The Japan
The
Japan Society
Soclety
of Mechamcal
Mechanical Englneers
Engineers
of
日 本機 械学 会
.
9.
9−
2012 年 度 年 次 大 会
[2012
一般 社 団 法 人
Cepyright◎ 2012
12]
日本 機 械学 会
KSME −JSME JointSymposium on CM
& CAE
2012
CO − KR −3
Shape
optimiZation
TranQua皿 g Dat ,Gang −Wbn Jang ,Hyu Sang Kwon
Seo
*
lens beamformers 索
of acoustic
*
Seung Hyun Cho
* *
,
Yb −Han Cho
**
,
Hee −Seon
and
* *
* **
「Depar
博
nt
MechanicalErlgineerlng
SejongUniversity
,
dong,
Gwan 創ingu ,
Seou1,
Korea
σ「
98Gunla
E −mail :9呵 ang @ sejong
lnst
吐ute
aGkr
Standardand Scienoe
・
ro ,
Yuseong −gu,
Daejon305 −340 ,
Korea
Research
ttKorea
σ「
267G 司eong
轍Agency fbr Defense Development
Gyungnam
10−62Chungjang−ro ,
Ji冂haegu ,
Changwon ,
6450t6
Korea
,
Abstrac ¢ ,
Sbape.
op
ispresentedby 曲 g the hybhd approa h 止 at
acoustics
as well as wave
acoustics ,
Geometricacoustics isused to obtain the
晦 loys geometric
er the fhlallens.
盟 ys ofacous
匠c wave 丘om the wave source to the exit planethatisp】
aced right af 世
’
to calcu 正
ate pa吐
hs ofrays and t nsmited pressuresthroughlenses
are calculated
Snells law iStised
by mu 耽ipb洫g 重he 血 cident wave with transmissioncoe 伍 cients .Dif量action of the wave 量s not
’め nsider6d in the
geometricacous 恒cs ,TWo me 耄hods are used to obtain the acoustic pressure
distrib
血iOna しthe pressue 且e 且d.
The 丘rst and second method uses theKit℃hhoffintegral
theo爬 m
,、
ド
’ヨ’
the
disnibution
from
{the
囲 dthe Bounda1yElementMethod (
EM
to
ca1
】
ate
acoustic
β
)
pressure
.
e 燼 p正
ane to thgimage p豆
ane
re $pectively
at the fbcalpojllt
as well as
;the pressure magnitude
design
is
formulated
as
the
optirniZation
th6se
at
side
lobes
can
be
calculated
.
A
1eris
;
problcm
鹽
顱
m 鋤 【im 僞
血e pr鰯 u e magnitUde
at the focalpOint
.The effectiveness of the
pmbl
pmposed appma6h isvcrified by showing a design example fbra spherical lenssystem .
伽
on
of an acou
ic lens野 st
航
(;
瓰
厂
【
,
Kay wordS
:
Acousticslenssystem ; Shape
ho跏 egr 舳 θo
;BEM
』K
opt
ization
; Geometric
acoustics
Wave
;
acoustics
;
1.Introduction
Due to 血 e
1imit(Ul range
to obtain underwater
available
a帥
very
1]isused
gdevice[
,
of
in underwater
environment
]
ight
is
supplied
.An
ifartificial
vlsibility
imageseven
as an altemative
to produceunderwater
lmage
,
theuse
acoustic
of an optical camera
camera
,
a
highr rsolution
〔
.Itcan be mounted
sequences
systern
on
isnot
ultrasound
autonomous
an
by a diverto observe potentially
harmfU1objectS .
Two types of acoustic cameras are widelyused an acoustic camera array and an acoustic le【ts camera .The acoustic
.The signals from an arTay of microphones are
c
em amy
ates an i皿 age l y using a set of phased microphones
c
血 ed and surnmed to form a single signal fromtheentire array .
An image of 岫 tensityof 出e sound source
ph 鄲
ofthe
camera
ismapped out [
2】
,
Thiscamera can be used to create an ult asonic image
dist
曲 ution throughouta 丘eld ofview
field
.However the main disadvantage
of using an acoustic came a ar y is that data fh m
with a sound source inthe 伽 」
underwater
vehicle
or carried
・
:
)
お
【
【
,
旧
)
of 山 e electronics
and it
is1imited
ina 丘equen 〔ッ ge [
3亅.
must be collect 〔,d,
in(嬲
ゆ lemicrophones
g 血 e complexity
[lhe acoustic
lenscameras havetheadvantage ofusing no power forbeamformingand ease to transmitand receive from血 e
mul
same
beam [
4].
In 面 s invesdgatio
叫 an
acoustic
lenscamera
No .
12 −1] 日 本 機 械 学 会 2012 年 度 年 次 大 会 講 演 論 文 集
[
system
〔2012
isoptimized
to obtain
acoustic
p
爬
ssure
with
higherintensi
妙
.
9.
9 − 12,
金沢 〕
一
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thefocalregion ofthe camera. Tb thisend, theacoustic pressurefieldiscalculated by using thehybrid
analysis
approach
by
K. Fink[5,
6]among other existing analysis method [7,8,9 and 1O].Initial
desigris
ofacoustic lenscan be obtained basedon
thegeometrical
acoustics (or
theray theory).
