TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 14, No. 1, April 2015, pp. 147 ~ 1
5
3
DOI: 10.115
9
1
/telkomni
ka.
v
14i1.740
2
147
Re
cei
v
ed
Jan
uary 25, 201
5
;
Revi
sed Ma
rch 1
1
, 2015;
Acce
pted Ma
rch 2
6
, 2015
Javanese Gong Acoustics and Its Modeling using Finite
Element Method
Guna
w
a
n De
w
a
n
t
oro*, M
a
tias H.
W. Budhianth
o
Dep
a
rtment of Electron
ics an
d Comp
uter En
gi
n
eeri
ng, Sat
y
a W
a
cana C
h
ri
stian Un
iversit
y
,
Dipo
n
e
gor
o Street 52-6
0
, Sala
tiga, Indo
nesi
a
*Corres
p
onding author, e-mail:
guna
w
a
n.
dew
a
ntor
o@staff.uks
w
.
edu
A
b
st
r
a
ct
In Centra
l Jav
a
, the Jav
a
n
e
s
e
Gong
is o
ne
of pr
o
m
i
n
e
n
t g
a
mel
an i
n
stru
me
nt to
mark t
he e
nd
of
m
u
si
ca
l pa
ssag
e
.
Th
e Go
ng
i
s
a d
i
st
inctive perc
u
ssion instrum
e
nt becaus
e
of its w
a
v
e
-like
so
un
ds
after
bei
ng struck i
m
me
diat
ely du
e to its traditiona
l m
anufact
u
re proc
edur
e
s
. Spectra for the gongs v
a
ry
substanti
a
lly
d
ue to var
i
atio
n in s
hap
e a
nd si
z
e
,
and
to di
me
nsio
n
a
l irre
gu
lariti
e
s
created
dur
in
g
ma
nufactur
e
a
nd w
h
ilst tunin
g
by soft-ha
mmer
ing
or
han
d-grin
di
ng. F
i
ni
te Element An
alysis is us
ed
to
predict the effect of a
range of variations
of
gong
geom
e
tries on
modal sh
apes as well as modal
freque
ncies.
T
he r
adi
ated
so
und
sp
ectra of
the
go
ng
are
also
meas
ure
d
an
d c
o
mpar
e
d
w
i
th th
e n
a
t
u
ral
freque
ncies o
b
tain
ed fro
m
F
i
nite Ele
m
e
n
t
Analysis.
T
h
roug
h the finit
e
ele
m
e
n
t mo
del, the effect of
geo
metric di
mensi
ons a
nd
materia
l
prop
erti
es of t
he gon
g on its soun
d ch
aracteristics ca
n be pre
d
icte
d.
Ke
y
w
ords
: Ja
vanes
e go
ng, mo
da
l frequ
en
cies, mo
de sh
a
pes
, finite el
e
m
ent method, ac
oustic spectra
Copy
right
©
2015 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. Introduc
tion
The Java
ne
se Gong play
s an impo
rta
n
t role in Ja
vanese cultu
r
e. In gamela
n
musi
c
ensemble, g
ong soun
d m
a
rks a
nd en
d
s
ce
rtain
p
a
ssag
e of a ga
melan
comp
osition [1]. The
gong
so
und i
s
al
so u
s
e
d
t
o
de
cla
r
e the
openi
ng a
n
d
clo
s
ing
of i
m
porta
nt eith
er religio
us
a
n
d
se
cula
r even
ts or va
riou
s rituals. T
h
e
roa
r
i
ng wav
e
like sou
nd of
the
gong is
a
s
soci
ated
by
Javan
e
se wit
h
Bima’s gig
g
le that creat
es a g
r
an
deu
r yet calming
feeling. Bima is kn
own a
s
a
cou
r
ag
eou
s
but hone
st and just hero, a great
lege
nd in Javan
e
se pup
pet sh
ado
w (wayan
g)
storie
s. The
numbe
r of wavelike soun
d repetit
ion cycles in a be
st soun
ding
gong can be
as
many a
s
12 t
o
13. A Go
n
g
is
still tradi
tionally
han
d
m
ade by
ca
sting, hamme
ring, forgin
g a
n
d
tuning a
s
wel
l
. In this rese
arch we studi
ed the 56
cm
diameter of i
r
on G
ong Ke
mpul, a se
co
nd
large
s
t gon
g in the compl
e
te set of Java
nese Gamel
a
n instru
ment. Although an i
r
on go
ng is le
ss
expen
sive kin
d
of gong tha
t
is mainly used for edu
cati
onal pu
rpo
s
e
s
, it is still cra
fted to produ
ce
the waveli
ke
sou
nd. The g
ong was tun
e
d
to tone 6 in
pelog
scale [1, 2].
