• Aucun résultat trouvé

Effect of contact with an elastic wall on the spectral characteristics of the scattered echo of a contrast microbubble

N/A
N/A
Protected

Academic year: 2021

Partager "Effect of contact with an elastic wall on the spectral characteristics of the scattered echo of a contrast microbubble"

Copied!
7
0
0

Texte intégral

(1)

HAL Id: hal-00810616

https://hal.archives-ouvertes.fr/hal-00810616

Submitted on 23 Apr 2012

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Effect of contact with an elastic wall on the spectral characteristics of the scattered echo of a contrast

microbubble

Alexander Doinikov, Leila Aired, Ayache Bouakaz

To cite this version:

Alexander Doinikov, Leila Aired, Ayache Bouakaz. Effect of contact with an elastic wall on the spectral characteristics of the scattered echo of a contrast microbubble. Acoustics 2012, Apr 2012, Nantes, France. �hal-00810616�

(2)

Effect of contact with an elastic wall on the spectral characteristics of the scattered echo of a contrast

microbubble

A. A. Doinikov, L. Aired and A. Bouakaz

INSERM U930 CNRS ERL3106, Universit´e Fran¸cois Rabelais, CHU Bretonneau, 2 Blvd.

Tonnell´e, 37044 Tours, France [email protected]

Proceedings of the Acoustics 2012 Nantes Conference 23-27 April 2012, Nantes, France

(3)

$ 5D\OHLJK3OHVVHWOLNH HTXDWLRQ LV GHULYHG WR PRGHO WKH UDGLDO RVFLOODWLRQ RI D FRQWUDVW DJHQW PLFUREXEEOH DWWDFKHGWRDQHODVWLFZDOO7KHGHULYHGHTXDWLRQVKRZVWKDWFRQWDFWZLWKWKHZDOODIIHFWVWKHEXEEOHRVFLOODWLRQDV LI WKH EXEEOH RVFLOODWHG LQ D OLTXLG ZLWK D FKDQJHG HIIHFWLYH GHQVLW\ $V D UHVXOW GHSHQGLQJ RQ WKH ZDOO SURSHUWLHVWKHUHVRQDQFHIUHTXHQF\DQGWKHRVFLOODWLRQDPSOLWXGHRIWKHDWWDFKHGEXEEOHFDQEHHLWKHUORZHURU KLJKHUWKDQWKRVHRIWKHVDPHEXEEOHLQDQXQERXQGHGOLTXLG1XPHULFDOVLPXODWLRQVZHUHPDGHWRLQYHVWLJDWH WKH DFRXVWLF UHVSRQVH RI DQ DWWDFKHG FRQWUDVW PLFUREXEEOH ,W ZDV DVVXPHGWKDWWKH EXEEOH VKHOO SURSHUWLHV DUH GHVFULEHG E\ WKH 0DUPRWWDQW PRGHO DQG WKH SURSHUWLHV RI WKH ZDOO FRUUHVSRQG WR ZDOOV RI 2SWL&HOO FKDPEHUV FRPPRQO\ XVHG LQ H[SHULPHQWV ,W KDV EHHQ IRXQG WKDW FRQWDFW ZLWK WKH ZDOO FDQ FRQVLGHUDEO\ FKDQJH WKH LQWHQVLWLHV RI WKH IXQGDPHQWDO FRPSRQHQW DQG WKH VHFRQG KDUPRQLF LQ WKH VSHFWUXP RI WKH EXEEOH VFDWWHUHG SUHVVXUHUHODWLYHO\WRWKHLUYDOXHVLQDQXQERXQGHGOLTXLG

,QWURGXFWLRQ

,QWHUHVWLQWKHSUREOHPXQGHUVWXG\LVPRWLYDWHGE\WKH IDFWWKDWERWKLQYLWURDQGLQYLYRWKHG\QDPLFVRIFRQWUDVW DJHQWPLFUREXEEOHVLVDIIHFWHGE\YDULRXVERXQGDULHVVXFK DV ZDOOV RI H[SHULPHQWDO FRQWDLQHUV DQG EORRG YHVVHOV ([SHULPHQWDO GDWD VKRZ WKDW WKH SUR[LPLW\ RI ERXQGDULHV FDQSURGXFHFRQVLGHUDEOHFKDQJHVLQWKHDFRXVWLFUHVSRQVH RIDFRQWUDVWPLFUREXEEOH>@)RUH[DPSOH*DUELQHWDO