Howeveg itisdifficult
to evaluate the convergence gainof the focused
beam in
thelensusing theray theoryWhi]e thewave thecnyjsmore accurate inpressurefie]dcalculation thantheray theory;very
complicated
calculation
isrequired to deal with transmissionof waves through differentmediums.
[[b deal with this,the
in [5,
6] isused in this study
1rybridmethod
where
the geometrical
acoustics
isapplied from thesource
lenses
and thewave acoustics isused ffomtheexit p]aneto theimageplane.
The geomeniesof spherical lensesforthickand dual-thin-lens
systenis
are
optimized
to
to theexit planeofthe
theeffeodveness
show
ofthe
proposedapproach.
2. Hybrid analysis
A hybrid method
approach
iscombined
the geometrical
acoustics
the wave
with
acoustics.
acoustics
Geometrical
isapplied from
to theinterface
of the Iens,
and waye acoustics isapplied in the image space. Geornetrical
acoustics, realized by
ray-tracing,
the
on
the
final
lens
interface.
acoustics
uses
those
calculate
complex pressures
Whve
as boundary
pressures
a source
inorder to solve theKirchhoffintegral,which gives theIllessureat points
inthefocalregion.
Geometricalacoustics orray acousticsis the equivalent principle
of geometrical
optics applied in acoustics. Geometrical
acoustios
describes
sound
thelaws governlng sound's behayiercan be described
prqpagation in temis of rays. So that,
values
using ray theory.
geometrically
ln thispqpegtheSnell's
law isused to describe
therelationship betweentheangles
refetTing to waves passing
througha boundarybetweeri
two difflirent
medium,
sina
of
incidence
and
refraction, when
c,
(i)
,inq=g
witheach e
meters
as
theangle
persecond
measured
thedensity
ofthe
or mls) andpas
And the transmission
coefficient
ffomthenormal,
from
one
medium
c as
p, e, cosq+p,
Acousticwaves
waves
are
longitudinal
waves
travel with the speedofsound
which
of acoustic
ray
intherespective
medium
(SIunits are
respective medium.
to theother
2Ac,
T=
thevelocity
medium
as
[11]:
cosq
(2)
c, cos4
thatexhibit phenomena 1ikedifltaction,
reflectiQn
depends on themedium
theyare passing through.
and
interference.
Acoustic
Zl tlsitrg
theKirehhoffintegratlon
methoth
The acoustics waves are applied to calculate thepressure
at a pointinthepressure
field
by using Kirchhoff
integraticm
method.
Figure 1 shows that,at focalregion thecomplex
integral
at points
inthe
pressurewas calculated by using Kirchhoff
field.
pressure
=[-'2k.'X
i,
;)
jTp(s)
R:`k
ill
S
p(x,y)
'
sdsdip
(3)
at pointPi
whereP(3c;Jl},
Pts),h R and d'k&(R?
refer to thecomplex
at point17?inimagespace, thecomplex
pressure
pressure
thewave numbeq
thedistance
betweenthepoint Pi on the exit plane and thepoint P2 inimage space and
on theexit plane,
thepoint-souroe
Green'sfunction,
respectively
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Y
y
Y・sPl
beL
Foeal?lme
z
z
A.A
theKirchhoffintegral
theorem
Fig. 1-ConfiguTationfor
We
can
approximate
al}ove
as
equation
theintegral
p(x, y)
in thispapeqwe
use
=
il))
"
- i2k}"
'
[
'
flp(s)
(4)
sdsdip
R:"", ,
Method to numerically
Romberg lntegration
eyaluate
thisintegral.
Z2 VsingtheBoundai l,ElementMlethod:
LerlsSystm
Image spaee
(GeonrctricalAcoustic9
ptEM)
'V-vp"As
-tV
i
P
FocalPoint
fortheBoundaryElementMethod
Fig.2 - Configuration
[hecomplex
was
pressure
calculated
by using BEM
at
pi=#.,l[l,p:gilitl-S-
where
p,,p g and
S refer
to thecomplex
theimagespace
pointinside
ari arbitray
pressurep at an
and thesurf/ace of
boundaryele[nents, theGreen'sfunction
£
as
arbitrary
elementJ'
follows:
(s)
.,S,gYop.S
the image space, thecomplex pressureon
pointinside
on
all
the boundary, respectively.
3.0ptimization formu}ation
inthispqpegwe proposean optimal designmethod fortheshapes ofthe acoustic lensthatleadsto a prescribedpressure
at the desired
focuspoint.
concentration
inthefluiaand especially a pressure
distribution
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The optimization problemisformulated
as:
Maximize
Pressureat focal
point
RL
SRS
Ru
Subjected
to
tL StStU
where
R, t refer to the radius, thickness
ofthe lens,
respectively. lhe flewchart ofthe
optimization
isshown inFig.
procedure
3
start
InitialyatueRork
Hybridmpetcb?TtssurtfnidantilysisDesigelvariablelrpdatc
NevvKt
cmpYes
Ne
@
Fig.3-Flow chart
of
the optimization
procedure
4. Design example
of ABS
Thicklensisdesignedforsonar devvice
operating at lOO kHz.[Iheshell of thelenswas made
]ensis71% FS5,29% FC72, ithassound
theshell is2040 mls [11].The fluid
mix isused inthethick
to 778.79mls and 1870kglm3,respectively.
thesound speedof
speed and density
refer
and
K
/
smismu
peedRin
Fig.4-The thicklenssystem
[[heoptirnized
values
fordesignvariables
fftelisted
in[tbbJe1.