Gamelan inst
ruments
makers us
ually
m
a
ke
mo
st of t
he metal
ba
sed in
stru
ment
s b
a
sed
on thei
r exp
e
riences and
in
tuitions. Th
ere are fe
w
stu
d
ies investig
a
t
ing their vibration a
nd
sou
nd
cha
r
a
c
teri
stics. Tsai et al.
[3] const
r
u
c
te
d
finite elem
ent model of
a Chin
ese co
pper
gong
an
d
obtaine
d the
natural
fre
q
u
enci
e
s an
d
correspon
di
ng
mod
e
sha
p
e
s
. Th
en, exp
e
rime
ntal mo
dal
analysi
s
wa
s
carrie
d out to
com
pare wit
h
the fi
ndin
g
s obtaine
d fro
m
finite elem
ent mod
e
l. The
sou
nd
spe
c
tra we
re m
e
a
s
ured to
identif
y to fundame
n
tal frequ
en
cy. Finite elem
ent analy
s
is
has
been
wid
e
ly use
d
to mo
d
e
l co
mplex
shape
s. Yu
sof
f
et al. [4] highlighted th
e d
e
tail de
scripti
ons
that lead to five-pha
se
su
p
p
ly with fixed vo
ltage and
freque
ncy by
usin
g Finite-Element Met
hod
(FEM). Identi
f
ying of specification on a
real
tran
sfo
r
mer ha
d bee
n done b
e
fore applie
d into
softwa
r
e
mod
e
ling. Th
eref
ore, Fi
nite-El
e
ment M
e
tho
d
provide
s
cl
early u
nde
rst
anda
ble in
te
rms
of visualize the geo
metry
modelin
g, co
nne
ction sch
e
me an
d out
put wavefo
rm
. Georg
e
et a
l
. [5
]
pre
s
ente
d
fin
i
te eleme
n
t modelin
g an
d re
sult
s of
a five-ph
a
se
perm
ane
nt m
agnet b
r
u
s
hl
ess
motor de
sign
ed
fo
r
hi
gh p
o
we
r den
sity appli
c
ation,
e
x
ploring
the
cha
r
a
c
teri
stics of
multiph
a
s
e
topology. Bre
t
os et
al. [6]
adopte
d
finite
eleme
n
t met
hod to
mod
e
l
the fre
e
pl
ates
and
box of
violin, exce
pting the
ne
ck.
Thro
ugh
the
validated finit
e
ele
m
ent m
odel, the
adj
ustment
of vi
olin
modal
prope
rties can
be
num
eri
c
ally
predict
ed
a
nd fitted to
de
sire
d
re
sonan
ce
pe
a
ks.
Macla
c
hl
an [7] employed
Finite Eleme
n
t Analysis to
predi
ct the e
ffect of a ran
ge of variatio
ns of
gong
geom
e
t
ries
on mo
dal fre
quen
ci
es. Th
e p
r
e
d
icted f
r
eq
ue
ncie
s of the
Finite Elem
ent
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TELKOM
NI
KA
Vol. 14, No. 1, April 2015 : 147 – 15
3
148
Analysis exp
e
rime
nt for g
ong mod
e
ls d
i
d not matc
h t
he acou
stic spectra for the
s
e go
ng
s. Lu [8]
pre
s
ente
d
a
study of the vibration
a
l be
h
a
viour
of
the
violin top plat
e and
explo
r
e
d
the p
o
ssibili
ty
of using
com
posite mate
ri
als a
s
a su
bstitute fo
r traditional wo
od in
making top p
l
ates. Num
e
ri
cal
simulatio
n
s
a
nd expe
rimen
t
al tests a
r
e
compa
r
ed
to v
a
lidate the
re
sults. Th
e two most p
opul
ar
method
s fo
r
nume
r
ical a
n
d
expe
rime
ntal vibrat
ional
analysi
s
,
the
Finite
Elem
e
n
t Method (F
EM)
and Experim
ental Modal
Analysis a
r
e
use
d
, respe
c
tively. Then, the sam
e
mo
deling an
d testing
techni
que
s were ap
plied o
n
two com
p
o
s
ite plates.