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

7KH SXUSRVH RI WKH SUHVHQW VWXG\ LV WR UHYHDO KRZ FRQWDFWZLWKDERXQGDU\FKDQJHVWKHDFRXVWLFUHVSRQVHRID FRQWUDVW PLFUREXEEOH 7R WKLV HQG D 5D\OHLJK3OHVVHWOLNH HTXDWLRQLVGHULYHGWKDWGHVFULEHVWKHUDGLDORVFLOODWLRQRIDQ HQFDSVXODWHG EXEEOH DWWDFKHG WR DQ HODVWLF ZDOO 7KLV HTXDWLRQ LV WKHQ XVHG LQ QXPHULFDO VLPXODWLRQV LQ RUGHU WR HVWDEOLVK KRZ FRQWDFW ZLWK WKH ZDOO DIIHFWV WKH UHVRQDQFH SURSHUWLHVDQGWKHVFDWWHUHGHFKRRIWKHDWWDFKHGEXEEOH

7KHRUHWLFDOPRGHO

7KHJHRPHWU\RIWKHV\VWHPEHLQJLQYHVWLJDWHGLVVKRZQ LQ)LJ,WLVDVVXPHGWKDWWKHEXEEOHLVVXUURXQGHGE\DQ LQYLVFLG LQFRPSUHVVLEOH OLTXLG DQG XQGHUJRHV UDGLDO DQG WUDQVODWLRQDORVFLOODWLRQVUHPDLQLQJLQFRQWDFWZLWKWKHZDOO DOOWKHWLPH7KHHIIHFW RIWKHZDOOLVDOORZHG IRUE\XVLQJ WKHPHWKRGRILPDJHVRXUFHV1DPHO\LQVWHDGRIWKHZDOO

)LJXUH$QHQFDSVXODWHGEXEEOHRVFLOODWLQJLQFRQWDFW

ZLWKDQHODVWLFZDOO

D YLUWXDO EXEEOH LV LQWURGXFHG DVVXPLQJ WKDW WKH PRYLQJ FHQWHURIWKLVEXEEOHLVDWWKHVDPHGLVWDQFHIURPWKHOLTXLG ZDOO LQWHUIDFH DV WKHPRYLQJ FHQWHU RI WKH UHDO EXEEOH DQG WKHUDGLLRIWKHEXEEOHVDUHUHODWHGE\5W İ5WZKHUHİ LVDFRQVWDQW

6FDWWHUHGILHOGLQWKHOLTXLG

7KHYHORFLW\SRWHQWLDOLQWKHOLTXLGFDQEHUHSUHVHQWHGDV ij/ ijijZKHUHijDQGijDUHJLYHQE\

Q FRV

Q Q

Q

D W 5 U 3

M T

f

¦

D

Q FRV

Q Q

Q

E W U G 3 T

¦

f E

Q FRV

Q Q

Q

D W 5 U 3

M T

f

¦

D

Q FRV

Q Q

Q

E W U G 3 T

¦

f E

+HUH3Q LV WKH /HJHQGUH SRO\QRPLDO DQGG 5 LV WKH GLVWDQFH EHWZHHQ WKH EXEEOH FHQWHUV (TXDWLRQV E DQG E DUH XVHG WR VDWLVI\ WKH ERXQGDU\ FRQGLWLRQV RQ WKH EXEEOHVXUIDFHV7KHIXQFWLRQVEQDQGEQFDQEHH[SUHVVHG LQWHUPVRIDQDQGDQE\XVLQJPDWKHPDWLFDOLGHQWLWLHVWKDW HVWDEOLVK OLQNDJH EHWZHHQ VSKHULFDO KDUPRQLFV LQ GLIIHUHQW FRRUGLQDWHV>@7KHUHVXOWLVWKHIROORZLQJ

P M

Q M QP

MQ P MP

P

&

E D

f

¦

ZKHUHM DQG&QP QPQP 7KH IXQFWLRQVDQ DQGDQ DUH IRXQG XVLQJ WKH ERXQGDU\ FRQGLWLRQV IRU WKH QRUPDO FRPSRQHQW RI WKH OLTXLG YHORFLW\ DW WKH VXUIDFHV RI WKHEXEEOHVZKLFKDUHZULWWHQDV

/ M MFRV MDW M M

M

5 [ U 5 W

U

M T

w

w

ZKHUH WKH RYHUGRW GHQRWHV WKH WLPH GHULYDWLYH DQG[MW LV WKH SRVLWLRQ RI WKH PRYLQJ FHQWHU RI WKHMWK EXEEOH RQ WKH D[LV] 1RWH WKDW IURP[ 5 ±5 DQG[ ±[ 5 LW IROORZVWKDW

[M M5

6XEVWLWXWLQJ(TVDQGLQWR(TRQHILQGV WKDWWKHIXQFWLRQVDQDQGDQFDQEHFDOFXODWHGDVIROORZV

DMQ 5 5HMDMQ

+HUHĮMQLVDWLPHLQGHSHQGHQWTXDQWLW\JLYHQE\

Proceedings of the Acoustics 2012 Nantes Conference 23-27 April 2012, Nantes, France

(4)

M QP

MQ Q P

P

D E

f

¦

ZKHUH EQPM LV FDOFXODWHG E\ WKH IROORZLQJ UHFXUUHQFH HTXDWLRQV

EQM GQ MGQ

> @

Q Q M MQ Q

Q H H

> @

IRU

P

M M M

QP QN N P N

N

' P

E E

!

