x T
estin
g a
nd
No
nB
ox T
estin
g a
nd
No
n--L
ine
ar
Da
mp
ing
Id
en
tifica
tio
nL
ine
ar
Da
mp
ing
Id
en
tifica
tio
n
Pre
se
nta
tio
n to
:P
rese
nta
tio
n to
:
No
nlin
ea
r N
on
line
ar A
ero
ela
stic
Ae
roe
lastic
Sim
ula
tio
n fo
r C
ert
ific
atio
nS
imu
latio
n fo
r C
ert
ific
atio
n
Un
ive
rsity o
f L
ive
rpo
ol 1
3U
niv
ers
ity o
f L
ive
rpo
ol 1
3--1
5 S
ep
tem
be
r, 2
01
0
15
Se
pte
mb
er,
20
10
Intr
od
ucti
on
•D
r. S
imo
n H
an
co
ck
•C
aro
lin
e H
avil
l
•P
roje
ct
Co
nsu
ltan
t –
Pro
f. J
an
Wri
gh
t
•P
resen
tati
on
Str
uctu
re•
Pre
sen
tati
on
Str
uctu
re
•T
he P
art
ial W
ing B
ox (
PW
B)
•M
odal T
esting
•F
ree-R
ele
ase T
esting
•N
on-L
inear
Dam
pin
g A
naly
sis
•C
onclu
sio
ns
2
Ob
jecti
ves
•O
vera
ll C
usto
mer
Ob
jecti
ve
•Is
there
any e
vid
ence o
f non-lin
ear
dam
pin
g in t
he
com
posite w
ingbox/e
ng
ine s
tructu
re that w
ould
alle
via
te t
he p
redic
ted g
ust / tu
rbule
nce r
esponse
loads?
•S
tirl
ing
Dyn
am
ics O
bje
cti
ve
•C
onduct
physic
al te
sting a
nd s
ubsequent
analy
sis
to
investigate
the d
am
pin
g c
hara
cte
ristics o
f th
e s
yste
m.
3
Part
ial
Win
g B
ox (
PW
B)
4
Ch
all
en
ges
•A
pp
roach
•G
VT
to identify
modes a
nd c
om
pare
again
st
dynam
ic
FE
model
•U
se identified m
odes t
o initia
te n
on-lin
ear
analy
sis
•H
igh a
mplit
ude im
puls
e t
o forc
e a
non-lin
ear
response
•C
hall
en
ges
•C
hall
en
ges
•H
ow
to e
xcite a
larg
e a
nd h
eavy s
tructu
re for
modal
testing?
•H
ow
to d
eflect
the P
WB
whils
t allo
win
g a
‘cle
an’
rele
ase?
•H
ow
to a
naly
se o
bta
ined d
ata
in a
n a
ppro
priate
m
anner
to e
xtr
act tr
ue m
odal dam
pin
g f
or
the P
WB
?
5
Mo
dal
Testi
ng
Mo
dal
Testi
ng
Pre
se
nta
tio
n to
:P
rese
nta
tio
n to
:
No
nlin
ea
r A
ero
ela
stic S
imu
latio
n fo
r C
ert
ific
atio
nN
on
line
ar A
ero
ela
stic S
imu
latio
n fo
r C
ert
ific
atio
n
Un
ive
rsity o
f L
ive
rpo
ol 1
3U
niv
ers
ity o
f L
ive
rpo
ol 1
3--1
5 S
ep
tem
be
r, 2
01
0
15
Se
pte
mb
er,
20
10
PW
B D
yn
am
ic T
esti
ng
8
23
4 9
5 10
6 11
7 12
121
20
16
14
22
21
20
19
18
17
16
15
14
13
12
11
10
13
Ori
gin
15
19
Ch
an
1 [