Result
s sho
w
that the vibrational beh
avior of
comp
osite pl
ates differs si
gnifica
ntly from tradi
tional
woo
den plate
s
. Facchin
e
tti et al.
[9] applied
finite elemen
t analysi
s
(F
EA) and
exp
e
rime
ntal mo
de an
alysi
s
(EMA) to stu
d
y the vibrati
o
n
behavio
rs of
reed
an
d
pip
e
in
cla
r
in
et. The
holog
ra
p
h
ic i
n
terfe
r
om
eter
wa
s
use
d
to o
b
serve
the
vibration m
o
d
e
s a
nd ei
gen
-freque
nci
e
s
o
f
the re
e
d
. Th
e experi
m
ent
al re
sults sh
o
w
ed th
at so
me
reed
s ha
d strong a
s
ymmet
r
ies; the
cau
s
e of modal
a
s
ymmetrie
s li
es mo
st pro
b
ably in the lack
of homoge
ne
ity of
the can
e
use
d
for the reed d
ue to its natural
cha
r
a
c
ter. To
understan
d the
vibration
beh
avior of m
u
si
cal in
strumen
t
s an
d t
hei
r sound
me
cha
n
ism, expe
rim
ental te
chniq
u
e
s
are
ne
ce
ssary. Wang [1
0] pre
s
e
n
ted th
e app
ro
ach o
f
virtual testin
g (VT
)
by th
e integ
r
ation
of
finite eleme
n
t analysi
s
(FE
A
) an
d expe
ri
mental
mo
dal
analysi
s
(EM
A
) techniqu
e
s
for the
desi
gn
analysi
s
of se
veral types of
percu
ssio
n
i
n
stru
ment
s.
First, the pro
c
e
dure fo
r mod
e
l verification
is
introdu
ce
d a
nd shown th
e ba
sic p
r
in
ciple for va
lid
ating the finite eleme
n
t model by ad
op
ting
FEA software
and
pe
rformi
ng EMA. Th
e
so
und
spe
c
trum of
percu
ssion
in
strum
e
nt ca
n the
n
b
e
measured to
identify the
most
contri
b
u
ted st
ru
ctural mode
s
an
d co
mpa
r
ed
with tho
s
e m
odal
para
m
eters
o
b
tained f
r
om
FEA and EM
A. Three
ty
pes
of pe
rcussion
inst
rume
nts, in
cludin
g
a
xylophone b
a
r
, a metallop
hone pl
ate a
nd a gon
g, are sho
w
n to d
e
mon
s
trate t
he idea of V
T
fo
r
the re
de
sign
of ne
w typ
e
of pe
rcu
s
sion in
st
rum
e
nts. Skrod
zka and
Se
k [11] ado
pted
the
traditional ex
perim
ental m
odal an
alysi
s
techniq
u
e
s
to get modal
freque
nci
e
s,
modal da
mpi
n
g
ratios, a
nd their
corre
s
p
ondin
g
mod
e
sha
p
e
s
of
a loudspea
ker
und
er di
fferent wo
rki
n
g
con
d
ition
s
. The vibration
freque
nci
e
s
and the mo
d
e
sha
p
e
s
for a semi
-co
n
e woofe
r
an
d a
tweeter
we
re
obse
r
ved. Fi
nite element
analys
i
s
mod
e
ling ha
s be
en appli
ed to
the desig
n
of
novel idioph
one
s for use within con
v
entional
Eu
rope
an mu
si
cal contexts [12]. Comp
uter
prog
ram
s
wh
ich phy
sically
model musi
cal in
strum
e
nts throu
gh
FEA modelin
g have re
ce
ntly
been
develo
p
ed for ele
c
tro
n
ic m
u
si
c
syn
t
hesi
s
[13].
T
h
is
wo
rk ad
o
p
ts FEA to
st
udy the vib
r
at
ion
cha
r
a
c
teri
stics of an i
r
on
Gong K
e
m
pul. It is ma
de of malle
a
b
le cast iron
, with materi
al
prop
ertie
s
a
s
follow: ela
s
tic modul
us
of 1
.