¦

+HUHįQP LV WKH .URQHFNHU GHOWD >P@ PHDQV WKH LQWHJHUSDUWRIPDQG

> @

P M

Q N Q M

M QP PN

QN P

P

P& &

' Q

Q P

H

H

f

¦

6FDWWHUHGILHOGLQVLGHWKHZDOO

,WLVDVVXPHGWKDWWKHPDWHULDORIWKHZDOOEHKDYHVDVDQ HODVWLF VROLG ZKRVH PRWLRQ LV JRYHUQHG E\ WKH IROORZLQJ HTXDWLRQ>@

: W

U w ' . P P w

X X ’ ’ ˜X

ZKHUHXLVWKHGLVSODFHPHQWYHFWRUȡ:LVWKHZDOOGHQVLW\

ȀLVWKHEXONPRGXOXVDQG—LVVKHDUPRGXOXV:HDVVXPH

X ’M:

ZKLFKPHDQV WKDW ZH DOORZ IRU ORQJLWXGLQDO FRPSUHVVLYH ZDYHV LQ WKH ZDOO PDWHULDO DQG QHJOHFW WUDQVYHUVH VKHDU ZDYHV7KHGLVSODFHPHQWSRWHQWLDOij:LVWDNHQDV

Q FRV

: Q Q

Q

F W 5 U 3

M T

f

¦

7R ILQGFQWKHERXQGDU\FRQGLWLRQIRUWKHQRUPDOYHORFLW\

DWWKHOLTXLGZDOOLQWHUIDFHLVXVHG

/ :

W

M wM

Q˜ ’ Q˜ ’ w

ZKHUHQLVWKHLQZDUGXQLWQRUPDOWRWKHZDOO7KHUHVXOWLQJ H[SUHVVLRQIRUFQLVIRXQGWREH

Q

Q Q Q

F 5

Q ªD H D º

¬ ¼

&DOFXODWLRQRIİ

7R ILQGİ WKH QRUPDO IRUFH EDODQFH RQ WKH OLTXLGZDOO LQWHUIDFHLVXVHG

S/ V]]DWU U

ZKHUHS/LVWKHWLPHYDU\LQJSUHVVXUHLQWKHOLTXLGDQGı]]LV WKH QRUPDO FRPSRQHQW RI WKH VWUHVV WHQVRU RI WKH ZDOO PDWHULDOJLYHQE\>@

] ]]

X

V . ’ ˜X P§¨©ww] ’ ˜X·¸¹

$V (T LV YDOLG IRU DQ\ SRLQW RQ WKH OLTXLGZDOO LQWHUIDFHRQHFDQXVHWKHOLPLWLQJIRUPRIWKLVHTXDWLRQDW U Uĺ’,QWKLVOLPLWWKHH[SUHVVLRQVIRUS/DQGı]]WDNH WKHIROORZLQJIRUP

/ /

S G 5 5

U GW

U H

]]

G 5 5 U GW

V E H

ZKHUHȡ/LVWKHOLTXLGGHQVLW\DQGȕLVJLYHQE\

: :

U Q E U P

P Q

.

.

ZLWKȞ GHQRWLQJ 3RLVVRQ¶V UDWLR 6XEVWLWXWLRQ RI (TV DQGLQWR(T\LHOGV

/

/

H E U U E

(TXDWLRQIRUWKHEXEEOHUDGLXV

7RREWDLQWKHHTXDWLRQIRU5WZHDSSO\WKHPHWKRGRI WKH /DJUDQJLDQ IRUPDOLVP 5HFDOO WKDW WKH SUHVHQFH RI WKH HODVWLF ZDOO LV UHSODFHG ZLWK WKH SUHVHQFH RI D YLUWXDO EXEEOH $V D UHVXOW ZH JHW WKH V\VWHP RI WZR EXEEOHV VXUURXQGHG E\ DQ LQILQLWH OLTXLG LGHQWLFDO WR WKH OLTXLG VXUURXQGLQJ WKH UHDO EXEEOH 7KH NLQHWLF HQHUJ\ RI WKLV V\VWHPLVJLYHQE\

