TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 5298 ~ 53
0
4
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.422
5
5298
Re
cei
v
ed Au
gust 26, 20
13
; Revi
sed
Jan
uary 28, 201
4
;
Accepte
d
Febru
a
ry 12, 2
014
Wind-Induced Vibration Analysis of Overhead
Working
Truck
Hongqi Jian
g
1,2
, Shuncai Li
2
, Xianbiao Mao
1
,
1
Chin
a Univ
ers
i
t
y
of Mini
ng &
T
e
chnolog
y;
Xuzho
u
, jia
ngsu,
2210
08; Ch
ina
2
Jiangs
u Norm
al Univ
ersit
y
；
Xuz
h
o
u
,jia
ngs
u, 2211
16; Ch
i
n
a
A
b
st
r
a
ct
As to the co
mp
licate
d
char
acteri
stics of over
hea
d w
o
rking t
r
uck
un
der effe
cts of rando
m
dyna
mi
c
w
i
nd, the tra
d
iti
ona
l
meth
od
is
difficu
lt to refl
e
c
t its dy
n
a
m
ic r
e
spo
n
se
in
rea
l
ti
me, i
n
th
e st
udy; it
prop
ose
s
the ran
d
o
m
w
i
nd i
nduc
ed v
i
b
r
ation r
e
spo
n
s
e
an
alysis
met
hod
bas
ed o
n
the finite
el
e
m
e
n
t metho
d
and
pseu
do-exc
i
tati
on
meth
od. A
n
it reg
a
rds th
e vibr
ati
on
of
the fluctu
ating
w
i
nd lo
ad
as
coher
ent ra
nd
o
m
vibrati
on un
der
stationary ran
d
o
m
excitati
on,
and it us
es D
a
venp
ort w
i
nd velocity sp
ectru
m
w
h
ich d
oes
not
chan
ge w
i
th h
e
ig
ht, the correlati
on of the
w
i
nd exci
tation are considered. It
ta
kes the folding type arm
overh
ead w
o
rk
ing truck as
e
x
ampl
e, the ra
ndo
m w
i
n
d
vib
r
ation
ana
lysis
are p
e
rforme
d, and
it gets
the
accel
e
ratio
n
r
e
spons
e sp
ectr
um a
nd r
oot
me
an
squ
a
re
the
of a
e
ria
l
w
o
rk pl
atfor
m
. T
he
ana
lysis r
e
sults
show
that the
l
o
w
-
order freq
u
ency w
ill c
aus
e
great vi
brati
o
n
of the w
o
rk
p
l
atform, a
nd th
e
vertical
on
e thi
r
d
of the ro
ot-me
an-sq
uare
of a
cceler
a
tion
is
bel
ow
inte
rn
ati
ona
l stan
dards
, it has n
o
unc
omfort
ed
effect o
n
oper
ation w
o
rk
ers.
Ke
y
w
ords
:
the pseu
do-
ex
citation
meth
o
d
, overhe
ad w
o
rkin
g truck, th
e w
i
nd vibrati
o
n respo
n
se, ra
ndo
m
vibrati
o
n
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introducti
on
As a
kind
of engin
eeri
n
g
machine
r
y and e
quipm
e
n
t, the overh
ead
wo
rkin
g
truck i
s
widely
used i
n
shipbuilding, constr
uction, munici
pal
construction, fire
cont
rol, et
c. The
stability of
workin
g pl
atform
and
security are o
n
e
of t
he
key
techn
o
logie
s
of overhea
d
wo
rki
ng t
r
u
c
k
resea
r
ch. Wit
h
the in
cre
a
se of high b
u
il
ding
s,
the op
eration
difficu
lty of
overhea
d wo
rki
ng tru
ck
height i
s
hig
h
e
r a
nd hi
ghe
r; the arm
sle
n
dern
e
ss
ra
tio is
mo
re and more big,
the wind
l
oad effect
is mo
re ap
pa
rent. As the
wind lo
adin
g
may pro
d
u
c
e
large
r
defo
r
m
a
tion and vib
r
ation [1-3], it will
seri
ou
s impa
ct on the safe
ty of
t
he operating arm a
n
d
operatio
n pe
rso
nnel.