9e11 Pa
,
poi
sson’
s ratio o
f
0.31, ma
ss
den
sity of 72
00
kg/m3, ten
s
il
e strength
of 861e
6 Pa, an
d yield
st
ren
g
t
h of 827e
6 P
a
. Figure 1
shows the
de
sign
of the go
ng
and it
s dim
e
nsio
ns. T
he
sou
nd frequ
e
n
cy respon
se
is al
so
mea
s
ured to
find
the
relation
shi
p
b
e
twee
n the d
y
namic m
ode
s an
d
soun
d
qualitie
s. Fro
m
the FEA m
odel, the
effect
of geometry d
i
mensi
o
n
s
an
d material p
r
o
pertie
s
on the
princi
pal fre
q
uen
cy is also observed.
Figure 1. Dim
ensi
on of gon
g kempul in millimeters
2. Finite Element Anal
y
s
is in Solid
w
o
rks
The Solid
Wo
rks i
s
an
engi
neeri
ng 3
D
CAD softw
are f
o
r Micro
s
oft
Wind
ows. It has three
degree
s of fu
nction fo
r the
need
s of o
r
g
anization
s.
The Solid
Wo
rks Stand
ard i
s
suitabl
e for f
a
st
modelin
g; de
sign i
n
2
D
and in
3D.
The Solid
Wo
rks Professio
nal is
th
e superstructu
r
e
of
SolidWo
rks S
t
andard. It improve
s
t
he efficien
cy and innovate
s
with
solution
s th
at are used by
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Ja
van
e
se Go
ng Acou
stics
and Its Model
ing usi
ng
Fini
te Elem
ent Method (Guna
wan
De
wanto
r
o)
149
millions of de
sign
ers. It contains ad
ditio
nal ex
tensio
n
module
s
as
Animator, Ph
otoWo
r
ks, etc.
The SolidWorks Premi
u
m
is the mo
st comprehensiv
e software. It
combi
n
es the capabilities of
the SolidWo
rks Professio
nal with sim
u
lations. T
he
Part of the SolidWorks Profession
al is
the
S
o
lidWo
r
ks S
i
mulat
i
on,
w
h
i
c
h p
r
ov
ide
s
b
a
si
c sim
u
la
tio
n
tools fo
r te
sting stress, st
rain, an
alyzin
g
the kinem
atics, dynamics a
nd it simulati
o
n
s conditio
n
s
of the real wo
rld [14].
2.1. Bounda
r
y
Condition
The mate
rial
pro
pertie
s
are
assig
ned
to the go
n
g
and
bou
n
dary
con
d
itions a
r
e
determi
ned.
The gon
g’s al
l degre
e
s of freed
om on
surface are taken. They a
r
e denoted
with the
gree
n flag in
Figure 2. The
s
e two
hole
s
are fixture
s
th
roug
h which
hangi
ng ro
pe
s hold th
e go
ng.
This
conditio
n
prevent
s the movement
of the surfa
c
e
in a spa
c
e.
Figure 2. Boundary conditi
ons
2.2. Mesh Co
nfigura
t
ion
Mesh
on
the
gong i
s
gen
erated auto
m
ati
c
ally
by Solid
Wo
rks. Th
e e
l
ement i
s
d
e
fined by
10 nod
es
whi
l
e each nod
e
has th
ree d
e
g
ree
s
of fr
e
e
dom at ea
ch
node. Th
e sp
atial element
has
16 Ja
co
bian
points an
d is suita
b
le fo
r modeli
ng o
f
the finite e
l
ement irregu
lar me
sh. Th
e
maximum
size of the
elem
ent is 33.8
6
0
7
mm
with tol
e
ran
c
e
of 1.6
9
mm. T
he m
e
sh
in
Figu
re
3
is created of
8523 el
ement
s and of 17
02
6 node
s.
Figure 3. Mesh of finite element of gong
2.3. Modal Analy
s
is of G
ong
The m
odal
analysi
s
i
s
carri
ed
out b
y
SolidWo
rks a
nd m
ode
sh
ape
s
and
natural
freque
nci
e
s a
r
e al
so calcul
ated. For thi
s
modal an
alysis the
dire
ct
solver i
n
clu
d
i
ng the FFEPl
us
method i
s
u
s
ed. The first
five mode
sh
ape
s are sho
w
n in
Figu
re
4, and the fi
rst five natu
r
al
freque
nci
e
s a
r
e sh
own in T
able 1.