/ 9 /

7 U G9

³

’M

ZKHUH9 LV WKH YROXPH RFFXSLHG E\ WKH OLTXLG (TXDWLRQ FDQEHUHFDVWWR

FRV VLQ

/ / U 5

7 5 5 G

S

SU M T T T

³

FRV VLQ

/5 5 / U 5 G

S

SU H M H H T T T

³

7KHFDOFXODWLRQRI(TJLYHVWKHIROORZLQJUHVXOW

/ 7 S 5 5 (

U H

ZKHUHWKHIXQFWLRQ(İLVGHILQHGDV

( H HHHDH D

Q

Q Q

Q Q

H Q D D

f

ª º

¦

¬ ¼

7KHSRWHQWLDOHQHUJ\RIWKHV\VWHPFDQEHZULWWHQDV

8 S 5 3 5 3 S5 3 3

H

ª º ª º

¬ ¼ ¬ ¼ ZKHUH3 DQG3 DUH SUHVVXUHV WKDW GR ZRUN RQ WKH UHDO EXEEOH DQG RQ WKH YLUWXDO EXEEOH UHVSHFWLYHO\ 7KH YLUWXDO EXEEOH LV DVVXPHG WR H[SHULHQFH WKH VDPH SUHVVXUH DPSOLWXGH LH _3_ _3_ EXW WKH SUHVVXUH VLJQ FDQ EH RSSRVLWH,IWKHEXEEOHVSXOVDWHLQSKDVHİ!DQG3 3

Proceedings of the Acoustics 2012 Nantes Conference 23-27 April 2012, Nantes, France

(5)

,I WKH\ SXOVDWH RXW RI SKDVHİ DQG3 í3 $V D FRQVHTXHQFH(TEHFRPHV

_ _ 8 S 5 3

H

6XEVWLWXWLQJ(TVDQGLQWRWKH/DJUDQJLDQIXQFWLRQ / 7í8DQGWKHQLQWRWKH/DJUDQJLDQHTXDWLRQ

G / / GW 5 5 w w

w w

RQHREWDLQVWKHIROORZLQJHTXDWLRQIRUWKHEXEEOHUDGLXV

/ 5 5 5 3 W

U W H

ZKHUHWKHIXQFWLRQIJİLVJLYHQE\

_ _

( H

W H H

7KHSUHVVXUH3WFDQEHZULWWHQDV

* / DF

5 5

3 3 3 3 6

5 5

J

§ · K

¨ ¸

© ¹

ZKHUH3* LV WKH HTXLOLEULXP JDV SUHVVXUH LQVLGH WKH UHDO EXEEOHȖ LV WKHUDWLR RI VSHFLILF KHDWV RI WKH JDVȘ/ LVWKH VKHDU YLVFRVLW\ RI WKH OLTXLG3LV WKHK\GURVWDWLF SUHVVXUH LQ WKH OLTXLG3DF LV WKH GULYLQJ DFRXVWLF SUHVVXUH DQG WKH WHUP6 GHVFULEHV WKH HIIHFW RI HQFDSVXODWLRQ 1RWH WKDW LQ PRGHUQ HQFDSVXODWLRQ PRGHOV VXFK DV >@ DQG >@ WKH VXUIDFH WHQVLRQ WHUP LV LQFRUSRUDWHG LQWR WKH PRGHO IRUPXODWLRQ 7KHUHIRUH ZH GR QRW LQFOXGH LW H[SOLFLWO\ LQ (T

7KH VFDWWHUHG SUHVVXUH SURGXFHG E\ WKH EXEEOH LQ WKH IDUILHOG ]RQH LH DWU !!5 FDQ EH HYDOXDWHG IURP (T VXEVWLWXWLQJ WKH YDOXH RIİ IURP (T 7KH UHVXOWLQJH[SUHVVLRQLVDVIROORZV

/

/

/

5 5 5 5

S U 5

U

U E

U E

!!

1XPHULFDOVLPXODWLRQV

(TXDWLRQ VKRZV WKDW IRU D EXEEOH EHLQJ LQ FRQWDFW ZLWKDZDOOWKHOLTXLGGHQVLW\JDLQVDGLPHQVLRQOHVVIDFWRUIJ WKDWGHSHQGVRQWKHPHFKDQLFDOSURSHUWLHVRIWKHZDOO$VD FRQVHTXHQFH WKH EXEEOH RVFLOODWHV DV LI LW ZHUH LQ D OLTXLG ZLWKDQHIIHFWLYHGHQVLW\ȡHII IJȡ/'HSHQGLQJRQWKHZDOO SURSHUWLHVIJ FDQ EH HLWKHU ODUJHU RU VPDOOHU WKDQ VR WKH HIIHFWLYHGHQVLW\FDQEHHLWKHUKLJKHURUORZHUWKDQWKHUHDO OLTXLGGHQVLW\7KLVPHDQVWKDWWKHUHVRQDQFHIUHTXHQF\ RI DQDWWDFKHGEXEEOHFDQEHUHVSHFWLYHO\ORZHURUKLJKHUWKDQ WKH UHVRQDQFH IUHTXHQF\ RI WKH VDPH EXEEOH LQ DQ XQERXQGHGOLTXLG