Natural win
d
in the pro
c
e
ss of flow
du
e to the influence of vario
u
s ob
sta
c
le
s on the
grou
nd, its speed p
r
e
s
ent
s the ra
ndo
m
fluctuating
chara
c
te
risti
c
s.
It is general
ly believed that
natural
wi
nd i
s
comp
osed
of the
averag
e win
d
a
nd fl
uctuatin
g wi
n
d
[4], the spe
ed of
wind
ha
s an
averag
e
com
pone
nt and
a
pulsating
co
mpone
nt. Th
eref
o
r
e, un
de
r the effe
ct of
natural wi
nd,
the
load
stru
cture
of wind i
s
co
mpos
ed of two part
s
: one i
s
the ave
r
ag
e calm l
oad
u
nder th
e a
c
tion
of the wi
nd; the second
is
fluc
tuating l
o
ad un
de
r the
action
of r
a
n
dom p
u
lse. T
he loa
d
stru
cture
cau
s
e
d
by th
e static defo
r
mation
can
b
e
obtain
ed
th
roug
h
static
analysi
s
of th
e structu
r
e; a
nd
fluctuating
wi
nd component will ca
use the induced vibration of
t
he structure,
the continuous
vibration will
cau
s
e
stru
ctu
r
e fatigue da
mage, and
al
so can cau
s
e
the discomfo
rt of worke
r
s.
In conventio
n
a
l desi
gn, it often take the
wi
nd lo
ad a
s
the static force and then ta
ke the
certai
n wi
nd
vibration
coe
fficient into consi
der
ation,
and the
cal
c
ulatio
n re
sul
t
s ca
n not fu
lly
reflect the dy
namic
re
spo
n
s
e of win
d
lo
ad excitation.
So it is nece
s
sary to ca
rry
out the dyna
mic
respon
se
ana
lysis of a
e
rial
work m
a
chin
ery und
er
th
e
fluctuating
wi
nd loa
d
, in o
r
der to
gra
s
p t
h
e
dynamic perf
ormance of the
structure and improve the re
liability of system design.
2. Basic The
or
y
of Pseud
o
-ex
c
ita
t
ion Metho
d
Acco
rdi
ng to
vibration the
o
ry, unde
r th
e ze
ro
i
n
itial
con
d
ition, the
con
s
tant
co
efficient
linear frequ
en
cy re
spo
n
se functio
n
of the
system
is th
e ratio of inp
u
t
vector and
o
u
tput harm
oni
c
conte
n
t, namely that:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Wind
-Indu
ce
d Vibration A
nalysi
s
of Overhe
ad Worki
ng Tru
c
k (Ho
ngqi Ji
ang
)
5299
H
Xt
Y
t
(1)
Whe
r
e,
H
is f
r
e
quen
cy
re
sp
onse fun
c
tio
n
；
X
t
is F
o
u
r
ier
tr
an
s
f
or
m of
x
t
；
Yt
is Fouri
e
r tra
n
sform of
y
t
.
Whe
n
the
lin
ear
syste
m
s i
s
affe
cted
by
the statio
nary
ran
dom
excit
a
tion fun
c
tion
F
t
of
the spe
c
tral d
ensity
FF
S
, and the respon
se of
powe
r
sp
ect
r
um is a
s
(2
) [5-6].