W.1
.Y]
Ch
an
2 [
W.1
A.Y
]
Ch
an
3 [
W.2
.Z]
Ch
an
4 [
W.3
.Z]
Ch
an
5 [
W.4
.Z]
Ch
an
6 [
W.5
.Z]
Ch
an
7 [
W.6
.Z]
Ch
an
8 [
W.7
.Z]
Ch
an
9 [
W.8
.Z]
Ch
an
10 [
W.8
.X]
Ch
an
11
[W.9
.Z]
Ch
an
12 [
W.9
.X]
Ch
an
13
[W.1
0.Z
]
Ch
an
14
[W.1
0.X
]
Ch
an
15
[W.1
1.Z
]
Ch
an
16
[W.1
2.Z
]
Ch
an
17
[W.1
2.X
]
Ch
an
18
[W.1
3.Z
]
Ch
an
19
[E.1
4.Z
]
Ch
an
20
[E.1
4.Y
]
Ch
an
31
[Fo
rce
]
Ch
an
28
[W.1
9.Y
]
Ch
an
29
[W.1
9.Z
]
Ch
an
30
[W.2
1.Z
]
Ch
an
22 [
E.1
6.Z
]
Ch
an
23 [
E.1
6.Y
]
Ch
an
32
[La
ser]
8
23
4 9
5 10
6 11
7 12
121
20
16
14
22
21
20
19
18
17
16
15
14
13
12
11
10
13
Ori
gin
15
19
Ch
an
1 [
W.1
.Y]
Ch
an
2 [
W.1
A.Y
]
Ch
an
3 [
W.2
.Z]
Ch
an
4 [
W.3
.Z]
Ch
an
5 [
W.4
.Z]
Ch
an
6 [
W.5
.Z]
Ch
an
7 [
W.6
.Z]
Ch
an
8 [
W.7
.Z]
Ch
an
9 [
W.8
.Z]
Ch
an
10 [
W.8
.X]
Ch
an
11
[W.9
.Z]
Ch
an
12 [
W.9
.X]
Ch
an
13
[W.1
0.Z
]
Ch
an
14
[W.1
0.X
]
Ch
an
15
[W.1
1.Z
]
Ch
an
16
[W.1
2.Z
]
Ch
an
17
[W.1
2.X
]
Ch
an
18
[W.1
3.Z
]
Ch
an
19
[E.1
4.Z
]
Ch
an
20
[E.1
4.Y
]
Ch
an
31
[Fo
rce
]
Ch
an
28
[W.1
9.Y
]
Ch
an
29
[W.1
9.Z
]
Ch
an
30
[W.2
1.Z
]
Ch
an
22 [
E.1
6.Z
]
Ch
an
23 [
E.1
6.Y
]
Ch
an
32
[La
ser]
X
Z
Y
18
16
15
17
Ch
an
21
[E.1
5.Z
]
Ch
an
25
[E.1
7.X
]
Ch
an
24 [
E.1
6.X
]
Ch
an
26 [
E.1
8.Y
]
Ch
an
27
[E
.18.X
]
X
Z
Y
X
Z
Y
Z
Y
18
16
15
17
Ch
an
21
[E.1
5.Z
]
Ch
an
25
[E.1
7.X
]
Ch
an
24 [
E.1
6.X
]
Ch
an
26 [
E.1
8.Y
]
Ch
an
27
[E
.18.X
]
7
Mo
dal
Testi
ng
•32 P
iezo
ele
ctr
ic a
ccele
rom
ete
rs
•R
ib 1
6, w
ing
tip
an
d e
ng
ine e
xcit
ati
on
•Id
en
tifi
cati
on
of
mo
des
•F
orc
e levels
up
to
+/-
400 N
•S
wept sin
e•
Sw
ept sin
e
•S
tepped s
ine
•B
urs
t ra
ndom
•H
ard
att
ach
men
t p
oin
t at
rib
16
•V
acu
um
pad
at
win
g t
ip (
fore
/aft
) an
d e
ng
ine (
late
ral)
•F
orc
e h
am
mer
tests
8
Sh
aker
9
Mo
dal
Test
Resu
lts
Mo
de
Nu
mb
er
Calc
ula
ted
F
req
uen
cy
/ [H
z]
Measu
red
F
req
uen
cy
/ [H
z]
Dam
pin
g/ [%
]D
escri
pti
on
13.8
23.6
80.4
8W
ing
vert
ical b
en
din
g 1
24.9
04.7
80.3
9V
ert
ical b
en
din
g 1
wit
h e
ng
ine p
itch
36.4
56.2
50.3
7E
ng
ine y
aw
411
.36
--
Win
g o
vert
on
e b
en
din
g w
ith
win
g f
ore
an
d a
ft.