,QWKH OLPLWLQJ FDVH RI D ULJLG ZDOOȕ ĺ’İ DQG (T JLYHVIJ )RU UHDO ZDOOV YDOXHV RIIJ DUH VPDOOHU $V DQ H[DPSOH OHW XV FRQVLGHU WKH ZDOO RI DQ 2SWL&HOO FKDPEHU 6XFK FKDPEHUV DUH ZLGHO\ XVHG LQ H[SHULPHQWV RQ FRQWUDVW DJHQW PLFUREXEEOHV >@

2SWL&HOO FKDPEHUV KDYH SRO\VW\UHQH ZDOOV ZLWK WKH IROORZLQJ PHFKDQLFDO SDUDPHWHUVȡ: NJP Ȁ

*3D DQG— *3D ,Q WKH FDVH WKDW WKHDGMDFHQW OLTXLGLVZDWHUZLWKȡ/ NJPRQHJHWVIJ 'LIIHUHQFHVLQWKHEHKDYLRURIDFRQWUDVWDJHQWPLFUREXEEOH DWWDFKHGWRDULJLGZDOODQGWKDWRIWKHVDPHEXEEOHDWWDFKHG WRDQ2SWL&HOOZDOODUHLOOXVWUDWHGLQ)LJ7KHVLPXODWLRQV KDYH EHHQ FDUULHG RXW E\ PHDQV RI WKH SURJUDP SDFNDJH 0$7+(0$7,&$ :ROIUDP 5HVHDUFK ,QF &KDPSDLJQ ,/ 7KH IROORZLQJ YDOXHV RI WKH SK\VLFDO SDUDPHWHUV ZHUH XVHG3 N3DȘ/ 3DÂVWKHVXUIDFHWHQVLRQRI ZDWHUı/ 1PWKHVRXQGVSHHGF PVDQGȖ 7KHHIIHFWRIHQFDSVXODWLRQRQWKHG\QDPLFVRIWKH EXEEOH ZDV VLPXODWHG E\ WKH VKHOO PRGHO GHYHORSHG E\

0DUPRWWDQWHW DO >@ $ PRGLILFDWLRQ RI WKLV PRGHO SURSRVHGE\2YHUYHOGHHWDO>@ZDVXVHG7KHYDOXHVRI WKH VKHOO SDUDPHWHUV IRU WKH 0DUPRWWDQW PRGHO ZHUH DOVR DGRSWHGIURP>@VKHOOYLVFRVLW\ț6 îNJVVKHOO HODVWLFLW\Ȥ 1P DQG LQLWLDO VXUIDFH WHQVLRQı5 1P 7KHVH YDOXHV ZHUH REWDLQHG LQ >@ IRU WKH SKRVSKROLSLGVKHOOHG FRQWUDVW DJHQW %5 7KH HTXLOLEULXPJDVSUHVVXUHLQ(TZDVFDOFXODWHGDV3*

3ı557KHEXEEOHUHVWLQJUDGLXVZDVVHW HTXDOWR

—P 7KH EXEEOH ZDV LQVRQLILHG ZLWK D F\FOH N3D

*DXVVLDQ SXOVH ZLWK D FHQWHU IUHTXHQF\ LQ WKHUDQJH ± 0+] 7KH SDUDPHWHUV RI WKH SXOVH FRUUHVSRQG WR WKH FRQGLWLRQV XQGHU ZKLFK WKH YDOXHV RI WKH VKHOO SDUDPHWHUV ZHUHHYDOXDWHGLQ>@