2
XX
FF
SH
S
(2)
Whe
r
e
H is the freq
uen
cy respon
se fu
nction,
which
mean
s wh
en
the rand
om
excitation
of incentive i
s
t
i
e
, the corre
s
p
ondin
g
harm
onic
re
spo
n
se is
it
X
tH
e
. If
the incentive
t
i
e
is
multiplied b
y
the con
s
t
ant
F
F
S
, namely
that co
nst
r
uct
a virtu
a
l incentives function
it
FF
F
tS
e
, then the correspon
ding vi
rtual re
sp
on
se is:
it
FF
X
tS
H
e
(3)
The a
c
tual
resp
on
se
can
be obtai
ned
from
po
we
r spe
c
tral de
n
s
ity and
cross po
we
r
spe
c
tru
m
den
sity and the calcul
ation formula are as f
o
llows:
2
2
F
FX
X
X
XX
H
S
S
(4)
it
it
F
FF
F
F
F
F
X
F
XS
e
S
H
e
S
H
S
(5)
it
i
t
F
FF
F
F
F
X
F
X
FS
H
e
S
H
e
H
S
S
(6)
Whe
r
e
X
X
S
re
pre
s
ent
s the
actu
al resp
onse of th
e
po
wer spe
c
tral de
nsity,
F
X
S
rep
r
e
s
ent
s th
e actu
al in
ce
ntive and the
actual
re
sp
o
n
se of
the
p
o
we
r spe
c
tra
l
den
sity,
X
F
S
rep
r
e
s
ent
s the actual resp
onse and a
c
t
ual in
centive cro
s
s-po
wer
spe
c
tral d
e
n
s
ity.
If the system
has m
o
re tha
n
one
re
spo
n
s
e, th
ro
ugh t
he type (4
) ~
(6) type, the
available
power spe
c
trum matrix ca
n be obtain:
T
FF
SX
X
，
T
FX
SF
X
，
T
XF
SX
F
Whe
r
e * rep
r
ese
n
ts compl
e
x conju
gate
and T re
pre
s
ents tra
n
sp
ose
3.
Wind Vibr
ation Respo
n
se An
aly
s
is
Fluctuatin
g wind loa
d
s
on
the structu
r
e ca
used by
vibration, ca
n be lo
oked
as mo
re
coh
e
re
nt ran
dom vib
r
ation
problem
un
d
e
r
stationa
ry rand
om excit
a
tion,
the dyn
a
mic
differe
ntial
equatio
n is a
s
(7
).
M
Zt
C
Z
t
K
Zt
F
t
(7)
Whe
r
e,
M
、
C
、
K
repre
s
e
n
ts th
e mass, dam
ping an
d
st
if
f
nes
s mat
r
ix
of stru
cture,
r
e
spec
tively;
t
Z
re
pre
s
e
n
ts t
he n
ode
di
spl
a
cem
ent ve
ct
or;
t
F
rep
r
e
s
ent
s the
wind
lo
ad
vector of fluct
uating.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5298 – 53
04
5300
Acco
rdi
ng to
the vibration mode de
compo
s
ition
method, the
Equation (7
) can b
e
rewritten a
c
cordin
g to the vibration mo
d
e
[7, 8].
1
q
jj
j
zt
u
t
ut
(8)
Whe
r
e, q is the sele
cte
d
numbe
r of
vibration m
ode,
j
u
rep
r
e
s
ents the di
splacement,
j
rep
r
e
s
ent
s vibration ve
ctor.
Acco
rdi
ng to
the spe
c
ification, the ge
neral
ta
ke
Davenpo
rt fluctuating win
d
velocity
spe
c
tru
m
is take
n as the
excitation sp
ectru
m
;
it does not chang
e with
height,
since the po
wer
spe
c
tru
m
of its expre
s
sion i
s
:
22
10
0
0
4
2
3
10
0
4
12
00
,
1
ff
KV
x
n
Sn
x
V
nx
(9)
Among th
em:
2
n
represents the p
u
lsating
wind
freq
uen
cy;
10
V
rep
r
e
s
e
n
ts ave
r
ag
e
wind
spe
ed when t
he heig
h
t is 1
0
m; K is the
coeffi
ci
ent wh
ich is related
to surfa
c
e rou
ghne
ss.