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TELKOM
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KA
Vol. 14, No. 1, April 2015 : 147 – 15
3
150
(a)
(b)
(c
)
(d)
(e)
Figure 4. Mode sh
ape
s of gong: (a
) First Mode
(b
) Secon
d
Mode
(c) Third M
ode
(d) F
ourth
Mode (e) Fifth Mode
Table 1. Natu
ral Fre
que
nci
e
s of Particul
ar Mod
e
Sha
pes
Mode
shape
1
2 3 4
5
Freque
nc
y
(
H
z)
78.506
224.74
344.2
397.84
533.53
3. Acous
tics
Spectra o
f
the Gong
We re
co
rde
d
48kHz samp
le tones of the Gong Ke
mpul usi
ng ARTA PC Software. A
controlled
go
ng stri
ke
r wa
s utilize
d
to
exert a
controlled imp
a
ct f
o
rce up
on th
e gong
bo
ss,
as
see
n
in Figure 5. First, a measurement
conde
ns
er
microph
one a
c
qui
red the a
c
ou
stic
signal
by
near field me
asu
r
em
ent from behin
d
of the boss,
externally po
we
red by a pha
ntom power. A
sou
nd
ca
rd
then inte
rfaced an
d digiti
zed thi
s
sig
nal in o
r
d
e
r that com
p
u
t
ers
are
abl
e to
recogni
ze.
Figure 5. Measu
r
em
ent se
tup
An impul
se
-gene
rated
re
spo
n
se
wa
s re
co
rde
d
t
o
an
alyze
i
n
both
the
time and
freque
ncy
do
main a
s
sh
o
w
n i
n
Fig
u
re
6. The
spe
c
tral pe
aks i
n
dicate
pa
rtial
s
with
signifi
cant
stren
g
th. Ta
ble 2 sh
ows the 18 con
s
iste
nt parti
a
l
s, averag
ed
from four trials, of the gong
con
s
i
s
ting of both harmoni
s and n
onh
armoic fre
qu
e
n
c
ie
s [15]. The
partials at 9
3
.02 Hz, 18
6 Hz,
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TELKOM
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ISSN:
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046
Ja
van
e
se Go
ng Acou
stics
and Its Model
ing usi
ng
Fini
te Elem
ent Method (Guna
wan
De
wanto
r
o)
151
279.1, 372.1,
and 46
4.9 Hz are the
stri
ct
integer m
u
ltip
les of t
he fun
damental freq
uen
cy. Hen
c
e,
these
partial
s are the fi
rst,
se
con
d
, third,
fourth
, and fi
fth harmo
nics, resp
ectively
. Such de
gree
of harmo
nicit
y
of the partials lea
d
s to the pi
tch
ed sound of the
Gong Kem
p
u
l
, differing it from
that of Chin
e
s
e g
ong
s
whi
c
h
sou
nd li
ke
a cra
s
h. Th
e
harm
oni
c an
d or i
nha
rmo
n
ic p
a
rtial
s
th
at
occur in
fairl
y
clo
s
e f
r
eq
uen
cy be
at togethe
r a
n
d
form
the
ro
aring
soun
d
whi
c
h
is of
ten
asso
ciated
wi
th Bima’s lau
ghter [16
-
17].
Figure 6. Aco
u
stics spe
c
tra
of the gong
Table 2. Parti
a
ls of the Spe
c
tra
No Parti
a
l
s
(Hz
)
Harmoni
c
s
1 93.02
1
s
t
2 158.2
3 160.5
4 182.7
5 186
2
n
d
6 213.9
7 242.9
8 248.2
9 251.6
10 253.4
11 275.8
12 279.1
3
r
d
13 368.9
14 372.1
4
th
15 433.9
16 462.3
17 464.9
5
th
18 475.7
Table 3. Diffe
ren
c
e
s
betwe
en pre
d
icte
d and mea
s
u
r
e
d
natural freq
uen
cie
s
(Hz)
Mode
1 2
3
4 5
FEA
78.506
224.74
344.2
397.84
533.53
Spectra 93.02
186
279.1
372.1
464.9
Absolute Error
(
%
)
15.6
20.82
23.32
6,91
14.7
As sh
own i
n
Table
3, the pre
d
icte
d frequ
en
cie
s
of the fin
i
te element
analysi
s
experim
ents f
o
r gon
g mod
e
l based on
manufa
c
tured
gong
s did no
t match the a
c
ou
stics spe
c
tra
for the
s
e
go
ngs due
to v
a
riou
s
effects of the m
anu
facturin
g p
r
o
c
e
s
ses whi
c
h
are
difficult
to
accurately model. The go
ng makers a
r
e u
s
ed to m
i
x the raw m
a
terial, co
mp
ose
d
by tin and
cop
per,
with
a certai
n ratio. Besi
de
s, they fi
ne
-tune
the g
ong
u
s
i
ng
soft ha
m
m
er
by tappi
ng the
outer pa
rt of boss, therefo
r
e,
there are many irre
gula
r
ities fro
m
on
e gong to an
o
t
her gon
g.
