Strain measurement and stress analysis in the vicinity of a Fiber Bragg grating sensor embedded in a composite material

Journal Pre-proofs Strain measurement and stress analysis in the vicinity of a Fiber Bragg grating sensor embedded in a composite material A.Y. Fedorov, N.A. Kosheleva, V.P. Matveenko, G.S. Serovaev PII: DOI: Reference:

S0263-8223(19)32101-4 https://doi.org/10.1016/j.compstruct.2019.111844 COST 111844

To appear in:

Composite Structures

Received Date: Accepted Date:

10 June 2019 30 December 2019

Please cite this article as: Fedorov, A.Y., Kosheleva, N.A., Matveenko, V.P., Serovaev, G.S., Strain measurement and stress analysis in the vicinity of a Fiber Bragg grating sensor embedded in a composite material, Composite Structures (2020), doi: https://doi.org/10.1016/j.compstruct.2019.111844

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© 2019 Published by Elsevier Ltd.

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h?2 bi`m+im`H KQ/2H `2~2+ib i?2 `2H b+?2K2 Q7 `2BM7Q`+2K2Mi- M/ i?2 K2+?MB+H +?`+i2`BbiB+b Q7 i?2 7#`B+i2/ TB2+2rBb2@?QKQ;2M2Qmb K2/BmK `2 `2T`2b2Mi2/ #v i?2 T`QT2`iB2b Q7 i?2 `2BM7Q`+BM; }#2`b M/ #BM/2`X q?2M i?2 bBKmHiBQM Q7  +QKTQbBi2 Ki2`BH Bb #b2/ QM  bi`m+im`H KQ/2H- Bi Bb +QKKQM T`+iB+2 iQ mb2  `2T`2b2MiiBp2 pQHmK2- r?B+? b?QmH/ `2HB#Hv `2~2+i i?2 #2?pBQ` Q7 i?2 Ki2`BH b  r?QH2X h?Bb b+H2 Q7 KQ/2HBM; Bb KQbi bmBi#H2 7Q` bim/vBM; i?2 K2+?MB+H T`QT2`iB2b Q7  +QKTQbBi2 Ki2`BH rBi? /Bz2`2Mi pQHmK2i`B+ `iBQb Q7 +QKTQbBi2 +QKTQM2Mib M/ /Bz2`2Mi ivT2b Q7 bi`m+im`2X AM Qm` TT2`- i?Bb KQ/2H rb MQi +QMbB/2`2/X 6Q` +QKTQbBi2 Ki2`BHb rBi?  HKBMi2/ bi`m+im`2- KmHiBHv2` KQ/2Hb `2 KQbi +QKKQMHv TTHB2/X AM i?Bb ivT2 Q7 KQ/2H-  +QKTQbBi2 Ki2`BH Bb `2T`2b2Mi2/ b  bi+F Q7 Hv2`b- 2+? #2BM;  ?QKQ;2M2Qmb MBbQi`QTB+ #Q/vX h?Bb KQ/2H HHQrb iFBM; BMiQ ++QmMi /Bz2`2Mi Q`B2MiiBQMb Q7 i?2 Hv2`b +QKT`BbBM; i?2 TQHvK2` +QKTQbBi2X h?2 KQbi +QKKQMHv mb2/ H`;2@b+H2 KQ/2H Bb i?2 KQ/2H Q7 i?2 S*J b  ?QKQ;2M2Qmb K2/BmK #mi rBi? i?2 2z2+iBp2 K2+?MB+H +?`+i2`BbiB+b Q7 i?2 Ki2`BH mM/2` +QMbB/2`iBQMX h?Bb KQ/2H /2[mi2Hv `2~2+ib i?2 #2?pBQ` Q7  S*J T`2T`2/ rBi? i?2 mb2 Q7 rQp2M 7#`B+ T`2T`2;bX AM //BiBQM-  F2v /pMi;2 Q7  ?QKQ;2M2Qmb KQ/2H Bb i?i i?2 bBKmHiBQM +M #2 /QM2 i i?2 HQr +QKTmiiBQMH +Qbi +QKT`2/ iQ Qi?2` KQ/2HbX i HQ/b `BbBM; BM i?2 i2+?MQHQ;B+H T`Q+2bb2b BMpQHp2/ BM i?2 7#`B+iBQM Q7  S*J- i?2 QTiB+H }#2`b 2K#2//2/ #2ir22M i?2 Hv2`b `2iBM i?2B` ;2QK@ 2i`v- r?2`2b i?2 T`2T`2; Hv2`b BM i?2 pB+BMBiv Q7 i?2 }#2` Q7i2M 2tT2`B2M+2 ~2tm`H bi`BMb- r?B+? +M H2/ iQ i?2 7Q`KiBQM Q7  TQ+F2i }HH2/ rBi?  TQHv@ K2` #BM/2`X h?Bb xQM2 Bb +QMbB/2`2/  i2+?MQHQ;B+H /272+i- ;2M2`HHv FMQrM 3