)LJXUH5HVRQDQFHFXUYHVIRUDWKHUDGLDORVFLOODWLRQDQG

EWKHVFDWWHUHGSUHVVXUHRIDQHQFDSVXODWHGPLFUREXEEOH RVFLOODWLQJLQDQXQERXQGHGOLTXLGGDVKHGOLQHLQFRQWDFW

ZLWKDULJLGZDOODQGLQFRQWDFWZLWKDQ2SWL&HOOZDOO )LJXUHD VKRZV UHVRQDQFH FXUYHV IRU WKH EXEEOH UDGLDO RVFLOODWLRQ5PD[ GHQRWHV WKH PD[LPXP YDOXH RI WKH EXEEOH UDGLXV5W GXULQJ WKH RVFLOODWLRQ 7KH GDVKHG OLQH FRUUHVSRQGV WR WKH EXEEOH LQ DQ XQERXQGHG OLTXLG )LJXUHE VKRZV UHVRQDQFH FXUYHV IRU WKH VFDWWHUHG SUHVVXUHRIWKHEXEEOHLQWKHIDUILHOG]RQH3PD[VWDQGVIRU WKH SHDN DPSOLWXGH RI WKH VFDWWHUHG SUHVVXUH FDOFXODWHG E\

(T DWU P $V RQH FDQ VHH LQ )LJ FRQWDFW ZLWKWKHULJLGZDOOGHFUHDVHVWKHUHVRQDQFHIUHTXHQF\RIWKH EXEEOH DV FRPSDUHG WR LWV UHVRQDQFH IUHTXHQF\ LQ DQ

Proceedings of the Acoustics 2012 Nantes Conference 23-27 April 2012, Nantes, France

(6)

XQERXQGHG OLTXLG ZKHUHDV FRQWDFW ZLWK WKH 2SWL&HOO ZDOO LQFUHDVHV WKH UHVRQDQFH IUHTXHQF\ RI WKH EXEEOH 7KH EXEEOHRVFLOODWLRQDPSOLWXGHFDQHLWKHUGHFUHDVHRULQFUHDVH GHSHQGLQJ RQ WKH YDOXH RI WKH GULYLQJ IUHTXHQF\

)LJXUHDVKRZVWKDWWKHUHVRQDQFHIUHTXHQF\RID—P UDGLXVEXEEOH ZLWKWKH0DUPRWWDQWVKHOOLVDERXW0+]

LQDQXQERXQGHGOLTXLG,IWKHEXEEOHLVGULYHQDWVD\

0+] FRQWDFW ZLWK WKH ULJLG ZDOO ZLOO LQFUHDVH WKH RVFLOODWLRQ DPSOLWXGH RI WKH EXEEOH ZKHUHDV FRQWDFW ZLWK WKH2SWL&HOOZDOOZLOOGHFUHDVHLW$W0+]WKHUHYHUVHLV WUXH 7KHVH UHVXOWV VXJJHVW WKDW WKH PRGHO RI D ULJLG ZDOO DSSHDUV QRW WR EH DQ DGHTXDWH DSSUR[LPDWLRQ IRU ZDOOV RFFXUULQJ LQ PRVW DSSOLFDWLRQV DVVRFLDWHG ZLWK FRQWUDVW DJHQWPLFUREXEEOHV

)LJXUH([DPSOHVRIDUDGLXVWLPHDQGESUHVVXUHWLPH FXUYHVIRUD—PUDGLXVHQFDSVXODWHGEXEEOHRVFLOODWLQJLQ DQXQERXQGHGOLTXLGDQGLQFRQWDFWZLWKDQ2SWL&HOOZDOO )LJXUHSURYLGHVH[DPSOHVRIUDGLXVWLPHDQGSUHVVXUH WLPHFXUYHVIRUWKHVDPHEXEEOHDVLQ)LJ,WLVDVVXPHG WKDW WKH EXEEOH LV LQVRQLILHG ZLWK D F\FOH N3D 0+] *DXVVLDQ SXOVH ,W LV RI LQWHUHVW WR QRWH WKDW WKH

³&RQWDFW´ FXUYH LQ )LJD VKRZV WKH LQLWLDWLRQ RI WKH VHFRQGKDUPRQLFLQWKHEXEEOHRVFLOODWLRQ7KHQRQOLQHDULW\

RI(TLQFUHDVHVWKLVHIIHFWLQWKHVFDWWHUHGSUHVVXUHDV IROORZV IURPWKH³&RQWDFW´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

