a ccp 16 - pikeroen.free.frpikeroen.free.fr/site/fb2402d4-cb34-4140-80ef-d1269df1a259_files/a... ·...
Post on 15-Sep-2018
213 Views
Preview:
TRANSCRIPT
3UREOqPH$OHKDXWSDUOHXUpOHFWURG\QDPLTXH
8QKDXWSDUOHXUpOHFWURG\QDPLTXHVFKpPDWLVpHQILJXUHHVWFRQVWLWXpG¶XQFKkVVLVVXUOHTXHOHVWIL[p OH FLUFXLW PDJQpWLTXH 6XU FHW HQVHPEOH ULJLGH HVW IL[p O¶pOpPHQW DFWLI GX KDXWSDUOHXUO¶pTXLSDJHPRELOH IRUPp GH ODPHPEUDQH HW GH OD ERELQHPRELOH /D OLDLVRQ DYHF OH FKkVVLV HVWDVVXUpHSUqVGXFHQWUHSDUOHVSLGHUSLqFHGHWRLOHULJLGLILpHSDUGXSODVWLTXHHWTXLMRXHOHUOHG¶XQUHVVRUWHW VXU OHSRXUWRXUSDUXQHVXVSHQVLRQSpULSKpULTXH/¶HQVHPEOHGH OD VXVSHQVLRQDVVXUH OHUDSSHOYHUV ODSRVLWLRQG¶pTXLOLEUHHW OHJXLGDJHHQWUDQVODWLRQSDUDOOqOHPHQWj O¶D[H]¶]/HFLUFXLWPDJQpWLTXH FRQVWLWXp G¶DLPDQWV SHUPDQHQWV JpQqUH XQ FKDPSPDJQpWLTXH %
JG UDGLDO HW XQLIRUPH
% 7GDQVO¶HQWUHIHU/DORQJXHXUWRWDOHGXERELQDJHGHODERELQHPRELOHYDXWO P/DPDVVHGHO¶pTXLSDJHPRELOHYDXWP J
/HVSDUWLHV$$HW$QHVRQWTXHWUqVSDUWLHOOHPHQWOLpHV
$(WXGHWHPSRUHOOHGXIRQFWLRQQHPHQW
$ 3RXUTXRLTXDOLILHWRQOHKDXWSDUOHXUGHFRQYHUWLVVHXUpOHFWURPpFDQLTXH"
$2QDSSOLTXHDX[ERUQHVGHODERELQHXQHWHQVLRQYDULDEOH ( )X W /DERELQHHVWDORUVWUDYHUVpH
SDUXQFRXUDQWG¶LQWHQVLWp ( )L W HWODPHPEUDQHVHGpSODFHDYHFODYLWHVVH ( )Y W
$-XVWLILHUSUpFLVpPHQWO¶DSSDULWLRQG¶XQHIpPLQGXLWH ( )H W DX[ERUQHVGHODERELQH
$/HVFKpPDpOHFWULTXHpTXLYDOHQWGHODERELQHHVWGRQQpHQILJXUHSDJHVXLYDQWH'RQQHU
OD UHODWLRQ TXL OLH ( )X W j ( )L W ( )( )G
GL W
L WW
= HW ( )H W 4XH UHSUpVHQWH FKDFXQGHV WHUPHV GH FHWWH
pTXDWLRQGLWHpOHFWULTXH"3RXUODVXLWHGXSUREOqPHRQSRVHUD ( ) ( )H W Y W % O= ⋅ ⋅
)LJXUHVFKpPDGHSULQFLSHGXKDXWSDUOHXUpOHFWURG\QDPLTXH
3OH1RUG
3OH6XG
3OH6XG0HPEUDQH
&KkVVLV%RELQHPRELOH
6SLGHU
6XVSHQVLRQSpULSKpULTXH
XW
LW
(QWUHIHU
]¶ ] %JG
%JG
%JG
$ 'RQQHU O¶H[SUHVVLRQ GH OD IRUFH pOpPHQWDLUH GH /DSODFH /G IJJG
H[HUFpH VXU XQH SRUWLRQ GH
FRQGXFWHXUGHORQJXHXU GO HQIRQFWLRQGH ( )L W GO %HW ]XJJG
$ (Q SUHQDQW O¶RULJLQH GHV ] FRPPH pWDQW OD SRVLWLRQ G¶pTXLOLEUH GX FHQWUH G¶LQHUWLH GHO¶pTXLSDJHPRELOH ERELQHPHPEUDQH OH SULQFLSH IRQGDPHQWDO GH OD G\QDPLTXH DSSOLTXp j FH