b  `2bBM TQ+F2iX h?2 ;2QK2i`v Q7 i?2 `2bBM TQ+F2i bB;MB}+MiHv /2T2M/b QM i?2 ivT2 Q7 T`2T`2;b M/ i?2 p`BMib BMpQHp2/ BM i?2B` HvBM;X 6Q` mMB/B`2+iBQMH T`2T`2;b- i?2`2 Kv #2 /Bz2`2Mi p`BMib Q7 i?2 }#2` M/ Hv2` ``M;2K2Mi H2/BM; iQ i?2 7Q`KiBQM Q7  `2bBM TQ+F2iX AM T`@ iB+mH`- BM i?2 +b2 r?2M i?2`2 `2 irQ Hv2`b (yfy) BM i?2 Hv2` T+F;2 M/ i?2 }#2` Bb HB/ #2ir22M i?2 Hv2`b T`HH2H iQ i?2 /B`2+iBQM Q7 i?2 Hv2` `2BM@ 7Q`+2K2Mi-  `2bBM TQ+F2i Bb T`+iB+HHv M2p2` 7Q`K2/c r?2`2b BM i?2 +b2 Q7  HKBMi2/ +QKTQbBi2 Ki2`BH +QKTQb2/ Q7 irQ Hv2`b (NyfNy) M/ i?2 QTiB+H }#2` Bb 2K#2//2/ #2ir22M i?2b2 Hv2`b T2`T2M/B+mH` iQ i?2 }#2` /B`2+iBQMHH Qi?2` 7+iQ`b #2BM; 2[mH- i?2 7Q`KiBQM Q7 i?2 KtBKmK `2bBM TQ+F2i Bb  +QKKQM Q++m``2M+2X h?2 i?2Q`2iB+H M/ 2tT2`BK2MiH `2bmHib T`2b2Mi2/ BM `27b (Ry- RR- Rk- R8) bm#biMiBi2 i?2 +HbbB+H U2v2@b?T2/V ;2QK2i`v Q7 bm+?  TQ+F2i U6B;X kVX

6B;m`2 k, SQHvK2` +QKTQbBi2 Ki2`BH rBi? M 2K#2//2/ QTiB+H }#2` M/ i?2 `2bmHiBM; `2bBM TQ+F2i, QTiB+H }#2` URVc TQHvBKB/2 +QiBM; Q7 i?2 QTiB+H }#2` UkVc `2bBM TQ+F2i UjVc  Hv2` Q7 i?2 TQHvK2` +QKTQbBi2 Ki2`BH U9V

AM i?Bb +b2- i?2 `2bBM TQ+F2i b?T2 ?b irQ t2b Q7 bvKK2i`v- M/ i?2 7QHHQrBM; ;2QK2i`B+ +?`+i2`BbiB+b,  Bb i?2 KtBKmK rB/i?- 2b Bb i?2 H2M;i?M/ γ Bb i?2 M;H2 i i?2 KQmi? Q7 i?2 `2bBM TQ+F2iX AM `27X (RR)- Bi rb MQi2/ i?i i?2 H2M;i? Q7 i?2 `2bBM TQ+F2i Bb 12÷16R1 UR1 Bb i?2 `/Bmb Q7 i?2 QTiB+H }#2` iQ;2i?2` rBi? i?2 T`Qi2+iBp2 +QiBM;VX Ai b?QmH/ #2 MQi2/ i?i BM KQbi rQ`Fb- a = 2R1 - Hi?Qm;? i?2 p`BMi rBi? a > 2R1 Bb [mBi2 TQbbB#H2 M/ b?QmH/ #2 BMp2biB;i2/ r?2M T2`7Q`KBM; MmK2`B+H bBKmHiBQMbX HQM; rBi? i?2 #Qp2@K2MiBQM2/ 2ti`2K2 QTiBQMb 7Q` i?2 ``M;2K2Mi Q7 i?2 QTiB+H }#2` N