)LJXUH)RXULHUVSHFWUDRIWKHSUHVVXUHWLPHFXUYHVVKRZQ

LQ)LJE

&RQFOXVLRQ

$ 5D\OHLJK3OHVVHWOLNH HTXDWLRQ KDV EHHQ GHULYHG WKDW GHVFULEHV WKH UDGLDO RVFLOODWLRQ RI DQ HQFDSVXODWHG EXEEOH DWWDFKHGWRDQHODVWLFZDOO,WKDVEHHQIRXQGWKDWWKHOLTXLG GHQVLW\LQWKLVHTXDWLRQJDLQVDGLPHQVLRQOHVVIDFWRUIJWKDW LV GHSHQGHQW RQ WKH PHFKDQLFDO SURSHUWLHV RI WKH ZDOO DQG WKHGHQVLW\ RIWKHDGMDFHQWOLTXLG$VDUHVXOWFRQWDFWZLWK WKH ZDOO DIIHFWV WKH EXEEOH RVFLOODWLRQ DV LI WKH EXEEOH RVFLOODWHGLQDOLTXLGZLWKDQHIIHFWLYHGHQVLW\ȡHII IJȡ/,Q WKHOLPLWLQJFDVHRIDULJLGZDOOIJ )RUUHDOZDOOV IJLVVPDOOHU,QSDUWLFXODUIRUSRO\VW\UHQHZDOOVRI2SWL&HOO FKDPEHUV XVHG LQ H[SHULPHQWV LI WKH DGMDFHQW OLTXLG LV ZDWHU IJ 7KXV GHSHQGLQJ RQ WKH ZDOO SURSHUWLHVIJ FDQ EH HLWKHU ODUJHU RU VPDOOHU WKDQ 7KLV PHDQV WKDW WKH HIIHFWLYH GHQVLW\ FDQ EH HLWKHU KLJKHU RU ORZHU WKDQWKHUHDO OLTXLG GHQVLW\ DQGKHQFH WKHUHVRQDQFH IUHTXHQF\ RI DQDWWDFKHG EXEEOH FDQ EH UHVSHFWLYHO\ ORZHU RUKLJKHUWKDQWKHUHVRQDQFHIUHTXHQF\RIWKHVDPHEXEEOH LQDQXQERXQGHGOLTXLG

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

Proceedings of the Acoustics 2012 Nantes Conference 23-27 April 2012, Nantes, France

(7)

,Q FORVLQJ LW VKRXOG EH QRWHG WKDW WKH SURSRVHG WKHRU\

LJQRUHV WKH YLVFRXV SURSHUWLHV RI WKH ZDOO DQG WKH RFFXUUHQFH RI WUDQVYHUVH ZDYHV ,W LV QRW LPSUREDEOH WKDW WKHVH HIIHFWV PD\ EH RI LPSRUWDQFH DQG KHQFH WKH GHYHORSPHQWRIDWKHRU\WKDWZRXOGWDNHWKHPLQWRDFFRXQW FRXOGEHRIJUHDWLQWHUHVW

5HIHUHQFHV

>@0 /DQNIRUG & = %HKP - <HK $ / .OLEDQRY 3 5RELQVRQ - 5 /LQGQHU ³(IIHFW RI PLFUREXEEOH OLJDWLRQ WR FHOOV RQ XOWUDVRXQG VLJQDO HQKDQFHPHQW LPSOLFDWLRQV IRU WDUJHWHG LPDJLQJ´ ,QYHVW 5DGLRO

>@6 =KDR ' ( .UXVH . : )HUUDUD 3 $ 'D\WRQ

³$FRXVWLF UHVSRQVH IURP DGKHUHQW WDUJHWHG FRQWUDVW DJHQWV´-$FRXVW6RF$P(/(/

>@9*DUELQ'&RMRF()HUUDUL('L)DEUL]LR0/- 2YHUYHOGH60YDQGHU0HHU1GH-RQJ'/RKVH 09HUVOXLV³&KDQJHVLQPLFUREXEEOHG\QDPLFVQHDUD ERXQGDU\ UHYHDOHG E\ FRPELQHG RSWLFDO PLFURPDQLSXODWLRQ DQG KLJKVSHHG LPDJLQJ´ $SSO 3K\V/HWW

>@06WUDVEHUJ³7KHSXOVDWLRQIUHTXHQF\RIQRQVSKHULFDO JDVEXEEOHVLQOLTXLGV´-$FRXVW6RF$P

>@-(%OXH³5HVRQDQFHRIDEXEEOHRQDQLQILQLWHULJLG ERXQGDU\´-$FRXVW6RF$P

>@$ 6KLPD < 7RPLWD ³7KH EHKDYLRU RI D VSKHULFDO EXEEOH QHDU D VROLG ZDOO LQ D FRPSUHVVLEOH OLTXLG´

,QJHQLHXU$UFKLY

>@(0%3D\QH6-,OOHVLQJKH$2RL50DQDVVHK

³6\PPHWULF PRGH UHVRQDQFH RI EXEEOHV DWWDFKHG WR D ULJLGERXQGDU\´-$FRXVW6RF$P

>@$$'RLQLNRY6=KDR3$'D\WRQ³0RGHOLQJRI WKHDFRXVWLFUHVSRQVHIURPFRQWUDVWDJHQWPLFUREXEEOHV QHDUDULJLGZDOO´8OWUDVRQLFV

>@$ $ 'RLQLNRY / $LUHG $ %RXDND] ³$FRXVWLF UHVSRQVH IURPD EXEEOH SXOVDWLQJQHDU D IOXLGOD\HU RI ILQLWH GHQVLW\ DQG WKLFNQHVV´ - $FRXVW 6RF $P