For mo
re un
d
e
rsta
ndin
g
of the geom
etric dimen
s
ion
s
and mate
rial
prop
ertie
s
’ effects o
n
the sou
nd chara
c
te
risti
c
s of the gong, finite
element model
s are create
d
with different
prop
ertie
s
. T
able 4
list
s
n
a
tural f
r
equ
e
n
cie
s
fo
r diff
erent
ca
se
s.
The first mo
d
i
fication d
oub
les
0
50
100
150
20
0
250
300
35
0
400
450
500
-4
-2
0
2
4
6
8
X
:
93
.02
Y
:
6.576
F
r
e
q
u
e
n
cy(
H
z
)
Log-
M
agnitude
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046
TELKOM
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Vol. 14, No. 1, April 2015 : 147 – 15
3
152
the thickne
ss from 5
mm t
o
10 m
m
, wh
erea
s, the
se
con
d
mo
dification chan
ge
the gon
g mat
e
rial
to copp
er-tin
alloy with ela
s
tic mo
dulu
s
of
1.1e011 P
a
, Poisson’
s ratio of 0.33, and ma
ss d
e
n
s
ity
of 8300 kg/m^3.
Table 4. Natu
ral freq
uen
cie
s
(Hz) for different p
r
op
erti
es
Mode
Original case
Double size of thickness
O
r
iginal size
(copper allo
y)
1 78.506
85.661
52.494
2 224.74
305.93
150.19
3 344.2
334.13
219.04
4 397.84
462.25
259.91
5 533.53
476.56
348.96
It is obvio
us
that increa
sin
g
the
si
ze
dim
ensi
o
n
s
will
gen
erally l
o
wer the fu
nd
amental
freque
nci
e
s
a
s
that foun
d i
n
gamel
an
se
t for both
pe
lo
g
an
d s
l
end
ro
scale.
Ho
wever, in
cre
a
si
ng
the thickne
s
s of the gong
will re
sult in
highe
r nat
u
r
a
l
frequen
cie
s
.
For lower
stiffness m
a
teri
al,
the natural freque
nci
e
s a
r
e lowe
r than t
hose of for higher
stiffness material.
4. Conclusio
n
In this study, the finite element model
of
a Javane
se gong i
s
co
nstru
c
ted. Th
e sou
n
d
cha
r
a
c
teri
stics of the
cop
p
e
r go
ng a
r
e a
l
so inve
st
igat
ed. The
re
sul
t
obtained fro
m
finite elem
ent
analysi
s
sho
w
mu
ch difference
si
nce
th
ere are m
any
con
c
avitie
s a
nd convexitie
s on th
e
surfa
c
e
of the gong
resulting fro
m
traditional
manufa
c
turi
n
g
esp
e
ci
ally durin
g fine-tu
ning process.
In
finite elem
en
t analysi
s
,
st
ructu
r
al
dim
e
nsio
ns an
d
material
p
r
op
erties of th
e
gon
g
ca
n b
e
cha
nge
d to better un
derstand th
e effect in vibrat
ion beh
avior and soun
d
cha
r
a
c
teri
sti
cs.
Thro
ugh th
e
s
e a
nalyses,
the gon
g
stru
ctur
e ca
n be m
odified to imp
r
o
v
e its so
un
d
c
h
arac
teris
t
ics
.
In future,
an experiment
al moda
l an
a
l
ysis n
eed
s t
o
be
ca
rrie
d
out to verify the
model ge
ne
ra
ted usin
g finite element me
thod.
Ackn
o
w
l
e
dg
ements
This resea
r
ch is finan
cial
ly suppo
rted
by
Satya
Wa
can
a
Ch
ri
stian University under
Competitive Grant Schem
e
no. 045/Penel./Rek./5/II/2014
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TELKOM
NIKA
ISSN:
2302-4
046
Ja
van
e
se Go
ng Acou
stics
and Its Model
ing usi
ng
Fini
te Elem
ent Method (Guna
wan
De
wanto
r
o)
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