Analyse de données de l`expérience VIRGO - HAL

Transcription

Analyse de données de l`expérience VIRGO - HAL
Analyse de données de l’expérience VIRGO
D. Grosjean
To cite this version:
D. Grosjean. Analyse de données de l’expérience VIRGO. Journées de Rencontre des Jeunes
Chercheurs 2005, Dec 2005, Aussois, France. IN2P3, pp.265-269, 2005. <in2p3-00188168>
HAL Id: in2p3-00188168
http://hal.in2p3.fr/in2p3-00188168
Submitted on 15 Nov 2007
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published 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.
N |
O M
$
%]
J š
.6
Ÿ
_¡
¢ ^£ )
+
.
.
.
=
))-,0/,0/
=
7 f Jš
Jš” %
!
+
Q
cl<g V}zrX„ful~gQu7w d[s;d9hm¨gXlˆul ufss}zl~gFu}zxlzs“ulzsMrOut
r•¨x“lˆulˆgXf9tpye!l~gŽe!f9s“gk†u}zpT}zl~g €|ý sngzw kmsMrT}zpTl<gTgl‹kiezk#–¤ul<g
gXf9tpye!l~gukmrXl~grXpyd[s;gXkmrXf9kipTl<g5e!fpXpTl<gXx“fs;ud9sr–›h†d›x„;d9gXlœgx;kºé
pyd[h†d[sMrXl‘u7w t;s£gX¨grX‚ 2l”okis;d9kmpTl”u7w }!rTf9kihml~g5–Hsl<trXpTf9s“gšft£ul
rXpTf9t“g_s;f9kipTg € lzs;ud9sMrNezl!rXrXl5x„;dglBhml~gNulzt’Vd9grXpTl<g{glpyd[xé
xpTfey„lzsMr|gft;gh\w lz÷lzr
ul#h†dVx“l<prTl#u7w }<slzpTj9kilœx;d9p} 2kigTgXkmfs
ý i } Vk†g
ul‹pTd¨f9ss;l 2lzsMr‡jpTdqkmrTdBrTkmfssl<h € cl˜gkij9s;d9h‘uw a
xlzs;ud9sMrše!l!rXrXlx„“d9gXll<grNu}<e!pTkmrx;d[pul~ge!fpXpTl<e!rXkif9s;g¥xfgré
sl s5rXf9s;kml<ssl<gˆd9tôå¦fp ƒd9hmk†g 2l—…Mt;d9upXtxf9h†d[kipTl € [@hŒgzw d[jkºr
u7w ts
14. .ë”gXkmjs;d[hHuf9sMrDh\w d Vx;hmkmrXt;ul l!rOhid¤å¦pT}<…Mtl<s;e!l
e!pTf9k†gTgl<srNud9s;gNhil5rXl 2x;g € c_dœe!f9s;s;d[k†gXgTd[s“e!lrX„}<f9pTki…Mtl5xpT}!é
ý i Ý sf[rT}Žu;d[s;gVh†dOgXtkmrXl ¥à›x“l<s;ud[sMr
e!k†gXlaut¤gXkmjs;d[hu7w a
e!lzrrTlFx„;d9gXlŽx“l<p 2lzr‡ul 2l!rrTpXlFl<s¤fMl<tqpXlŽts;lQd[s;d9hm¨gXl
o;dg}<l›gXtp”t;sl 2}!rT„ful2uv
l g“hºrTpTd9j9lHdud[xrT} € ] f9rXf9s“g”…Mtl
e!l‘gkij9s“d[h“u}zxlzs;u‡xpXkis;ezkmx;d9hml 2lzsMrul~gšx“d[pyd 2‚!rTpXl~gkisrTpXkisé
gX‚<…Mtl<g›…Mtl‡gXf9sMr#hid 2dgXgXl‡ul~gHul<t’˜f9o >•lzrTgHut g¨grX‚ Vl
Õ ã Ö €
cw }!rTd9í x“lƒx;pX}<hmk 2kms;d9kmpTlƒ–arXftrXlŒd9s;d[hi¨glƒe!fs;gXkigrXlƒ– >pTl!é
=
=
9
+
Q
$ !
æN|N |
O M
=
Q
=
*
$
.
+
?
.
!
.
F?
!e fs;grXpTtkmpTl hilZgXkij9s;d9hu7w fs;ulœjpTdqkmrTdBrTkmfssl<hmhil € [@hg<w d9j9kmr–
x;d9prTkmpNut2gkij9s“d[hlzsƒgXf9pXrXkilul5h\w kisMrXl<på¦}<pXf V‚zrXpTl Ý 2l<gXtpXl5ul
u}<x„;d9gTd[jlHul2h†n
d g;jtpXl2u7w kmsMrTlzpXå¦}zpTlzs;ezl~à|uw kisq9lzpygXlzp‘h‰w l!÷¹l!r
ul5pT}zxf9s;gXlutƒu}!rTl<e>rTlztpNxf9t;pe!f9s“g•rTpXtkipTlh†dZg}<pXkilšrTl 2xf[é
pTlzhihml Õ ÓÖ e!fsMrXlzs“d[sMr›h\w kiså¦fp ƒdBrTkmfsÆulŽu}!å¦fp ƒdBrTkmfsÆutl
ý iV€ù fsrTpXkiotl‹– ezl!rrTl‹gX}zpTkilQtrXkihikigTd[ohilDx“d[pahml~g£d9hºé
–Æh\w a
j9fpXkmrX„ Vl~g#u7w d[s;d9hm¨gXl2hmlŒo;pXtkmr›utÆu}!rXl~e>rTlzt_
p Õ ÓÖ d9t;…Mtlzh
ý i  Ñ Õ ÓÖ €
g<w 2d >•f9trTl‘t;sa}<q9l<srTtlzhgXkij9s;d9h¹uw a
%
)
;
=
P
< ‚~ghif9pygz<hid 2}!rX„;fulul+g;hºrTpTd9j9lšdud[xrX}xlztrXéc;zrXpTl 2k†gl
lzsƒfl<tqpXl € è hihml‘e!f9s“gk†g•rTl|–#ezd9hiezthilzpts;l
e!fpXpT}zh†dBrTkmfs›l<srTpXl
Õ ÓÖ l!r
Õ Ó Ö ë
c l<gf9s“ul<gj9pydqkºrydBrTkmfsslzhihil<ggXf9sMr5tsl‘xpX}~uk†e>rXkif9saul‘hid
rX„}<f9pTkmlVulHh†d‡Ï|lzh†dBrXkiqkºrT} i }<s}zpyd[hil € cw kmså¦f9p 2d[rXkif9sQgXtp‘hid
qBd[pTkid[rXkif9s2utVey„“d 2x›jpTdqkmrTd[rXkif9ssl<hu7w t;sVfo >•l!rdg•rTpXfx„¨é
gk†…MtlŒgXlƒxpXfx;d[jl›x“d[pœh\w kisMrXlzp 2}<uk†d[kipTl2ulŒe!l<gZfs;ul~g#–ahid
qkºrTl<gTglŒul2h†dŽhmt Vki‚zpTlƒgl<hmfs‹ulzt’‹}!rTd[rTg#ulVxf9h†d[pTk†gXd[rXkif9s €
!
.
!