As the flu
c
tu
ating wi
nd
ra
ndomn
e
ss, if
take th
e
correlation
bet
ween diffe
rent
ran
dom
excitation,
coh
, the level of cross
spe
c
tru
m
of fluc
tuating win
d
velo
city can b
e
e
x
presse
d
as
[9]:
ij
jj
ii
ij
coh
S
S
S
(10)
Whe
r
e
10
2
1
2
z
2
y
2
V
z
C
y
C
x
n
coh
x
C
exp
10
C
C
16
C
z
y
x
,
repre
s
e
n
t the space attenuatio
n coeffici
ent
z
y
x
,
,
are the coordinate differe
nce of the two points.
Thro
ugh
(7
) a
nd (8), th
e lo
ad p
o
we
r
sp
e
c
trum
matrix
PP
S
can b
e
obtai
ne
d, obviou
s
ly
that
PP
S
is the Hermite matrix
, so it can be deco
m
po
se
d throug
h LDL
*
method. Thus th
e
(11
)
is obtai
n
ed.
T
PP
DL
L
S
*
(11)
Whe
r
e, L is t
he triang
ula
r
matrix, D is a diago
nal matrix.
If tak
e
the firs
t k
c
o
lumn if the vec
t
or
k
L
, D no
k
diag
o
nal ele
m
ent
s
k
d
,
c
a
n co
ns
tr
uc
t
virtual excitation vector n a
s
follows:
n
2
1
k
e
d
L
t
x
t
i
k
k
k
,
,
,
,
~
(12)
The virtual re
spo
n
se of t
he stru
cture
can
be obtaine
d.
t
i
k
k
T
k
e
d
L
H
t
z
~
(13)
Whe
r
e
H
repre
s
ent
s the freq
uen
cy respon
se fun
c
tion.
22
1
2
j
jj
j
H
i
(14)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Wind
-Indu
ce
d Vibration A
nalysi
s
of Overhe
ad Worki
ng Tru
c
k (Ho
ngqi Ji
ang
)
5301
Whe
r
e
j
、
j
rep
r
esent the n
a
tural fre
que
ncy and
dam
ping ratio, Throu
gh (3), the
Power s
p
ec
trum matrix
z
is as
(1
5):
T
k
n
1
k
k
zz
z
z
S
~
~
(15)
4. Wind Vibration Respo
n
se An
aly
s
is
In the study, the wo
rk
high
arm is
co
mp
ose
d
of re
cta
ngula
r
cro
ss
se
ction of the
uppe
r
arm, lowe
r arm. The uppe
r arm head
wo
rk platfo
rm are used fo
r tra
n
sp
orting p
e
o
p
le and go
od
s,
the arm
up
a
nd do
wn
are
throu
gh the
oil cylind
e
r lif
ting, and a
d
o
p
ts the lig
ht
vehicle
ch
assis
(whi
ch
is
as sho
w
n
in Fi
gure
1).
Wh
en the
wo
rk
arm i
s
in th
e
elevated p
o
s
ition, the
st
eel
pro
c
e
ssi
ng
can b
e
a
dopt
ed in
oil
cyli
nder,
upp
er
arm
and
lo
wer
arm
can
use
the
ele
m
ent
simulatio
n
of Euler Bern
oulli beam, oil cylinde
r can be
simu
lated throp
u
gh usin
g a one-
dimen
s
ion
a
l bar ele
m
ent. the co
nstraint pro
c
e
ssi
ng a
r
e adopte
d
in the lower a
r
m oil cylinde
r an
d
the lowe
r arm
,
the simplified operation a
r
m is a
s
sh
o
w
n in Figure 2 ,
It is the finite
element mod
e
l
whi
c
h is
com
posed of sev
en nod
es a
n
d
seven unit
s
.
The
wo
rki
n
g
hei
ght i
s
a
bout 1
4
,
13
5.
9
5
lm
，
36
5.
6
lm
，
23
0.
4
9
5
lm
，
56
1.
4
lm
，
67
0.
45
l
m
，，
E=207
00M
Pa
Upp
e
r arm
A
1
=3.8
6×1
0
-3
m2
，
I1=3.85×10
-5
m4
, L
o
w
e
r
ar
m A2=
3
.64×
1
0
-
3
m2
，
I2=3.07×10
-5
m4. Oil
cylinde
r A=7.