V\VWqPH GRQQH OD UHODWLRQ VXLYDQWH ( ) ( )GG ] ]YP L W O % X N ] W X YW
λ⋅ = − ⋅ ⋅ ⋅ − ⋅ ⋅ − ⋅
G JJG JJG G ,QWHUSUpWHU OHV
GLIIpUHQWVWHUPHVGHFHWWHUHODWLRQ
(Q GpGXLUH XQH pTXDWLRQ UHOLDQW ( )L W j ( )] W HW VHV GpULYpHV ( )( )G
G] W
] WW
= HW ( )( )
G
G] W
] WW
=
/¶pTXDWLRQDLQVLREWHQXHHVWDSSHOpHpTXDWLRQPpFDQLTXH
$5pJLPHVLQXVRwGDOIRUFp
/DWHQVLRQDSSOLTXpHHVWVXSSRVpHVLQXVRwGDOHGHIUpTXHQFHI ( ) ( )FRVPX W 8 Wω= ⋅ ⋅ HW Iω π= ⋅ ⋅ 1RXV XWLOLVHURQV OH IRUPDOLVPH FRPSOH[H TXL j WRXWH IRQFWLRQ VLQXVRwGDOH GX W\SH
( ) ( )FRVPD W $ Wω ϕ= ⋅ ⋅ + DVVRFLHODIRQFWLRQFRPSOH[H ( ) ( )M WPD W $ H ω ϕ⋅ ⋅ += ⋅ 2QUDSSHOOHTXH MHVWOH
QRPEUHFRPSOH[HWHOTXH M = −
$(FULUHOHVpTXDWLRQVPpFDQLTXHHWpOHFWULTXHHQXWLOLVDQWOHIRUPDOLVPHFRPSOH[H
$(QGpGXLUHO¶H[SUHVVLRQGHO¶LPSpGDQFHGXKDXWSDUOHXU ( )( )( )
X W=
L Wω =
)LJXUHVFKpPDpOHFWULTXHGHODERELQH
( )X W ( )H W
5/( )L W
)LJXUHSRUWLRQGHFRQGXFWHXUVRXPLVjODIRUFHGH/DSODFH
U% % X= ⋅JG JJG
]XJJG
Xθ
JJG
UXJJG
GO
( )L W
!!
$&HWWH LPSpGDQFH ( )= ω FRUUHVSRQGj ODPLVHHQVpULHGHGHX[ LPSpGDQFHV O¶XQH ( )H= ω DSSHOpH LPSpGDQFH SURSUH TXL QH FRQWLHQW TXH GHV WHUPHV UHODWLIV DX FLUFXLW pOHFWULTXH HW O¶DXWUH
( )P= ω DSSHOpH LPSpGDQFH PRWLRQQHOOH TXL QH GpSHQG TXH GHV FDUDFWpULVWLTXHV PpFDQLTXHV GX
V\VWqPH3UpFLVHUOHVH[SUHVVLRQVGH ( )H= ω HW ( )P= ω
$ 0RQWUHU TXH O¶DGPLWWDQFH PRWLRQQHOOH ( )( )
PP
<=
ωω
= SHXW V¶pFULUH VRXV OD IRUPH
( ) P P
P P
< M &M / 5
ω ωω
= ⋅ ⋅ + +⋅ ⋅
3UpFLVHUOHVH[SUHVVLRQVGH P& P/ HW P5 HQIRQFWLRQGHO%N
PHWλ2QGRQQHN 1PHWλ NJVYpULILHUTXH )P& −= ⋅ P+P/ = HWP5 = Ω
$3URSRVHUXQVFKpPDpOHFWULTXHpTXLYDOHQWGHO¶LPSpGDQFH ( )= ω GXKDXWSDUOHXUGDQVOHTXHOYRXVIHUH]DSSDUDvWUH5/ P& P/ HW P5
$2QSHXWpJDOHPHQWSRVHUTXHO¶LPSpGDQFHGXKDXWSDUOHXUVHFRPSRVHG¶XQHSDUWLHUpHOOH 75HW G¶XQH SDUWLH LPDJLQDLUH 7; ( ) 7 7= 5 M ;ω = + ⋅ 0RQWUHU DORUV TXH O¶H[SUHVVLRQ GH 75 HVW OD
VXLYDQWH
P7
P PP
55 5
5 &/
ωω
= +§ ·
+ ⋅ ⋅ −¨ ¸⋅© ¹
$ (Q XWLOLVDQW OD FRXUEH ( )75 I ω= GH OD ILJXUH GpWHUPLQHU OD YDOHXU QXPpULTXH GH ODUpVLVWDQFH5HWPRQWUHUTXHODIUpTXHQFHGHUpVRQDQFHYDXW +]I = 9pULILHUODFRKpUHQFHGHODYDOHXUGH I DYHFOHVGRQQpHVGHO¶pQRQFp
)LJXUHFRXUEHUHSUpVHQWDQW 75 HQIRQFWLRQGHω
100 ω UDGV
57 Ω
!