!
v
=
=
cdFå§d9kmo;hmlŽd 2xhikºrTt;ulFul~g›fs;ul~gHjpTdqkmrTdBrTkmfssl<hmhil<gHs}!é
!e l~gXgXkmrXlŒu7w d9ufxrXl<p#tsl£e!f9shg;j9tpydBrTkmfsOfxrXk†…MtlŒxhit;g›e!f Vé
xhil!’l|…Mtl
ezlzhihml|u7w tsƒkisMrXlzpXå¦}zpTf 2‚zrXpTl5gXk Vx;hml €Mý sVrXpTf9tqlzpyd
ul~gu}!ryd[kihiggtphid|ezf9^
s g“j9tpydBrTkmfs
f9xrXk†…t;E
l g;s;d9hmlul K[•Ï i#ý
ud9s;gZ² ! ³ €
cl›u}zrXl~e>rXl<tp[•Ï i#ý å§d9kºr‘x;d[pXrXkilHutFpT}<gXl<d9tQulHu}zrXl~e>é
rXl<tpTgakisMrXlzpXå¦}zpTf 2}zrXpTki…Mtl~g‡u7w ýai ² ß ³Zd9t>•f9t;pTu7w „tk‘lzs½u}!é
q9l<hmfxx“l 2lzsMr € [@h¥d[rrTlzkis;upydŒxpTfey„;d[kisl 2l<sr
gTd‡gXlzs“gkiokihmkmrX}
sf 2kis;d[hilaf9áÆts;l£xpTl 2ki‚zpTl£u}zrXl~e>rXkif9sÂl<grVl<sqMk†gTd[j9l~d[ohil €
ù l!rXrXl2}<ey„}~d[s;ezl›ul ƒd[s;ul2ul ƒd †rXpTkigXlzp”hml~g”ftrXkih†g‘uw d9s;dBé
hm¨gXl”ul”uf9ss;}zl<gd9ud9xrX}~gšd9t’2ukº÷¹}zpTlzsMrTgr•¨x“l~gul”gftpTezl<g
l!r
d9t;gXgXkulœxpT}zx“d[pTlzph‰w d[s;d9hm¨gXlZlzsŽpX}~gl~d[t €
cšw }<q9fhmtrTkmfs)ul gTd—gl<s;gkiokihmkmrX} l<grDx“fs;e>rTt}zlÂulÆpTts;g
rXl~ey„sk†…t;l<g € A|xpT‚<gFdqf9kip£kisMrXpTfutkºrFh†d V}zrX„fulÆul˜u}!é
ý i dql<e [•Ï i#ý lzr”hil<g|x;pXkis;e!kixl<g|j}zs}<pTd9t’
rXl~e>rXkif9sOul<g a
u7w d[s;d9hm¨gXlZd9xxhiki…Mt}~gd[t’‡gX¨g•rT‚ 2l<g5o;kms;d9kmpTl<g<f9saxpT}<gXlzsMrXl
…Mtlzh†…Mtl<gZpT}<gXthmrTdBrygœu7w d[s;d9hm¨gXlVx;pX}<hmk 2kms;d9kmpTl2ut˜pXtsOrXl~ey„é
sk†…t;l ù¾€_ý sˆu}!ryd[kihmhil2lzs;gXtkmrXlƒh\w kisMrX}<p ;zrHul2hidŽpTl<ey„l<pTey„;l
ul<g2gX¨g•rT‚ 2l<gHokms“d[kipXl~gHul£rXpTf9t;gHsf9kipygHlzr›hil<g›}!rTd9x“l~gHs;}!é
e!l~gXgTd[kipXl~gN–#gTd Vk†gXl|lzsƒflzt;qMpTll!÷¹l<e!rXkiq9l|xf9t;ph‰w d[s“d[hi¨gXl|ul
uf9s;s}zl~g € è^
s g;s~ud9s;ghile<d9upTlšulšhidx;pX}<x;d[pydBrTkmfsZulšh\w d9s;dBé
hm¨gXlQlzs—pT}<gXl<d9tfs—xpX}~gl<sMrXlQts;l 2}!rX„;fulD…Mtk”xlzp 2l!r
u7w d 2}zhikmfpXl<pFhid¤pT}<gXf9hitrTkmfsõrTl 2x“fpXl<hmhil9”x;d[pyd 2‚zrXpTlOtrTkmhil
x“ftp|h†dVhmfezd9hmk†gTdBrXkif9saul<ggXf9t;pTezl<g €
$
=
=
!
#
f
.
.
ç ft;gŒh\w lz÷lzrŽuw ts;l a
ý i tsælzs“gl HohilDul 2dgXgXl<g‡hmkiopTl<g
u k†gxfgX}zl~gšl<s£ezlzpye!hil‘gXtokipTdHtslZe!fsrTpTde>rTkmfs‡ud[s“gšts;l‘ukmé
pTl<e>rTkmfsOlzrœtslŒe!fsMrXpyd9e>rTkmfsOud9s;g‘hidŽukipTl<e>rTkmfsOxlzpTxlzs;ukmé
e!t;hid9kmpTl € cw kmsMrTlzpXå¦}zpTf 2‚!rTpXl K[•Ï i#ý qBd£uf9s;e›pX}<x“fs;upTl›d9t
ý i x;d[p‡tsl 2fuk g“ezd[rXkif9s—ukm÷}<pXl<sMrXkilzhihml
x;dgXgTd[jlŽuw ts;l a
W ulZhidVhif9sjtlztp W ulœezl<gul<t’‡opyd9g € cT w d 2xhikºrTt;ulœul
h\w fs;ulZj9pydqkºrydBrXkif9s;slzhihml‘l<gr|d[hif9pyg‘ë Ò ' T €
clFu}!rTl<e>rTlztpƒkisMrXl<på¦}<pXf V}zrXpTki…Mtlau7w f9s;ul~gVj9pydqMkmrTd[rXkif9sé
slzhihil<g Ý ýai àK[•Ï i#ý ² ³d[x;xpXfey„lul5gXd”gl<s;gkiokihmkmrX}sf Vkmé
s;d[hil € < d[s;g5ezl”e!fsMrXl!’rTl9Mhml~g 2}zrX„ful~guw d9s;d[hi¨gl‘ul”ufsé
s}zl~guf9kiq9l<sMr ;!rTpXl‘xkp ;!rTl<gx“ftprXpyd[kmrXl<pt;s£k 2x“fpryd[sMrø“t’
ul›uf9ss}<l<g €¹ý sFxpT}<gXlzsMrTl#hml~g|xpTkis;e!kix“l~g
j}zs}<pTd9t’auw d9s;dBé
hm¨gXl‘d9xxhiki…Mt}~g5–Hh\w }zrXt;ulZul<g5g¨grX‚ Vl~gokms“d[kipXl~g € cl~gxlzpXé
å¦f9p ƒd[s;ezl<gHulŒhidDey„;d úsl‡u7w d[s“d[hi¨gXlƒxf9tp›h‰w }!rTt;ul‡ut pXts
rXl~ey„sk†…t;l ù¾ gfsr5kisrTpXfut;kºrTl<g €ý sad[of9pyul|}zjMd[hil 2lzsMrhid
2kigXlOl<sõflzt;qMpTlOulOh†dÆpTl<ey„l<pTey„;lDul˜g¨grX‚ 2l~g‡okis;d9kmpTl<g
ul‘rXpTf9t;gsfkmpyg € è^
s g“stslZd 2}zhikif9pydBrXkif9sŒul”h†dHpT}<gXf9hitrTkmfs
rXl Vxf9pTlzhihilQud[s;g2hilQezdupTlau7w tslQd9s;d[hi¨glŽl<sÂpT}<gXl<d9tÂl~g•r
xpT}<gXlzsMrX}<l €
%
I ; "" (v%
'æ+*
3 ŽE#E#Y aUNUA 9I
$
^a`b]
)
%
ß ¾ Þ
 ã Ò ' Õ YS'Ö& %Õ $ ÖÕ Y Ö Ð Y
!#" " Y
Ú
) ))(
Ý\Þ9Þ € à
ß ¾9¾
Ý f9áŽhilZrXkihiul#u}<gXkmjslZhid›rXpyd[s“g•å¦fp 2}zlZul#ê;f9tpTkml<pyà €
ý Ž
s kisMrXpTfutkºr|d9hmfpTghilœpTd9xx“fprgXkmjs;d[hgXtpopTtkmr#ë
S !
Ò
.