512.9
4-
-W
ing
fo
re a
nd
aft
615.8
614.2
11.4
7W
ing
overt
on
e b
en
din
g a
nd
en
gin
e p
itch
726.4
816.1
61.6
6O
ute
r w
ing
to
rsio
n. D
uring the test engin
e
late
ral a
s w
ell
829.4
0-
-W
ing
fo
re a
nd
aft
overt
on
e
8A
-18.2
02.0
7W
ing tors
ion w
ith s
ym
path
etic e
ngin
e y
aw
and
pitch
934.6
332.2
71.2
0
Win
g 2
nd
overt
on
e b
en
din
g a
nd
en
gin
e a
nd
o
ute
r w
ing
to
rsio
nM
easure
d m
ode h
as o
vert
one b
endin
g a
nd
engin
e p
itch. N
o tors
ion o
bserv
ed
10
58.1
162.8
20.3
6E
ng
ine y
aw
an
d w
ing
ben
din
gN
ote
no w
ing b
endin
g o
bserv
ed d
uring test
10
Fre
eF
ree--R
ele
as
e T
esti
ng
Rele
as
e T
esti
ng
Pre
se
nta
tio
n to
:P
rese
nta
tio
n to
:
No
nlin
ea
r A
ero
ela
stic S
imu
latio
n fo
r C
ert
ific
atio
nN
on
line
ar A
ero
ela
stic S
imu
latio
n fo
r C
ert
ific
atio
n
Un
ive
rsity o
f L
ive
rpo
ol 1
3U
niv
ers
ity o
f L
ive
rpo
ol 1
3--1
5 S
ep
tem
be
r, 2
01
0
15
Se
pte
mb
er,
20
10
Rele
ase M
ech
an
ism
12
Fre
e R
ele
ase
13
An
aly
sis
of
Dam
pin
g
An
aly
sis
of
Dam
pin
g
Ch
ara
cte
risti
cs
Ch
ara
cte
risti
cs
Pre
se
nta
tio
n to
:P
rese
nta
tio
n to
:
No
nlin
ea
r A
ero
ela
stic S
imu
latio
n fo
r C
ert
ific
atio
nN
on
line
ar A
ero
ela
stic S
imu
latio
n fo
r C
ert
ific
atio
n
Un
ive
rsity o
f L
ive
rpo
ol 1
3U
niv
ers
ity o
f L
ive
rpo
ol 1
3--1
5 S
ep
tem
be
r, 2
01
0
15
Se
pte
mb
er,
20
10
Ex
pe
cte
d N
on
-Lin
ea
r D
am
pin
g T
ren
d
•S
imil
ar
test
perf
orm
ed
in
th
e 1
950s:
•T
est conducte
d o
n a
modifie
d w
ing:
C-4
6D
Aircra
ft.
•T
est specim
en v
ibra
ted a
t bendin
g m
ode @
1.6
9H
z
•O
nly
first 2-3
cycle
s s
how
ed a
ny indic
ation o
f
15•
Only
first 2-3
cycle
s s
how
ed a
ny indic
ation o
f
hig
her
frequency m
odes.
•D
am
pin
g o
f bendin
g m
ode f
ound t
o incre
ase:
from
0.0
02 @
am
plit
ude o
f ±
0.0
5
to0.0
06 @
am
plit
ude o
f ±5
•A
ero
dyn
am
ic d
am
pin
g w
ou
ld s
ho
w a
lin
ear
incre
ase o
f d
am
pin
g w
ith
am
pli
tud
e
Es
tim
ati
on
of
No
n-l
ine
ar
Da
mp
ing
fr
om
Fre
e D
ec
ay
Re
sp
on
se
Da
ta
•F
or
an
SD
oF
no
n-l
inear
syste
m:
•C
ycle
-by-c
ycle
logarith
mic
decre
ment
analy
sis
would
yie
ld a
variation o
f in
sta
nta
neous d
am
pin
g a
gain
st
am
plit
ude.
•A
naly
sis
would
be p
seudo o
r pie
cew
ise lin
ear
•A
naly
sis
would
be p
seudo o
r pie
cew
ise lin
ear
•F
or
an
MD
oF
no
n-l
inear
syste
m
•P
resence o
f m
ore
than o
ne m
ode m
eans t
hat any
SD
oF
appro
ach is m
eanin
gle
ss
Unle
ss
it is p
ossib
le t
o d
ecouple
the m
odes into
SD
oF
usin
g a
modal tr
ansfo
rmation
•A
ltern
atively
an M
DoF
curv
e f
itte
r w
ould
need t
o b
e
em
plo
yed;
analy
sis
would
be p
iecew
ise lin
ear
16
Th
eo
reti
ca
l In
ve
sti
ga
tio
n f
or
an
MD
oF
S
ys
tem
•A
naly
sis
pro
gra
m b
ased
on
th
e P
oly
refe
ren
ce m
eth
od
w
ith
ab
ilit
y t
o
•U
se tim
e o
r am
plit
ude “
bin
s”
•U
se s
ingle
or
multip
le t
ransducers
•T
ransfo
rm to m
odal coord
inate
s•
Tra
nsfo
rm to m
odal coord
inate
s
•T
heo
reti
cal 3D
oF
mo
dal m
od
el u
sed
to
test
pro
gra
m:
•M
odes e
xtr
acte
d f
rom
FE
model.