>@$ $ 'RLQLNRY/ $LUHG $ %RXDND] ³$FRXVWLF VFDWWHULQJ IURP D FRQWUDVW DJHQW PLFUREXEEOH QHDU DQ HODVWLF ZDOO RI ILQLWH WKLFNQHVV´ 3K\V 0HG %LRO

>@$ $ 'RLQLNRY ³7UDQVODWLRQDO PRWLRQ RI WZR LQWHUDFWLQJ EXEEOHV LQ D VWURQJ DFRXVWLF ILHOG´3K\V 5HY(

>@/ ' /DQGDX ( 0 /LIVKLW]7KHRU\ RI (ODVWLFLW\

3HUJDPRQ3UHVV2[IRUG

>@3 0DUPRWWDQW 6 YDQ GHU 0HHU 0 (PPHU 0 9HUVOXLV 1 GH -RQJ 6 +LOJHQIHOGW ' /RKVH ³$

PRGHO IRU ODUJH DPSOLWXGH RVFLOODWLRQV RI FRDWHG EXEEOHV DFFRXQWLQJ IRU EXFNOLQJ DQG UXSWXUH´ -

$FRXVW6RF$P

>@6 3DXO $ .DWL\DU . 6DUNDU ' &KDWWHUMHH : 7 6KL ) )RUVEHUJ ³0DWHULDO FKDUDFWHUL]DWLRQ RI WKH

HQFDSVXODWLRQ RI DQ XOWUDVRXQG FRQWUDVW PLFUREXEEOH DQG LWV VXEKDUPRQLF UHVSRQVH 6WUDLQVRIWHQLQJ LQWHUIDFLDO PRGHO´- $FRXVW 6RF $P

>@02YHUYHOGH9*DUELQ-6LMO%'ROOHW1GH-RQJ ' /RKVH0 9HUVOXLV ³1RQOLQHDU VKHOO EHKDYLRU RI SKRVSKROLSLGFRDWHG PLFUREXEEOHV´8OWUDVRXQG 0HG

%LRO

Proceedings of the Acoustics 2012 Nantes Conference 23-27 April 2012, Nantes, France

Références

Documents relatifs

7KHSURGXFWLRQRIDGHVFULSWLRQRIWKH$87LVDNH\HOHPHQWLQ RXUSURFHVVDVWKLVGHVFULSWLRQLVXVHGLQERWKWHVWJHQHUDWLRQ DQGGHYHORSPHQWDFWLYLWLHV)RUWKHModelling of the

In the presented work, a reciprocal modulation intensity was observed through the PR-MO structure, in the different magnetic field configurations: Faraday, longitudinal and

be seen in Figure 24, and again in Table VI as to the friction factor. The value of the friction factor for this case is lower than the case of random large obstacles,

$IWHUVHYHUDOIHUPHQWDWLRQVWKHORVVHVRIPDVVEHWZHHQWKH EHJLQQLQJDQGWKHHQGRIWKHIHUPHQWDWLRQHYROYHLQWKHVDPH SURSRUWLRQV LQGHSHQGHQWO\ RI WKH TXDQWLW\ XVHG

Figure 2: (a) The magnitude of the fundamental component in the spectrum of the bubble scattered pressure versus driving frequency for the OptiCell wall.. (b) The deviation of the

WR HQVXUH WKDWDOO DVSHFWV RI UHSURGXFWLYH DQG VH[XDO KHDOWK LQFOXGLQJ LQWHU DOLD PDWHUQDODQG QHRQDWDO KHDOWK DUHLQFOXGHG ZLWKLQ QDWLRQDO PRQLWRULQJ DQG UHSRUWLQJ

Li frvwv duh qlo/ wkh pdlq fkdqjhv duh lq vroxwlrq wr S 6= lq idfw htxdwlrq +54, ghvfulehv d vlwxdwlrq lq zklfk wkh sulqflsdo ghflghv wr lqyhvw lq LW iru doo w|shv ri djhqwv/ dqg wkh

Lq wklv sdshu zh vwxg| lq d jlyhq txlwh jhqhudo frpsohwh qdqfldo pdunhw wkh vwdelolw| ri wkh rswlpdo lqyhvwphqw0frqvxpswlrq vwudwhj| dv ghqhg e| Phuwrq +4&lt;:4, zlwk uhvshfw wr