Ñ ã)
š ã
&
݉ÞÞ € ß à
cl~gƒqBd[hilztpyg Õ ã Ö ezd9pTde>rX}<pXk†gTd[sMr›h†dˆgftpye!lal!r‡u}zé
Õ ÓÖ sw }zrTd9sí rŽx;dgaezf9sstl~gŽd xpTkif9pTk‰f9söuf9kmr
g“hºrTpXl<p|hml~g
ufss}<l<g|dql<e‘tsFlzs“gl Hohil#ulœå¦fp 2l<g
u7w fs;ul~g
Õ ÓÖ €šù l!rHl<s;gXl Ho;hml‡ul£ezd9hi…Mtl~g
rT„}zfpXk†…Mtl<gHf9tÆe<d[h†…t;l<g
l~g•r2e!fs;g•rTpXt;kºrHl<sÆtrTkmhikigTd[sMrHt;s d[hij9fpXkmrX„ 2lŒul£xh†d9e!l 2lzsMr
² [³…t;kx“l<p 2lzrHulƒe!f9t;qMpTkipœh‰w l<gXx;d9ezlƒul<gZx;d9pTd 2‚!rXpTl<g ¹f9s
ezf9s;grXpTtkmr|d[kis;gktslZj9pTkmhihilZul#ezd[h†…Mtl<g €
èsQe<d[h†e!th†d[sMr|h†dƒe!f9pTpT}zh†dBrXkif9s£lzsMrXpTlœhil<g
uf9ss}<l<g5pTl<ezf9s;gé
rTpXt;kºrTl<gOl!rOh\w lzs;gXl ›ohmlÂul<gOezd[h†…Mtl<g<
fs)l<gr‹e<d[x;d9ohmlÂul
u}!rXl<p 2kislzp›hidŽx;pX}~gl<s;e!lƒftˆh‰w d[o;gXlzs“e!lŒu7w tsÆgXkmjs;d[hšuw ýai
Ý u7w d 2xhikºrTt;ulHgXt ŒgXd9sMrXl~àud9s;g5hil<gufss}zl~g €
g“skigTgTd[sMr
!
.
O
=
dq9l<e
ts‡t;ski…MtlZezd9hi…MtlZe!fpXpTl<gXxf9s;ud9sMrd[t‡gXkij9s;d9h“kis>•l<e!rX}à
ulFhid˜x;pXl Vki‚zpTlŽl!r‡ulFh†dˆul<pXski‚zpTlŽx“}<pXkiful<g‡u7w kis >•l~e>rXkif9s €
ftpZe!l<g‘x}zpTkmful~g”d9kms“gk{…Mtl›hil<gZul<t’Dd[trXpTl<g<;rTf9trTl<g‘hml~g
ç ] ÏÆul~gkis >•l<e!é
kms >•l~e>rTkmfs;ggXf9sMr_u}zrXl~e>rX}<l<g € c_dqBd[pTkid[rXkif9sœul ^
rXkif9s;g 2lzsMrXkif9s;s}zl‘xpT}<e!}~ul 2lzsMr5l<grfo;gXlzpTq9}zl € c_dHs;l!rrTl
d 2}zhikmfpTd[rXkif9sFul›hid£gl<s;gkiokihmkmrX}VutlV–Œh\w d[rrX}<st;dBrTkmfsDulHh†d
hmt 2ki‚zpTlHukm÷t“g}<lHd[xpT‚<g…Mtl<hi…Mtl~g >•ftpTg
ul#pTtsQglZrTpTdutkmr
ç ] Ï Ý ß ¿ àsl!rXrXlzé
x;d[ph†d2u}!rTl<e>rTkmfsFul<gkis >•l~e>rXkif9s“g|–2ul<g h
ç ] Ï ƒd[’k Ht ul£hidFuk†grXpTkmotrXkif9s
Vl<sMr›gt;x“}<pXkilztpyg#d9t ^
ulœopTtkºr Ý ! à €
.
8
!
O
=
+ =
HTž
$#"n$
+
"
¢ ^
¡ ^
"
"
('2^
"
)
=
clZe!f Vk†gTgkif9skisjHutau}zrXl~e>rXl<tp K[•Ï i#ý dHezf 2lzs;ez}
<l s£s;fBq9l ›opTl ß  ! € < lzxt;kigu}~e!l HopTl ß 9 “hilœu}!rTl<e!rXlzt;p
å¦fs;e>rTkmfsslŒud9s;gœgTd£ezf9s^g;jtpydBrXkif9sOf9xrTki…Mtl\g;s“d[hil Ý kmsMrTlzpXé
å¦}<pXf 2‚!rXpTlDpTl<ez¨e!hi}~à € cw }zqf9hitrXkif9s½ut½ezf 2kigTgkif9s;kmsjÂl<gr
xf9s“e>rXt;}zl›ul#pXt;s;grTl<ey„sk†…Mtl<g”…Mtk_xlzp 2l!rXrXlzsMr”ul›ut} g;skip
hil<g5xlzpXå¦f9p ƒd[s;ezl<gutŽu}!rTl<e>rTlztp € clœgXkº’ki‚ 2l‘pXts ù¾ gzw l<gr
u}zpTf9thi}‡l<sÂd[fÈr ß 9 Þ xlzs;ud9sMr >•f9t;pTgVdq9l~eŒts™e!¨e!hil
€
trXkihml#ul » Þ
cdFgXlzs“gkiokihmkmrX}ƒdBrXrXl<kmsMrXlƒxlzs“ud[sMrHe!lƒpTtsˆda}!rT}Œd 2}zhikmf9é
pT}zlŽx;d9p2pTd9xx“fprŒd9tÂpTts ù Þ ² Þ ³”gXtpVrXftrXlFh†d‹o;d[s“ulFul
å¦pT}<…Mtl<s;e!l›u7w l<sqMkipTf9sFtsQfpTupXl#ul›j9pyd[s;ulztp € èhihml2dBrXrXlzkisMr
mÃ~Ä ó
ò & ±
V– Äć±| € ŠQd[hij9pT}›ezl!rXrXlƒd 2}zhikif9pydBrXkif9sOul
î
î
gXlzs“gkioíXkií hmkmrX}hidFgrTd[rXkif9ss“d[pTkºrT}2ulƒh‰w kmsMrTlzpXå¦}zpTf 2‚!rTpXlVl<gr#x“l<t
gTdBrTkigå§d[k†gTd[sMrXl € < kº÷¹}zpTlzsMrXl~gd 2}zhikmfpTd[rXkif9s;gNd9t‡e!ftpTgutŒpTts
Ý dBrXrX}zst;d[rXkif9sDul#hmt Vki‚zpTl›ukº÷¹t;gX}zl9pT}<d[hikij9sl Vl<sMr
utFå§d[k†gé
ezl<d9tõgt;p‡h†d ezdqkmrX}QfxrXk†…MtlOuw l<srTpX}<lQxlzp Vlzrryd[sMrau7w f9oé
rTlzskipVtsÆxpTSf g;hul‡xt;kigTgXd9s;e!l‡jd[t“gXgXkml<sd V}<hmkif9pydBrTkmfsˆul
h†d grTd9okihmk†gXd[rXkif9s—l<sæxtk†gXgTd[s“e!lDutõå§d[k†gXezl<d9t“à2f9sMrax“l<p 2k†g
uw d[rrXl<kms“upXl5ts;l5ukigrTd9s;e!l„f9pTkizf9s Ý uk†grTd[s“e!l–
h†d9…Mtl<hmhilts
gX¨g•rT‚ 2l2okis;d[kipXlƒu7w }!rTf9kihml~gœ–aslztrTpXfs;gZul ƒd9gTgl € F
Š ç ] Ï*ul » à
fxrXk ƒd[hil 2lzsMrŒfpXkilzsMrX}Žl~g•rŒu}zrXl<e!rX}Qdql<eats ^
gXtx}zpTkml<tpTlZ– ! 9 C e €
ä|s;lQul<g 2}!rT„ful<g2xlzp 2l!rXrTd[sMrŒularXl~g•rTlzpƒhil<g2xlzpXå¦f9pXé
ƒd9s;e!l~g”ul›hid£ey„;d úslVu7w d9s;d[hi¨glHx“l<s;ud[sMr‘hml›pXtsOe!f9s“gk†g•rTl
ý i gt;p K[•Ï i#ý lzs2k 2xfgTd[sMrd[t’
–œgXk HthilzpNh\w lz÷lzru7w tsl a
2kipXfkmpygNulof9trulopyd9gul~g 2f9tql 2lzsMryg Vfuk g“d9srhilzt;p
hif9s;j9tl<tp € cw d 2xhikºrTt;ulFrTpX‚~g2å§d[kiohilDulQe!l~g 2f9t;q9l 2l<sryg
l~g•r‘u}!rTlzp Vkis}<lœlzsŽå¦f9s“e>rXkif9sFutFs;kmql<d[tFulœo;pXtkmr”dqBd[sMr|hil
u}zotrNut›pXts € c_dqBd[pTkid[rXkif9s#ut›skmql<d9t#ulo;pXtkmr¥gXlrTpTdutkmr
ç ] ϗd9t;…Mtlzhhil<gškm2s >•l<e>rTkmfs;ggXf9sMršu}zé
x“d[pts;l|qBd[pTkid[rXkif9s2ut ^
rTl<e!rX}zl~g € A|tŒe!ftpygNut2pXts ù¾ f9sMrl<tVhikilztƒ…Mt;dBrTpXl5x}zpTkmful~g
uw kis >•l<e!rXkif9s;g €
ç ] ÏæforXlzé
cv
d g;jtpXl Þ9Þ € 2fsrTpXl‘hil<gukigrXpTkiotrXkif9s“gul ^
stl~g{x;d[pNt;sl|d[s;d9hm¨gXl 2fsf[é@ezd9hi…Mtl Ý f9\
s g;hmrXpTl5hml~gNuf9s;s}zl~g
)
%
.