53×10
-3
m2
，
I
=
1.39
×1
0
-5
m4.
Land
scap
e coefficient K is 0.039, the basi
c
wi
n
d
pre
s
sure i
s
0.9 KN/m2, the Davenpo
rt
fluctuating
wi
nd spee
d spe
c
trum i
s
lo
oked a
s
the
sta
ndard wi
nd
speed. T
h
ro
ug
h the softwa
r
e of
ANSYS, the f
i
nite element model of operating arm is
established. In the model analysis, the fi
rst
4 ord
e
r vib
r
a
t
ion mode i
s
sele
cted, th
e model
dam
ping ratio is
set a
s
0.02.
The de
scri
ption
mode shap
es and diag
ram
are a
s
sh
own
in Table 1 an
d Figure 3.
Figure 1. Di
agra
m
of the Wo
rkin
g Arm
Table 1. The
First Fo
ur O
r
der Vibration
Mode
Orde
r time
Natural fre
quenc
y /Hz
Modal descriptions
1
2
3
4
4.85
12.07
18.40
48.23
Overall vertical arm sw
inging
Upper a
r
m bent
Upper an
d lo
w
e
r
arms
Under th
e arms
bent
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046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5298 – 53
04
5302
Figure 2. The
Finite Element Model Ope
r
ation
Ar
m
Figure 3. The
First 4 Order Modal Vibrati
on
Mode
In the frequ
ency ra
nge
of 0.2Hz to
50Hz, throu
g
h
the Matlab
simulation
prog
ram,
the assignm
ents a
r
m at the front of node 1 h
o
ri
zontal and ve
rtical di
spla
cement and t
he
accele
ration
power spe
c
trum are
sho
w
n in Figure 4 to Figure 7.
Figure 4. Hori
zontal Po
we
r Spectrum of Nod
e
1
Figure 5. Acceleratio
n
Power Spe
c
trum
of
N
o
de
1
Figure 6. Vertical Di
spl
a
ce
ment Powe
r
Spectrum of Nod
e
1
Figure 7. Vertical Accele
r
at
ion Powe
r
Spectrum No
de 1
From the Fi
g
u
re 4 to Fig
u
re 7 it can b
e
see
n
that, in the first order natural frequ
ency of
5Hz a
n
d
second
order na
tural frequ
en
cy 12
Hz, vi
bration
re
spo
n
se of
nod
e 1
work platform
is
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TELKOM
NIKA
ISSN:
2302-4
046
Wind
-Indu
ce
d Vibration A
nalysi
s
of Overhe
ad Worki
ng Tru
c
k (Ho
ngqi Ji
ang
)
5303
obviou
s
, in the othe
r fre
quen
cy, the
vibration i
s
relatively sma
ll, the natura
l
freque
ncy
of
vibration fre
q
uen
cy and th
e main vibrati
on mode freq
uen
cy are ne
arly the sam
e
.
Re
cent stu
d
i
e
s have
sh
o
w
n that [10], freque
ncy
se
nsitive freq
ue
ncy of huma
n
body in
the up and do
wn fluctuatio
n
is betwee
n
4
and 8Hz,
an
d the sen
s
itive freque
ncy o
f
vibration ba
ck
and fo
rth i
s
betwe
en 1
-
2
H
z,
and
so
me a
r
ea
of the b
ody can
pro
d
u
c
e
re
sonan
ce,
with
the
increa
se
of frequ
en
cy, se
nsitivity, and
the vi
bratio
n will
influen
ce th
e
comf
ort. The
severe
vibration resp
onse is le
ss t
han 30
Hz, an
d the influen
ce of vertical vibration o
n
co
mfort is ab
out
70%, hori
z
o
n
t
al vibration
is a
bout 1
2
%. In order
to
study the
effect of vib
r
ati
on on
pe
rson
nel
comfo
r
t deg
ree, the resp
onse spe
c
tru
m
is
cal
c
ulat
ed through
p
s
eu
do-excitat
i
on metho
d
,
i
n
freque
ncy ra
nge of 1 to 20Hz, a serie
s
of discrete freque
ncy poin
t
s are sele
cted, throug
h the
type (13), the
mean sq
ua
re
root of accel
e
ration
can b
e
cal
c
ulate
d
.
r
r
f
f
zz
d
S
12
.