[fable
1 - Designvarial)les beforeand
Designvalue
lnitial[mm]
after Qptimization
Optimized[mm]
Rout
132.5
113.5
Rin
107.5
100.15
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asu!=$e-ssoeB.NL"Ee
X-coerdi"atetm]
Fig.5-Focal depth
field(star
1ine:initial
along the center 1ineof the acoustic
pressure
thatthepressure distribution
at
the
focal
by
the
use
of
the
objective,
the
distribution).
As was irrtended
pressure
distribution,
solid 1ine:
optimized pressure
behavior,which should be resolved in a future
shows fluctuating
Nonetheless,
thepressuredistribution
pointisincreased
Figure 5 shows
research.
Figure6 shows
field
near thefocal
point.
pressure
theacoustics
gua.pm. Eos
"ne
"f
tta ats
.zata
e.ta
field
Fig.6 -Tlieacoustics pressure
5. Conclusions
basedon thehybridanalysis method thatuses both
presented
to have
used
as designvariables
and aperture sizes were
acoustics, The geometries
geometrical acoustics and wave
of the use of
sound
waves in 1OO kHz and 1 MHz. The benefits
at focalpointswith frequency
maximized
pressureintensity
theacoustic lenssystem are simple structure, low cost, and simple electronics fordataacquisition and processing.Future
forclearer
formulationsto consider more acoustic responses
on optimization
works
in thisarea involveinvestigations
Design optimization
underwater
imagesand
of an acoustic
rnore
lenscamera
was
generalparameterizationoflens geometry.
References
[l]E. O. Belche4B. Matsuyameg and
G M. Trimble, "Object
with
identification
acoustic
in Proceedings
of
lenses,"
Oceans MTSIIEEE, 2001.
airbome
taigetswith an acoustic camera array"
source
imagingof low-flying
[2] S. Brandes,R. H. Benson,
Applied AcousticsXlolume68,Issue7,Pages752-765,July2007.
University
Noise Analysis",
MS thesis,
Wind TUrbineAeroacoustic
of an Acoustic Amay for
E. J.SimleM "Deyelopment
[3]
'OI
'Il
"Sound
ofColorado,2010.
NII-Electionic
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[4]E.
of Mechanical
Mechanical Engineeis
Engineers
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Belcheg B. Matsuyama, G Trimble,
"tObject
with
AcousticLenses",MTSAEEE
Identification
Conferenceancl
Exhibition,
Xlolume1, Pages6 - l1 200 1.
"Computer
of
MS thesis,University
of Pressure
FieldsGeneratedby AcousticLens Beamformers",
Simulation
[5]K. Fink,
,
Washington,1994.
E. M. Viggen,
[6]U. R. Kristiansen,
Methods ln Acoustics", Department of Electronics and
"Computational
lblecommunications,NTNU,2010.
Calculationofthe Sound FieldFocused by Acoustic Lenswith an
Zhang,K.H. Liu,Y: Liu,
and
frequency
control,
IEEE transactionson ultrasonics, ferroelecnics,
Axisymmetric Sound SpeedDistribution",
Atbitrary
X. H. Yan, Y: R
[7]
`CNumerical
Xk)1.
54,No. 4,Apri12007.
of
Distribution
and Measurementsof Sound Pressure
[8]S. Hisad4 Il Sunici,S. Nakahara, T. Fejit4
Jpn.J.Appl.Pbys.Nbl. 41, Pages.33l6-3324,
Real-Time Holographic interferometry"
wnve by Stroboscopic
Ultrasonic
"Visualization
2oo2.[9]
basedon ellipsoidal coordinate", Diroct and lnyerse
the acoustic pressurefield
YL Ruiliang,
G Long. "Reconstructing
on,
and
Acoustic Wave Theory,2008. DIPED 2008. 13th InternationalSeminarfWotkshop
Problemsof Electromagnetic
Pages155 - 158,Sept,2008.
fieldprodncedby
modeling
of the acoustic pressure
[10]M, A. Ayerlciou,L. A. Crum.M. E Hamilton,
J.Acoust. Soc.Am. Nlo1ume 98,Issue5,pp,2941-2941, 1995.
cornmercial
lithotripters'1
"Fundamentals
ofAcoustics",
Fourthedition, 2000.
L. E. Kinsleq
A.R,FreMA. B. Coppens,J.V Sanders,
[11]
C`Ultrasonic
ofApplied
Physics,Nlo1ume5l, Issue 1,pp.
Joumal
pentene-1)'1
propertiesofpoly (4-methyl
[l2]B. Hartrriann,
310-314,l980.
"Theoretical
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