%
!
!
.
%
=
+ =
%
+
=
%
2
!
=
<
N
=
;
.
N
ÞÞ € < kigrXpTkiotrXkif9s£ul ^
ç ] ϗxf9tphid#xpXl 2km‚<pXl|lzrh†d
ulzpTski‚zpTl‘x}zpTkifulZuw kis>•l<e!rXkif9s € Ý ù 6ôë;gkij9s“d[hgXk ›thid9sMr5t;sl
e!fd9hml~gXezlzs;ezlZokms“d[kipXl
 6tpTgr#ë“gXkij9s;d9hgk Ht;hid9sr|t;slHgXf9tpye!l
k 2xth†gXkmql~à
+
N
ù lzrrXlad[s;d9hm¨gXl‡ul~g#kis>•l<e!rXkif9s;g›x“l<p 2lzr2ulae!fs;e!hitpTl‡d[t
å¦f9s;e!rXkif9ssl 2lzsMr5ezf9pTpXl~e>r5ul”h†dHey„“d úsl‘uw d9s;d[hi¨gl›ëMpTl<ezf9s;gé
rXpTt;e>rTkmfse!fpXpT}zh†dBrTkmfs‡xtk†gu}zrXl<e!rXkif9s €
ä
s½d[trXpTlOd9gXxl<e>rŽk Vxf9pXrTd9sMraul‹h‰w d[s“d[hi¨gXlOezf9s;gXk†g•rTlO–
e!l›grTdul›–‡e!f 2xpTlzs“upXlHhml~g
}<q9}zs;l 2lzsMrTg‘ul›opXt;kºrZ–Œ„;d9tr
^ç ] Ï Ý ß  à…Mtkd9xx;d9pTd9kigTgl<sMršhmfpTgT…Mtw f9sƒå§d9kºrtslœd9s;d[hi¨gl
e!f 2xhi‚!rTl €ù lzt’é@e!k¹gfsMrut;g5–Hul<gsf9sé@grTdBrTkmfss;d9pXkmrX}~gut
opXt;kºrutƒu}zrXl<e!rXl<tp 2€ < d[s“gNhmle<d9g{k†u}<d9hu7w t;sVo;pXtkmrg•rydBrTkmfsé
ç ] ϙd[té@ulzh†–
s;d[kipXll!rNjMd[t;gTgkilzs~h†d‘xpTf9o;d9okmhikmrX}5u7w dqf9kip_t;s h
ç ] ÏôezpXfkigé
utDgXlztkih¥u}<e!pTf †r
lz’xf9s;lzsMrXkilzhihml 2lzsMr‘dql<eZts h
gXd9sr €
.
+
=
.
h
D
<
ß ¾¿
d9p›h\w }zrXt;ul£ul~gHezd9s;d[t’˜d9t’kmhikid9kmpTl<gHut u}zrXl<e!rXl<tp<¥f9s
d xt 2lzrrXpTl2lzs‹}zqk†ulzs;ezl›h\w f9pTkmjkmsl2ul2sf HopTlzt’Q}<q9}<sl!é
a
2lzsMrTg2ulaopTtkºrƒ–Q„“d[tr ç^] Ï € [@hg<w d9j9kmrHx;d9p›lz’l 2xhmlŽul
sf9sé´grTd[rXkif9ss;d9pXkmrX}Oud[s;g‡hml‹e!ftpTd9sMr£ulOezlzpXrTd9kms;g£d9e!rXkif9sé
slzt;pTg<;ulœgTdBrXt;pTd[rXkif9s£ul#gkij9s;d9t’£ulœezf9pTpXl~e>rXkif9s €m€i€
ù lzrrTl‡}!ryd[xlŒxlzp VlzrVul£u(} g;s;kmp›tsˆskiq9l<d9tÆul‡…Mt;d9hmkmrX}
ul<gƒuf9ss}<l<g € ftp2hml~gƒuf9s;s}zl~gVd¨Md[sMr›t;sla…Mt;d9hmkmrX}FgXtåúé
g“gTd[sMrXlhilQrTpTdqBd[kih”ezf9s;gXk†g•rTlDlzs“gtkmrXl‹– ut} g;skipaul<g£q9l!rTfg
Ý }zrXt;ul2ulVhid‡pX}<x;d[pXrXkmrXkif9sQut ^
ç ] ϸlzsQå¦f9s;e!rXkif9sOulHh†dƒå¦pT}!é
…Mtlzs;ezl9 €i€i€ à
)
.
%
#u
Ÿ
¢#"
] ¡ $ n$ # ¡ $
"!$
"%$
`
¡
$ ¡
"
"%$
"
"
"5¡
¢
"
"
¡
^
$
N
cf9pygX…Mtw f9sFgXl#xh†d9ezlHud[s“g|hil›ezdupTl#ulHh\w d9xxpTf’k ƒdBrTkmfs
slts5rTf9skilzs;sl9[hilpyd[xxf9pXr{gXkij9s;d9hgtpNo;pXtkmrl<gršufss}5x“ftp
tsl#gXf9tpye!lœgXkºrTt}zlœ–Vh†dƒukigrTd9s;e!l Ð x“d[pZë
S !
Ð Å #
Ý\Þ9Þ € ! à
8 9)9
) Ò Õ p p p p Ö Ë%#XÅ Õ ô
€
Ö u}<gXkmjslh†d 14. Ú ftpHts;lŒ u}!rTl<e>rTkmfsƖ ç^] Ï gí ’}9d9tj 2lzsMrTlzp#h†d
14.