1
89
.
0
3
1
(16)
Table 2 an
d table 3 lists th
e operating a
r
m head
re
sp
ectively the horizontal an
d vertical
1/3 freq
uen
cy
multiplicatio
n
ope
ration
pl
atform a
c
cele
ration
root m
ean
squ
a
re.
Acco
rdi
ng to
the
internatio
nal
stand
ard ISO
2631 b
ody fatigue/effici
e
n
cy lower lim
it, the accel
e
r
ation root m
ean
squ
a
re
of the
type of overhead
wo
rki
n
g
truck are
sta
ndard 8 ho
urs working effi
cien
cy und
er
the
lowe
r limit, which
ca
n en
sure th
at wo
rkers in eig
h
t small ba
sic i
s
not influen
ce
d by win
d
vibration
in the working time.
Table 2. Mea
n
Square Ro
ot of Accele
ra
tion
of One T
h
ird Frequ
en
cy Dou
b
ling (hori
z
ontal
)
Center
frequenc
y /Hz
1 2 3
4 5 6
7
8
9
10
1
3
/
1
/
s
m
0.002
5
0.003
9
0.005
2
0.006
5
0.008
1
0.010
3
0.018
5
0.024
2
0.016
9
0.015
4
Center
frequenc
y /Hz
11 12 13
14 15 16
17
18
19 20
1
3
/
1
/
s
m
0.031
6
0.084
5
0.090
1
0.087
6
0.065
7
0.018
2
0.011
2
0.010
2
0.010
1
0.009
7
Table 3. Mea
n
Square Ro
ot of Accele
ra
tion
of One T
h
ird Frequ
en
cy Dou
b
ling (vertical
)
Center
frequenc
y /Hz
1
2 3 4 5 6 7
8 9
10
1
3
/
1
/
s
m
0.006
5
0.0072
0.0151
0.0174
0.0194
0.033
0.0572
0.0893
0.0568
0.0463
Center
frequenc
y/Hz
11
12 13 14 15 16 17
18 19
20
1
3
/
1
/
s
m
0.095
2
0.255
0.2906
0.2649
0.1936
0.0611
0.0403
0.0387
0.0348
0.0277
5. Conclusio
n
As the
com
p
l
e
x ch
ara
c
teri
stics of
wo
rki
ng
tru
c
k u
n
d
e
r
rand
om
dynamic wi
nd l
oad, the
traditional
de
sign
ca
n not reflect its dyn
a
m
ic respon
se
accurately, in the stu
d
y, the finite elem
ent
method
and
pse
udo
-excit
ation meth
od
are
ado
pted
in the
wind
indu
ced
vibration
re
spo
n
s
e
analysi
s
of worki
ng tru
c
k, it can both a
c
curately
reflects the o
peration arm vib
r
ation respon
se
cau
s
e
d
by a f
l
uctuatin
g wi
n
d
load,
and
al
so
can
imp
r
o
v
e the efficie
n
cy of
comp
u
t
ing, and it
ca
n
provide a fea
s
ible
way for wind in
du
ced
vibration an
al
ysis of wo
rki
ng truck.
Thro
ugh the
analysi
s
of the level of operatio
n pl
atform, vertical displa
ce
m
ent and
accele
ration
power
sp
ectrum, the first and
se
co
nd
ord
e
r frequ
ency vib
r
atio
n re
sp
on
se
are
signifi
cantly, and the vert
ical vibratio
n
resp
on
se i
s
gre
a
ter th
an the hori
z
ontal vibration
respon
se.