•Q
uadra
tic d
am
pin
g a
pplie
d t
o b
endin
g m
ode.
•T
heo
reti
cal te
st
cases
•T
ime b
ins m
ore
suitable
than a
mplit
ude b
ins
•T
ransfo
rmin
g to m
odal coord
inate
s m
akes a
naly
sis
pote
ntially
sim
ple
r1
7
Te
st
Da
ta
Sa
mp
le r
ate
:
25
6 p
ts /
se
c
18
25
6 p
ts /
se
c
•D
om
inate
d b
y M
od
es 1
an
d 2
•S
om
e e
vid
en
ce o
f 2 v
ery
clo
se m
od
es a
rou
nd
3.5
-3.6
Hz
An
aly
sis
of
Fre
e-R
ele
as
e R
es
po
ns
es
•It
is
po
ss
ible
to
an
aly
se
th
e d
ata
in
on
e o
f s
ev
era
l w
ays
•T
ip d
isp
lace
men
t
•S
ing
le / m
ultip
le a
cce
lera
tion
•M
od
al a
cce
lera
tion
•M
od
el a
cc
ele
rati
on
s o
bta
ine
d u
sin
g m
od
e s
ha
pe
s
ob
tain
ed
fro
m G
VT
ob
tain
ed
fro
m G
VT
•7
acce
lera
tion
s fro
m w
ing
& e
ng
ine
an
aly
se
d
•T
ran
sfo
rmed to
2 m
od
es u
sin
g p
se
ud
o-inve
rse.
•T
ime
da
ta d
ec
ima
ted
by f
ac
tor
of
16
to
re
du
ce
sa
mp
le r
ate
s
o t
ha
t p
oin
ts p
er
cyc
le a
re o
f o
rde
r (4
/5)
•C
on
sid
er
en
tire
tim
e h
isto
ry i
nit
ially (
i.e
. n
o b
ins
) th
en
la
ter
an
aly
se
re
sp
on
se
s in
mu
ltip
le o
ve
rla
pp
ing
bin
s
19
Mo
de
Sh
ap
es
fo
r M
od
es
1 a
nd
2 i
nv
olv
e
dif
fere
nt
Re
lati
ve
Win
g /
En
gin
e M
oti
on
s
Mode 1
has
win
g /
engin
e in
phase
Mode 2
has
win
g /
engin
e
out of phase
20
Vari
ati
on
of
Fre
qu
en
cy/D
am
pin
g w
ith
Am
plitu
de:
Mo
de 1
•O
nly
po
ssib
le t
o c
on
sid
er
en
tire
tim
e h
isto
ry d
ue t
o
pre
sen
ce o
f tw
o c
lose
freq
uen
cie
s m
od
es.
•D
am
pin
g s
ho
ws a
lin
ear
•D
am
pin
g s
ho
ws a
lin
ear
incre
ase, as e
xp
ecte
d f
or
qu
ad
rati
c d
am
pin
g
21
Vari
ati
on
of
Fre
qu
en
cy/D
am
pin
g w
ith
Am
plitu
de:
Mo
de 2
•(A
lmo
st)
SD
OF
decay
fro
m m
od
al
tran
sfo
rmati
on
.
•N
um
ber
of
overl
ap
pin
g t
ime b
ins
22o
verl
ap
pin
g t
ime b
ins
used
on
resp
on
se f
or
each
lo
ad
•D
am
pin
g t
ren
d -
fitt
ed
cu
bic
cu
rve.
Re
sult
s su
pp
ort
ed
by
lo
g-d
ec
an
aly
sis
of
SD
OF
de
cay
.
Co
mp
ari
so
n o
f N
orm
ali
sed
Mo
dal D
am
pin
g v
s R
MS
Mo
dal A
ccele
rati
on
wit
h M
eta
llic
Win
g R
esu
lts
Test data
norm
alis
ed
for
0.4
4%
dam
pin
g
and 0
.2 r
ms
23
Su
mm
ary
of
Resu
lts
•M
od
e 2
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24
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26
Qu
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