¹xlzp 2l!r{u7w d9tj 2l<srTlzp_hmlqf9hit 2lšgXf9s;u}šl!r¥uf9s;eu7w de>é
e!pTf †rXpTlZhidVxpTf9o;d9okihmkmrX}œulœu}zrXl<e!rXkif9s €
cl<gNfo >•l!ryg{pXl<s;e!fsMrXpT}<g_hmfpTgT…Mtlh†d
14. {e!pTf †r{gXf9sMr
ul<g¥gX¨grX‚ 2lokis;d[kipXl~gulšrXpTf9t;gsf9kipTg Ý 65±é 65±”àf9t#ul~g_gX¨g•é
rX‚ Vl~g{okis;d[kipXl~g Vkm’rXl~g¥rXpTf9tHs;f9kip_é}zrXfkmhil–‘sl<trXpTf9s“g Ý 65±é
]”ç à € cd 2}!rT„ful›ulHpTl<ey„l<pTey„l#ul<g‘gkij9s;d9t’auw a
ý i } Vk†g
x;d[p5ul”rXl<hmhil<g5gXf9tpye!l~gl<grgXk Vkih†d[kipXl‘–He!l<hmhil Vk†gXl
lzsœtqpXl
ud[s“ghml#e<d9gul~gg¨grX‚ Vl~gokis;d[kipTl<gu7w }!rTf9kihml~g–2slztrTpXfs;gZë
pXl~e!fs;g•rTpXt“e>rXkif9se!f9pTpT}zh†dBrXkif9sMu}zrXl~e>rXkif9s €
c_dFukm÷}<pXl<s;e!lƒl~gXgXlzsMrXkilzhihil›rTkml<sMrHd[t‹å§d[kmrH…Mtlƒhml~gZå¦f9p 2l<g
u7w f9s;ul~grT„}zfpXk†…Mtl<g Ý f9orTlzstl<g|x;d[p
u}zq9l<hmfxxl 2lzsMr|xfgré
stl s5rTf9skilzs—l<s - )£fáÆl<gr‡h†d˜qkºrTl<gTglFfpXokmrTd9hmlŽlzr )ahid
qkºrTl<gTgl|ul5h†dZhmt Vki‚zpTl~à_trTkmhik†g}<l<gNxf9tpu}<e!pTkipXl5hil<ggX¨g•rT‚ 2l<g
okis;d[kipXl~g”uw }zrXf9kihil<gZ–Œsl<trXpTf9s“g
sl2e!fsqMkilzs;slzsMr”x;hmt;gZud9s;g
hml#e<d9gul#gX¨g•rT‚ 2l<g 65±é 65±nf99
t 65±é ]”ç¹€
ù l~g{u}zqlzhif9xxl 2lzsMryg_gXf9sMr¥gXt ŒgTd 2lzsMr¥x;pX}~e!k†ghif9pygX…Mtl
hidu¨s;d 2k†…Mtl½ut g¨grX‚ Vl½l<gr å§d9kmohil 2l<sr¤pTlzh†dBrXkiqkigrXl
Ý )zà €ù w l<grhil”ezdgxf9tpul<ggX¨grX‚ 2l<go;kms;d9kmpTl<g ]”ç é ]”ç
ý i ud9s;gHh†dFo;d9s;ul
hmfpTgT…Mtw f9sÆg<w kisMrX}zpTl<gTgXlŒ–Qh\w } Vk†gTgkif9sÆu7w a
ul£å¦pX}~…t;lzs;ezl ( Ò X Ä2±|9ã '[ÄÄ9ÄV±||ul£o“fsslŽgl<sé
gkiokihmkmrX}2ut‹u}!rTl<e>rTlztp € cd‡u¨Ms“d 2ki…MtlVulzqkilzsMr
å¦fprTl 2lzsMr
pXl<hid[rXkiqkigrXl£lzs g“s ulax„;d9gXl£gXxkipTd9hid9sMrXlŒfáÆx“ftpVtsÂgX¨g•é
ý i gfsMr‘} Vk†gXl<g
rX‚ Vl ]‘ç é ]”ç ul 2dgXgXl € 9é € aŠ hml~g a
–2tsl‘å¦pT}<…Mtlzs“e!l#ul ! € Þ C±| €
ftpul<gšg¨grX‚ 2l~g{okms“d[kipXl~E
g 6±|é 65±™f9
t 65±é ]”ç 9hid”å¦pT}!é
ý i –2hi\
…Mtlzs;ezlHul~g a
d g;sQulœhidƒx;„;d9gXl#gx;kmpyd[h†d[sMrXlZl~g•r
ud9s;g
hidŒo;d[s;ulHul#å¦pT}<…Mtl<s;e!l ( Ý lzhihil#qBd[tr‘lzsqkmpTf9s Þ  ±|
x“ftpts‡gX¨grX‚ 2l”ul‘ulzt’VrXpTf9t“gšsfkmpygul ƒd9gTgl  Š à €
cl~gQu}zqlzhif9xxl 2l<srygŽx“fMg•rXé\s;tl s5rXfskilzs;g Ý u}zqlzhif9xxl 2lzsMr
ul ¥d¨hmfpyà_sl”e!f9s“g•rTkºrTtlzsMršxhit;gd[hif9pygNtsl
d9xxpTf’k ƒdBrTkmfs
gXd[rXk†g•å§d9kigTd[sMrTl €
f9á
8G9)9 %
.
.
!
=
=
.
=
.
%
=
!E
.
) 8G9 9 +
.
=
1
O
.
.
E
=
!
=
.
!
=
.
N
=
N
)
?
+
%
?=1
.
=
.
"%$
¢
.
.
ftp5x;d[hihikml<p5–2ezl”xpTf9o;hm‚ Vlul<gu}<q9l<hmfxx“l 2lzsMrTgxhit;g
x pT}<ezkigOx“l<tq9l<sMrB;zrXpTlÂtrTkmhik†g}~g € ä|s;lÂxpTl 2ki‚zpTlÂd V}<hmkif9pydBé
rXkif9sŽe!fs;gXkigrXlœ–VslZx;d9g5pTl<grXpTlzkis;upTl
hilZrXl<p 2lœu7w d 2xhikºrTt;ul
–Qh\w d[xxpTf’k ƒd[rXkif9sˆsl s5rXf9s;kml<ssl ƒd9kigVulahmlau}zqlzhif9xxlzp
e!f VlšhmlšrXlzp 2lšulx„;d9gXlšud9s;ghil<g_u}zqlzhif9xxl 2l<srygxfgré
sl s5rXf9s;kml<s;g Ý 2fu‚<hml _d¨hif9pœd 2xhikmrXt;ul zà € ä|sl‡pXl~gf ›é
ƒdBrTkmfsVulu}<q9l<hmfxx“l 2lzsMr¥xfgré´sl s5rXf9s;kml<s›xlzp 2l!ru7w f9oé
rXl<skip5ul 2lzkihihml<tpXl~gxpXfxpTkm}zrX}<gulœe!fsMqlzpTj9l<s;e!l Ý d[xxpTf’kºé
ƒdBrTkmfs›ul d9u}à² ¾ ³ € ä|s Vfu‚<hmll!÷¹l<e!rXkmå“è ý 6 Ý >lz÷l~e>rXkiq9l
f9s;l‘ofu¨ zà5dV}zjMd[hil 2lzsMr}!rT}œu}zqlzhif9xx}2²  ³ €
cl
x;pXfohm‚ 2l
pTlzs;ezf9sMrXpT}rXkilzsMrd[tƒå§d9kºr…Mtl
hil<g5ukm÷¹}zpTlzsMrTg
2fu‚zhil<gd9hmfpTgNukigXx“fskiohml~g 2f9sMrXpTlzsMrul~ge!f Vxf9pXrXl 2lzsMrTg
ukm÷}<pXl<sMrTg €ù l~e!k‘l<gr£…Mt;d[sMrXk g;}Olzsõe<d[h†e!th†d[sMr£ul<t’—j9pyd[sé
ul<tpTgZh
ë g“u}zhikmrX}œl!r|lz÷l~e>rTkmqkmrX} €
ç ] Ïnu}!é
c_
d g“u}<hmkmrX}#…Mt;d9srTk g“l‘hilœpTl<e!ftqpXl 2lzsMr Ý ut ^
rXl~e>rT}~à‘lzsMrTpXl2ezd9hi…Mtl~gœul Vfu‚<hml~gœukm÷}<pXl<sryg ƒd[k†g‘u(} g;sk†g
x;d9p¥hil<g ; Vl~gNx;d9pTd V‚zrXpTl<g¥ul ƒd9gTgl € ä|sl5rTlzhihml5j9pyd[s“ulztp