$(WXGHpQHUJpWLTXH
1RXV IHURQV O¶K\SRWKqVH TXH OD WUDQVIRUPDWLRQ GH O¶pQHUJLH PpFDQLTXH GHV SDUWLHV PRELOHV HQpQHUJLHDFRXVWLTXHV¶HIIHFWXHVDQVSHUWH
$(WDEOLUOHELODQGHSXLVVDQFHpOHFWULTXHJOREDOVRXVODIRUPH
( ) ( )( )
( )( ) ( )( )G
GPDJQ
- /
(X W L W 3 L W 3 Y W
W⋅ = + +
3UpFLVHUOHVH[SUHVVLRQVGH PDJQ( ( )( )-3 L W HW ( )( )/3 Y W
,QWHUSUpWHUFKDFXQGHVWHUPHVGXELODQ
$(WDEOLUOHELODQGHSXLVVDQFHPpFDQLTXHJOREDOVRXVODIRUPH
( )( )( )( )( )
( )( )( )( )( )
G G
G GF SH
$ /
( Y W ( ] W3 Y W 3 Y W
W W+ + =
3UpFLVHUOHVH[SUHVVLRQVGH ( )( )F( Y W ( )( )SH( ] W HW ( )( )$3 Y W
,QWHUSUpWHUFKDFXQGHVWHUPHVGXELODQ
$'pGXLUHGHVGHX[UHODWLRQVSUpFpGHQWHVTXH
( ) ( )( )
( )( )( )( )
( )( )G G
G GPDJQ 0
- $
( ( WX W L W 3 L W 3 Y W
W W⋅ = + + +
$0RQWUHUTXHODSXLVVDQFHPR\HQQH ( )63 W IRXUQLHSDUO¶DOLPHQWDWLRQpOHFWULTXHHVWUHOLpHj
OD YDOHXU PR\HQQH GX FRXUDQW DX FDUUp FRQVRPPp SDU OH KDXWSDUOHXU ( )L W HW j OD YDOHXU
PR\HQQHGHODYLWHVVHDXFDUUpGHO¶pTXLSDJHPRELOH ( )Y W SDUODUHODWLRQ
( ) ( ) ( ) 63 W 5 L W Y Wλ= ⋅ + ⋅
/HTXHOGHFHVWHUPHVFRUUHVSRQGjODSXLVVDQFHXWLOHPR\HQQH ( )X3 W "(QGpGXLUHO¶H[SUHVVLRQGX
UHQGHPHQWη
!!
$/DWHQVLRQ ( )X W DSSOLTXpHDX[ERUQHVGXKDXWSDUOHXUHVWXQHWHQVLRQDOWHUQDWLYHVLQXVRwGDOH
GH YDOHXU HIILFDFH HII8 /D ERELQH HVW DORUV WUDYHUVpH SDU XQ FRXUDQW ( )L W DOWHUQDWLI VLQXVRwGDOG¶LQWHQVLWpHIILFDFH HII, 2Q UDSSHOOH TXH OH KDXWSDUOHXU SHXW VH PRGpOLVHU FRPPH LQGLTXp HQ ILJXUH 0RQWUHU TXH OH
UHQGHPHQWηGpILQLHQTXHVWLRQ$DSRXUH[SUHVVLRQ 7
7
5 55
η−
=
$2QGRQQHHQILJXUHODUHSUpVHQWDWLRQGXUHQGHPHQWηHQIRQFWLRQGHODSXOVDWLRQω3RXUTXHOOH IUpTXHQFH OH UHQGHPHQW HVWLO PD[LPDO" (VWFH HQ DFFRUG DYHF OHV YDOHXUV QXPpULTXHVSUpFpGHQWHV"-XVWLILHUYRWUHUpSRQVH
$ 'DQV TXHOOH JDPPH GH IUpTXHQFHV O¶XWLOLVDWLRQ GX KDXWSDUOHXU HVWHOOH LQWpUHVVDQWH"5DSSHOHUO¶LQWHUYDOOHGHIUpTXHQFHVGDQVOHTXHOO¶RUHLOOHKXPDLQHHQWHQGOHVVRQV
$([SOLTXHUSRXUTXRLOHVHQFHLQWHVDFRXVWLTXHVFRPSRUWHQWSOXVLHXUVKDXWSDUOHXUV
)LJXUHPRGpOLVDWLRQGXKDXWSDUOHXU
( )X W 77
;/ω
= ( )L W
75
0 100
0,1
)LJXUHFRXUEHUHSUpVHQWDQWOHUHQGHPHQWηHQIRQFWLRQGHODSXOVDWLRQω
η
ω UDGV
top related