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5298 – 53
04
5304
One third a
cceleratio
n
mea
n
squ
a
re
root
of the worki
n
g
arm op
erati
on platform a
t
each
freque
ncy poi
nt is belo
w
the intern
atio
nal body fatigue/efficie
n
cy
standa
rd
s of
ISO2631, an
d it
has n
o
sig
n
ificantly effects
on the wo
rkers.
Referen
ces
[1]
Sun D
o
n
g
ke, L
i
n L
i
n
ha
o, Z
h
ang
Yah
u
i, etc.
T
he
w
i
nd
in
du
ced ra
nd
om vi
bratio
n a
nal
ys
i
s
of comp
le
x
structures.
Jou
r
nal of mech
an
ical e
ngi
ne
erin
g.
2001; 5(
3): 55-61.
[2]
XU
You
lin, Z
H
ANG W
ensho
u
,
KO J M, et al.
T
he Pseu
do -
e
x
citatio
n
met
hod for
vibr
atio
n an
al
ysis
o
f
w
i
nd - Ex
citedstructures.
Jou
r
nal of W
i
nd E
ngi
neer
in
g and
Industrial Aer
o
Dyna
mics
. Tu
rn
ed
1
9
99:
443-
454.
[3]
WT
X u, JHL in, YHZ
Hang. 2 d movin
g
elem
ent method
for
rand
om vibrati
on an
al
ys
is of
of vehicl
es
o
n
Kirchh
off plate
w
i
th K
e
lvi
n
fo
und
atio
n.
Jour
nal
of Lati
n
A
m
er
ic
a - S
o
li
d
and Str
u
ctures
. 200
9; 6:16
9-
183.
[4]
W
ang F
a
n
g
li
n, Gao
w
e
i, C
h
en Ji
anj
un. Pr
escrib
ed
b
y
rit
ual l
a
w
i
n
ce
nti
v
e ante
n
n
a
structure u
nde
r
rand
om vibrati
on an
al
ysis.
Jo
urna
l of eng
ine
e
rin
g
mecha
n
ic
s
. 2006; 23(
2): 168-
172.
[5]
Lin
ha
o Z
h
an
g Ya
hui.
Ra
nd
om vibr
atio
n o
f
the ps
eu
do-
exc
i
tatio
n
met
hod. B
e
ij
in
g: s
c
ienc
e pr
ess.
200
4.
[6]
Sun Z
u
o
y
u,
w
a
ng h
u
i. Structu
r
al ra
nd
om vibr
ation an
al
ysis
of
eq
uiva
lent e
x
citati
on
m
e
tho
d
.
Journ
a
l of
eng
ine
e
ri
ng mecha
n
ics
. 20
10
; 27(1): 20-23.
[7]
W
ang
w
e
i
do
n
g
, Sun
Li
nin
g
Du Z
h
i
jia
ng. M
o
ve th
e arm v
i
bratio
n a
nal
ys
i
s
base
d
on
ps
eud
o-e
x
citati
on
method.
Jour
n
a
l of jili
n un
iver
sity (engi
neer
in
g scienc
e).
201
0; 40(4): 10
82-
108
5.
[8]
Bu Guo Xio
n
g
T
an Ping, zh
ang
yi
ng, etc. Large ra
nd
o
m
w
i
nd vi
br
ati
on resp
ons
e o
f
tall buil
d
in
g
analy
sis.
Journ
a
l of Harb
in ins
t
itute of technol
ogy.
201
0; (2): 175-
179.
[9]
Sun Jia
n
rui
Xu Ch
angs
he
ng
. Marine d
e
ck
cr
ane b
oom
structure
w
i
n
d
vi
bratio
n res
p
onse stu
d
y
.
Journ
a
l of liftin
g
the transp
o
rt mac
h
i
nery
. 20
09; 12: 20-
23.
[10]
Li Li
ng
xuan S
ong Gu
iqi
u
, flo
w
,
etc. Base
d
on ANSYS,
th
e an
al
y
s
is of t
he effect of na
tural vibr
atio
n
character
i
stics of passen
ger tr
ain.
Jour
nal
of vibrati
on an
d s
hock
. 201
1; 30
(1): 121-12
3.
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