l<grk 2x“fpryd[sMrXlšu;d[s;gts#otr{u7w l<grXk 2d[rXkif9s#ulšx;d[pyd 2‚!rTpXl~g €
cw l!÷¹l<e>rTkmqkmrX}ƒl~g•r#ts;l Vl~gt;pXlŒut˜pTl<ezf9tqpTl 2lzsMr 2d[’kºé
ƒd[h…Mtlh\w fs#x“l<tr_forXl<skip_l<srTpXlezd[h†…Mtl<g_ulNå§d Vkihihml~g_ukm÷¹}!é
pTlzsMrTg €ù lpXl~e!ftqpXl Vl<sMr ƒd[’k ƒd[hxlztr ;!rXpTlf9orXlzst2xf9tp
ul~g#x;d9pTd V‚zrXpTl<gœul 2dgXgXl Õ ã Ö ukm÷}<pXl<sMrTg €{ù w l<grHhid
…Mt;d[sMrTkºrT}‡xlzpXrXkislzsMrXla…Mt;d[s;uÆf9s g<w d[í rryd9ey„lŒt;ski…Mtl 2lzsMr2–
u}zrXl<e!rXl<p‘t;s‹gXkmjs;d[
h 7e!lƒ…MtkNe!f9s“g•rTkºrTtl2sf[rTpXlVxpTl 2kml<pZf9oé
>•l<e!rXkmå €
clƒey„f9km’Out 2fu‚zhilŒ–atrXkihmk†gXlzpœxf9tpœh†dapXl~ey„lzpyey„l2ul<g
gX¨grX‚ 2l<gŒo;kms;d9kmpTl<g£ulQrTpXft;g£sf9kipTg‡x;d9gTgXlQx;d[p£tsl‹e!f Vé
x;d9pTd9kigXf9sDul<gZukm÷}<pXl<sryg 2fu‚zhil<g 2lzsMrXkif9ss;}<g‘xpT}<e!}~ul Vé
2lzsMr €Ný s˜sl‡ufsslzpydŽx;dgœkiezkšhil<gœpT}<gXthmrTd[rTg#u}zrTd9kmhihm}~g#ul
h\w d9s;d[hi¨gl € cr
d g;j9t;pXl ÞÞ € ß 2f9sMrXpTl#h†dŒqBd[pTk†dBrXkif9sQulHh\w lz÷l~e>é
rXkiqkºrT}‘ul‘u}zrXl~e>rXkif9sau7w tsae<d[h†…Mtl _d¨hif9pšd Vx;hmkmrXt;ul x;d[p
ts2ezd9hi…Mtl du} šlzs›å¦f9s;e!rXkif9s2ulh†d ƒdgXgXlšrTf[ryd[hil5utVgX¨g•é
€ < d[s“gh†dZpX}<j9kif9sƒul<gš„;d[trXl<g 2dgXgXl<g<[h\w lz÷l~e>rTkmqkmrX}|l~g•r
rX‚ 2l å§d[kiohil Ý"! ;€ ¿[ xf9t;p#tsl ƒd9gTgXl2rXf[ryd[hilŒul  Š à €_ç txé
xfgXf9s;g”…t;lHhil 2fu‚zhil _d¨hif9p|d 2xhikmrXt;ul #ezf9pTpXl~gxf9s;ul
d[t‹gkij9s“d[h¥x„¨gXk†…t;l›} Vk†g‘x;d[p‘h†d£gXf9tpye!l € ê¥kihºrTpXl<pZhml~g‘uf9sé
s}<l<g{dq9l~eul~g{ezd[h†…Mtl<g du} fezezdgkif9s;slzpyd|ts;lxlzpXrXl5ul
^ç ] Ï&kipXpT}<ut“e>rXkiohil‡utlŽd[t 2d9tqBd[k†g#pTl<ezf9tqpTl 2lzsMrHl<srTpXl
e!l~g
e<d[h†…t;l<g € A¸e!lzrrTl#x“l<prTlHg<w 2d >•f9trTl#e!lzhihilHutlHd9tFx;dqBd[jl
ç ] ϸglHrXpydBé
ul›h‰w l<gXx;d9ezl›ul~g|x;d9pTd 2‚!rXpTl<g €¹ù l~g
xlzpXrXl~g”ul ^
utk†gXlzsMr”x;d9p
ts;lVuk 2kmstrTkmfsDutDrTd[t’Ful›u}zrXl<e!rXkif9s Ý tsl
ç ] Ï*ul Þ
xlzpXrXlQul ^
gXl£rTpTdutkmrŒx;d[pƒt;slQuk VkistrXkif9s
utarTd9t’£ulœu}zrXl~e>rXkif9sFul Þ
à € [@h7å§d[tr|ufs;e‘hmk 2kºrTlzp
ezl<g
xlzpXrXl<g € èsFx;pXl Vkilzphikilzt“f9sFey„lzpyey„lœ–Vhmk 2kºrTlzp”hml~gx“l<prTl<g
utl~gd[tFey„fkº’‡ul~g|ezd9hi…Mtl~g5x“ftphi
l g“hºrTpTd9j9l €
ftp£ezlzh†dtslOgrXpydBrT}zjkmlQezf9s;gXkigrXlO– u}<q9lzhif9x;x“l<pŒtsl
sftq9l<hmhilœå§d 2kihmhil2ul›e<d[h†…t;l € [@h¥g<w d9j9kmr‘ulVezd9hi…Mtl~g
lz÷l~e>rXkmå§g
sfsõx„¨gk†…Mtl<gŽezf9s;grXpTtkmrTgaul‹å§d !fs½–™dq9fkmp£ts½pTl<ezf9té
qpXl 2lzsMr ƒd[’k ƒd[hdq9l~e‡h\w lzs;gXl ›ohmlŽul~g Vfu‚<hml~gƒuk†gxf[é
skiohil<g € cl<g¥u}!ryd[kihig¥gt;p_h†d
ezf9s;grXpTt;e>rTkmfs#ulezl!rXrXlå§d 2kmhihilul
ezd9hi…Mtl~gulHu}zrXl~e>rXkif9sŽxlztqlzsM?
r ;!rTpXlZrTpXftq9}~gud[s“gœ² ¾ ³\_² ¿ ³´
² » ³;l!r|² #B³ 2€ d[pezf9s;grXpTt;e!rXkif9sBe!lzrrTl5å§d 2kmhihil|ul|ezd9hi…Mtl~g{x“l<pé
2l!ru7w f9orTlzskipNtsVo“fs›pTl<ezf9tqpTl 2lzsMr{dq9l<ešh‰w lzs“gl Hohilul<g
ezd9hi…Mtl~g‘l!’kigrTd9sMrTg €7ç f9t;g‘h\w „¨x“f9rX„‚~glƒ…Mtl2h†d£ezf9s >•fs;e>rTkmfs
ul~g‘ukº÷¹}zpTlzsMrTg 2fu‚<hml~g‘ukigXx“fskiohml~gZpXl~e!ftqpXl<sr‘hml2gXkmjs;d[h
x„¨gk†…Mtl 2kml<t’—…t;lDey„;d9ezts—ul<g Vfu‚<hml~gŒxpTk†gŒg}<x;d[pT}!é
< .
!
?
?
9
.
:?
+
.
!
. +
$
?=1
.
!
%
)
?
)
+
. < +
=
5?
.
.
2
=
.
!
= =
.
=
?
?=1
!
?
5?
=
+
=
=
!
+
+
!
.
0.95
=
N O
Model1 : taylorAmplitude, po: 2.5, ao: 0.0
Model2 : vicb_pade, po: 2.5, ao: 0.0
0.9
0.85
0.8
0.75
0.7
m1 = m2 = 0.5*MassTot
0.65
m2=1.4 ,m1 = MassTot-m1
0.6
0
5
10
;
15
20
25
30
35
40
Masse totale ( M )
Þ9Þ € ß
d[pTkid[rXkif9sŽulHh\w lz÷l~e>rTkmqkmrX}Hul›u}!rTl<e>rTkmfsQu7w ts
e<d[h†…MtlˆkigTgXt¸u7w t;s Vfu‚<hml _d¨hif9pFd 2xhikmrXt;ul ˜x;d9pFts
e<d[h†…Mtl du} Vl<sˆå¦f9s“e>rXkif9sÂul‡h†d ƒd9gTgXlƒrXf9rTd[hil‡ut™g¨gé
rT‚ 2lœokis;d[kipTl
?
=
=
1
?
?=1
!
Q
5?
2l<sr~e!lzrrXl›å§d!2kihmhil2l<gr‘t;s‹d[rXf9tr‘xf9tpZh†d‡pTl<ey„;lzpyey„lHul~g
gX¨g•rT‚=2
l<g5o;kms;d9kmpTl<gulZrXpTf9t;gsfkmpyg €
cw }!ryd[xl”gXtkiqd9sMrXl
qBd›e!f9s“gk†g•rTlzp–#q9}<pXk g;l<pše!lzrrXlZul<pXski‚zpTl
„¨xf[rX„;‚<gXl9xtk†g–Hk+2
xhi}=2 lzsMrXl<p5hml~ge<d[h†…Mtl<gulœu}!rTl<e!rXkif9s
u;d[s;g_hid”ey„;d úslu7w d9s;d[hi¨gl €ù lzrrXl}!ryd[xlšs}~e!l~gXgXkºrTl…Mtl<hi…Mtl~g
dud[xrTdBrTkmfs;gd9tVpTlzjMd[pyuHul
hid‘å§d !f9sƒufsMršgfsrj}zs}<pX}~gNe!l~g
€ < l2xhit;g<7h‰w l<gXx;d9ezl›ul~gZx;d[pyd 2‚zrXpTl<g
–ae!fs;gXkiu}<pXl<p
e<d[h†…Mtl<g l~g•rFul‹uk 2l<s;gkif9s ! e!l‹…Mtk”s;}<e!l~gXgXkmrXlDt;sl 2}!rT„ful˜ul
x“dqd9j9lZukm÷}<pXl<srTl €
!
N
H
$#"n$
+
¡¥$Z !
"e"
¢ "
$"$
] $ ¡ ]
"z$
¡
" æ$
!
^
" ^
`b] " "
.
4
`
+ O
=
.
: .
=
.
=
. 2
%
=
.
!
=
.
.
1.6
1.4
f9tp_jd9pTd9srTkmp¹ts;le!ftq9l<prTtpTl{ezf 2xhi‚!rTlšut#e!kilzhl!rxf9té
qf9kipœl!’e!hitpTl2hml~gœ}zq}zsl Vl<sMrTgœulƒopTtkmrHdq9l~e ze!l<prTkºrTt;ul [
t;slVd9s;d[hi¨glHlzsDpT}<gXl<d9tFl<gr‘s;}<e!l~gXgTd[kipTl € èhihilVl~g•rZu7w d[tryd[sMr
x;hmt;gDs}<ezl<gTgXd9kmpTl˜d[tnpXl<jd9pTu½utöå§d[kiohmlˆs;f Ho;pXlÆu7w }zq}zslzé
2l<srygHd[rrXl<s;ut;g›dq9l~e2hidŽxpTl 2ki‚zpTlŒj9}<s}zpydBrTkmfs‹ul‡u}!rTl<e!é
rTlztpyg € clOrXpydqd9kmhZ…Mtl˜h‰w f9s½xpT}<gXlzsMrXl‹kiezkZl<grŽhil‹pX}~gthmrTd[r
uw ts;l5ezf9hihid9o“fpTd[rXkif9s#dql<eh\w l!’x“}<pXkilzs“e!ld 2}zpTkie<d[kisl
c [ i#ý›€
cw d[s“d[hi¨gXl5lzs2pT}<gXl<d[tVxlzp VlzrrTpTdZ}<jd[hil 2l<srul5å§d9kmpTl|ul~g
}zrXt;ul<gVd9grXpTf9x„¨gk†…Mtl<g ¹x;d[p#lz’l 2xhil9_ul£u}zrXlzp 2kms;lzp#h†d
hifezd9hmk†gXd[rXkif9saul<ggXf9tpye!l~g € A_q9l~e
rTpXfkig5u}zrXl~e>rXl<tpygukigrTd9sMrTg<
fs‡xlztrpTl<ezf9s;grXpTtkipXl|x“d[ptsl 2}!rX„;ful‘ul”rXpTk†d[sjthid[rXkif9s
ulzt’Hd9sj9hil<g¥u}!rTlzp 2kms;d9sMr¥h†d|xfgXkºrTkmfs›ulh†d”gXf9tpye!lud[s;g¥hil
ezkml<h € cd5hifezd[hik†gXd[rXkif9sZu7w t;slšgXf9tpye!lNgXlzpydu7w d9trTd9sMr Vl<kmhihilztpTl
…Mtl‹h†d pT}<gXf9hitrXkif9særXl 2xf9pTlzhihml˜gXtpŽhmlOrXl Vx“gaulOqf9hZl<gr
å§d9kmo;hml €
ý saxpXfx“fMgl”tsl 2}!rT„ful#u7w d 2}zhikmfpTd[rXkif9s‡ulZezl!rXrXlZpX}zé
gXf9hitrTkmfs™gTd9ey„;d9sMrV…MtlŽhid 2lzkihmhilzt;pXlŽpT}<gXf9hitrXkif9sÆl~g•rƒforXlzé
stl”ud[s;gšhml”ezd9gu7w tsl
d9s;d[hi¨gl 2f9s;f[é@ezd[h†…Mtl 2€ < d[s“ghil”ezdg
Ý ƒd[tqBd9kigpXlzé
uw ts;l‘d9s;d[hi¨gl|dql<e5tsl‘j9pTkihmhil9hml B
1 ezf9tqpTl 2lzsMr>à
l<sMrXpTl2e<d[h†…Mtl2l!rHgXkmjs;d[hNl<srTpTd †s;lVt;slƒx“l<prTl
ulœpX}~gfhmtrTkmfs €
cw k†u}zlŽul‡o“d9gXl‡xf9tp2e!f Vxlzs“gl<p›h\w lz÷lzr2ut B
1 .
=
%
=
)
=
=
¡ " "!"("
%
.
l<gr›tsl£sf9t;q9lzhihil£u}tg;skmrXkif9s ut rXl Vx“g›ul£pX}zå¦}zpTlzs;ezl‡ul~g
}zq9}<sl 2l<sryg € < lÆå§d zf9sôgrTd9s;ud9pTu7‘e!l rXl 2x;g‹l~g•r˜u}(g;s;k
e!f 2l
hil|rTl 2x;gut£u}<e!hilzs“ey„l 2lzsMr Ý u}tg;skx;d[phml
rXl Vx“g
ut 2d[’k ›t ôl<sVgXf9pXrXkilu\
t g;hºrTpXl|dud[xrX}~à{d9t;…Mtlzhg<w d >•f9trXl
hid2utpT}zlœulœh†dVx„;dglœgXxkmpyd[h†d[sMrTl €
cl£sftq9l~d[t rXl 2x;g2ulŽpT}!å¦}<pXl<s;e!la…t;lah\w f9sÂu(} g;skmrƒl<gr
ezd[h†e!t;hm}‹lzsöd >•f9trTd[sMrFd[tõrXl 2x;gŽutnu}~e!hilzs;ey„l 2lzsMrat;sl
utpT}zl|ut} g;skil
e!f 2lhilrXl 2x;g 2kigšx“ftphil
gXkmjs;d[hu7w f9s“ul
j9pydqMkmrTd[rXkif9ss;lzhihmlOx“ftpŽx;d9gTgl<pFu7w t;sl‹å¦pX}~…t;lzs;ezl A Ý å¦pX}zé
…t;lzs;ezlHo;dgXgXl›ulVh†dŒå¦l<h
s ;!rTpXlVulVgXlzs“gkiokihmkmrX}2utOu}!rXY l~e>rTlztp>à
–ƒtslHå¦pX}~…t;lzs;ezl –Œu}!rTlzp 2kmsl<p € cdŒpTd9kigXf9sŽxf9tp‘hid[é
Y
…t;lzhihml|fs2x“l<trg<w d[rrTlzs;upTl|–Ztsl”d 2}zhikmfpTd[rXkif9sƒulh†dœpT}<gXf[é
hmtrTkmfs‡rTl 2xf9pTlzhihml‘rXkilzsMr|–›hidVpT}zx;d9prTkºrTkmfs‡lzs£å¦pT}<…Mtlzs“e!lZul
ç ] ϗxk†…t;}zl”–Ho;d9gTgXlå¦pX}~…Mtlzs;ezl Ý ß 9 ±
~à €
hid#ulzs;gXkºrT}‘ul ^
cl<g£pX}~gthmrTd[rTg£f9orTlzst;g£lzsõd9xxhiki…Mt;d9sMrae!lzrrTlOsftq9l<hmhil
u(} g;s;kºrTkmfsaut£rXl 2x;gulZpX}zå¦}zpTlzs;ezl”gXf9sMrkmhihit;g•rTpX}~g5gtp5h†!
d g;é
j9tpTl ÞÞ € ! € èhihml 2f9sMrTpXlZ…MtlZhid›pX}~gfhmtrXkif9sŒrTl 2xf9pTlzhihmlœgXtp
hmlƒrTl 2x;g›ulŒq9fhlzsMrTpXlƒhil<g›u}!rTl<e>rTlztpyg [•Ï i#ý lzrVc [ i#ý
±
d[så¦f9pyu‡dBrXrXl<kmsMr5ts 2kisk Ht &xf9t;ptsl”å¦pX}~…t;lzs;ezl‘u7w lzsé
qMkipTf9s ß 9 ±
 € cl<g2rTpTd9kºrygƒ„fpXkizfsryd[t’„;d[tr£l!rŒo;dgƒkmsé
uki…Mtl<sMrVpTl<gXx“l~e>rTkmql 2lzsMr›h†dOpX}~gfhmtrTkmfsˆrXl 2x“fpXl<hmhil£forXlzé
sMt;l2dql<e›hidŽut} g;skmrXkif9s˜g•ryd[s;u;d[pyuOutOrXl 2x;g#ul2pT}!å¦}zpTlzs“e!l
l!rZhid Vl<kmhihilztpTlHpT}<gXf9hitrXkif9sQ…MtlVh\w fsQx“l<trZf9orTlzskip €ý sOgXl
pTd9xxpTfey„;l‡slzrrXl 2lzsMr‡ulFe!lzrrXlFul<pXs;km‚<pXlal!rƒf9s™jd9j9slŽ–
ß 9 ±|Ztsaå§d9e!rXl<tp ß gXtp5h†d›pT}<gXf9hitrTkmfs‡g•ryd[s;u;d[pyu €;ý s£foé
rXkilzsMršhil \; 2lr•¨x“l
ulpX}~gthmrTd[rx“ftpšu7w d[trXpTl<gezf9txhil<gšul
u}!rTl<e>rTlztpyg €
res.(ms)
Effectivite
ß ¾9»
=
?
=
=
=
)
:
!
9 8
1.2
1
0.8
%
.
?
9 8
0.6
0.4
100
1000
stop freq.(Hz)
;
=
Þ9Þ € !
d[pTkid[rXkif9sŒul‘h†dHpT}<gXf9hitrXkif9s2rTl 2xf9pTlzhihmlZgt;phil
rXl 2x;g‘ulVq9fhlzsMrTpXl K[•Ï i#ý l!rZc [ i#ý ±
d9så¦f9pyuŽlzsDå¦f9s;e!é
Xr kif9sŽul =
#T
Y
!
" ^
$ v
ý sadHxpT}<gXlzsMrT}‘ukm÷¹}zpTlzsMrTg5d9gXxl<e>ryg5ul”h\w d[s;d9hm¨gXl”ulœufsé
s}zl~g5x“ftphidVpTl<ey„l<pTey„;l‘ul~g5f9s;ul<g5j9pydqkºrydBrTkmfsslzhihil<g”ëpXlzé
ey„lzpyey„lŒul~g›gX¨g•rT‚ 2l<gHokms“d[kipXl~g ]”ç é ]‘ç  2k†gl‡lzsÆflzt;qMpTl
=
<
h
D
ß ¾ #
=
ulZhid›pTl<ey„l<pTey„l‘ul<g5gX¨g•rT‚ 2l<gokis;d[kipTl<g-65±é 6±Hu}zqlzhif9xé
x“l 2lzsMr”ulZh\w d9s;d[hi¨glZlzsapT}<gXl<d[t €
[@h†gOx“ftpXpTf9sMr7;zrXpTlˆrXl~g•rT}<gDgXtpOhml~gQxpTl 2ki‚zpTl<gQufss}<l<g
gXezkml<sMrXk g“…Mtl<g5xpTk†gl~g5x;d[
p [•Ï i#ý utpyd[sMrh‰w d[s;s}zl ß 99¾;€
.
%]B] ¡
"
=
"%$
² ³ ç kmrXl#ulZh\w lz’x}zpTkilzs;ezl [•Ï i#ý 
„MrrXx˜ë -- s%s%s € qkipXjf € kmså¦s € kmr
²ß v
³ A|trTpXl~gu}!rTl<e!rXlzt;pTg5kisMrXlzpXå¦}zpTf 2}zrXpTki…Mtl~gz
c [ i#ý „rXrXx˜ë -- s%s%s € hikmjf € ezd[hmrXl~ey„ € l<ut
i è ý „MrXrXxˆë -- s%s%s € j9l<f ¾9€ tskm鴄;d[ss;fBq9lzp € ul9
A”7
Š An„MrrTx‹ë -- „MrrXx‹ë -- ryd ƒd[jf € #kr C € s;d9f € 9d e € >•x
1
=
!
u l h\w l!’x“}<pXkilzs“e!l [•Ï i#ý
u}<ukm}<l£–Fh†dDu}zrXl~e>rXkif9sÂul<g›f9s;ul<g#jpTdqBd9kºrydBrXkif9s;slzhihml~gz
5„‚<gXlœulœc €8< lzpTf 2l
„MrrXx˜ë -- rXlzh € ezezgTu € e!spyg € å¦p - rTlzhmé 99 ! ¾ ² 9³ d[pTkid9ohilœxhide!l Vl<sMr|f[å{rXl Vx;hid[rXl<g|rXl~ey„sk†…t;l#kmsQd ß <
x;d[pyd 2lzrXlzpˆgXx;d9ezl¤å¦f9pÆo;kms;d9pX¨ôkms;gXxkipTd9h‡gXl<d[pyey„l~gz#ê €
6l<d[t;qMkihihmlal!r‡d9h €  ù hidgXg € ”t;d9srTt i pydq € ßß Ý\ß  Þ à
ß » Þ é !  #
² Þ ³ ù f9tpTol<g5ul#gXlzs;gXkmo;kmhikºrT}<gul [•Ï i#ý 
„MrrXx
ë -- s%s%se<d9gTe!kis;d € qkmpTj9f € kiså¦s € kºr - < dBryld A|s“d[hi¨gXk†g ù d[hikmo;pTd[rXkif9s - gl<s;g € „Mr 2h
² ¾ ³vA € 6tf9s“d[ssf“
 €šù „lzsNŠ € d9hmhikigXsl<pXk\ „M¨g € Ïlzq €
<”¾¿› ß  ¾ Ý‰ß 9 ! à
² ¿ ³vA € 6tf9s“d[ssf“ €šù „lzsNŠ € d9hmhikigXsl<pXk\ „M¨g € Ïlzq €
<”¾¿   ßÞƒÝ‰ß 9 ! à
² » ³vA € 6tf9s“d[ssf“ €šù „lzsNŠ € d9hmhikigXsl<pXk\ „M¨g € Ïlzq €
<”¾ #   ¿ Ý‰ß 9 à
² #[³vA € 6tf9s“d[ssf“ €šù „lzsNŠ € d9hmhikigXsl<pXk\ „M¨g € Ïlzq €
<Z¿[  9 !ŒÝ‰ß 9 à
²  ³ < l!rXl~e>rTkmsj 6kms;d9pXH
¨ 6hidDe C™±
f9hil<g skºrT„æl Œezkml<srŽd[s;u
€ < d 2f9t;p< 6 € Ï € [@¨lzp~ 6 € 繀¹ç dBé
pXl<hid9kmo;hmlœrTl 2xh†dBrTl<g< rX„¨d9xpySd CBd9gX„d[kp m
kiqQë jpé@…e - 9 ß ¿B
² ! ³Hcl™g¨grX‚ 2l™ulÂu}zrXl~e>rXkif9s
1
.
!
.
=
1
!
O