BM  bi+F Q7 mMB/B`2+iBQMH T`2T`2;b- i?2`2 `2 KMv Qi?2` p`BMib r?2`2 i?2 QTiB+H }#2` Kv #2 HB/ #2ir22M i?2 Hv2`b b (yfy)- (NyfNy)- (yfNy) i /Bz2`2Mi M;H2b iQ i?2 /B`2+iBQM Q7 i?2 Hv2` `2BM7Q`+2K2MiX 6Q` i?2b2 p`BMibi?2 ;2QK2i`v Q7 i?2 `2bBM TQ+F2i rBHH #2 bvKK2i`B+- M/ Bib bT2+B}+ b?T2 +M #2 /2i2`KBM2/ #v 2tT2`BK2MiH K2bm`2K2Mib mbBM; p`BQmb K2i?Q/b (Rk)X h?Bb T`Q#H2K i?Qm;? Bb 7` 7`QK i`BpBHX >Qr2p2`- BM MmK2`B+H KQ/2HBM; Q7 i?2 bi`2bb bii2 BM i?2 pB+BMBiv Q7 i?2 QTiB+H }#2`- M 2t?mbiBp2 b2`+? Q7 i?2 QTiBQMb +M #2 TTHB2/ iQ /2i2`KBM2 i?2 p`BMib Q7 i?2 `2bBM TQ+F2i ;2QK2i`v M/ iQ Q#iBM 2biBKi2b 7Q` i?2 KQbi mM7pQ`#H2 QTiBQMbX aBM+2 7Q` HKBMi2/ +QKTQbBi2 Ki2`BHb KMm7+im`2/ QM i?2 #bBb Q7 7#`B+ T`2T`2;b i?2`2 Bb MQ `2HB#H2 BM7Q`KiBQM QM i?2 ;2QK2i`v Q7 i?2 `2bBM TQ+F2ib- Km+? ii2MiBQM ?b #22M ;Bp2M iQ i?2 T`2T`iBQM Q7 HKBMi2/ +QK@ TQbBi2 b2+iBQMb M/ iQ i?2B` BK;2bX 6B;m`2 j T`2b2Mib M BK;2 Q7  i?BM b2+iBQM Q7  +QKTQbBi2 Ki2`BH #b2/ QM }#2`;Hbb T`2T`2;b i R9yt K;MB@ }+iBQMX h?Bb HHQr mb iQ +QM+Hm/2 i?i +?M;2b BM i?2 /Bbi`B#miBQM Q7 i?2 /?2bBp2 Hv2` ?p2 Q++m``2/ BM i?2 pB+BMBiv Q7 i?2 QTiB+H }#2`- #mi bB;?i Q7 i?2 +imH 7Q`KiBQM Q7 i?2 `2bBM TQ+F2i Bb H+FBM;X

optical fiber weft fibers

warp fibers

6B;m`2 j, AK;2 Q7  b2+iBQM Q7 ;Hbb }#2` #b2/ QM rQp2M 7#`B+ T`2T`2;b rBi? M 2K#2//2/ QTiB+H }#2`

AM i?Bb bim/v- iQ MHvx2 i?2 bi`2bb bii2 BM i?2 pB+BMBiv Q7 i?2 QTiB+H }#2` 2K#2//2/ BM i?2 +QKTQbBi2 Ki2`BH- r2 +QMbB/2`2/ M/ +QKT`2/ b2p@ 2`H p`BMib Q7 /2bB;M b+?2K2b U6B;X 9V,  ?QKQ;2M2Qmb Q`i?Qi`QTB+ 2HbiB+ K2/BmK rBi? M 2K#2//2/ QTiB+H }#2` rBi? M/ rBi?Qmi  `2bBM TQ+F2ic  Ry

KmHiBHv2` KQ/2H Q7  TQHvK2` +QKTQbBi2 Ki2`BH- rBi? i?2 }#2` 2K#2//2/ #2ir22M i?2 Hv2`b (yfy)- r?B+? /Q2b MQi H2/ iQ i?2 7Q`KiBQM Q7  `2bBM TQ+F2ic M/  KmHiBHv2` KQ/2H Q7  S*J rBi? i?2 }#2` 2K#2//2/ #2ir22M i?2 Hv2`b (yfNy) Q` (NyfNy)- r?B+? H2/b iQ i?2 7Q`KiBQM Q7  `2bBM TQ+F2i M/ i?mb Bib BM+HmbBQM BM i?2 +QKTmiiBQMH KQ/2HX 6Q` i?2b2 p`BMib- r2 b2H2+i2/ i?2 ;2QK2i`v Q7 i?2 `2bBM TQ+F2i rBi? irQ t2b Q7 bvKK2i`v U6B;X kV M/ H2M;i? 2b- r?B+?- 7QHHQrBM; `27X (RR)- rb /2i2`KBM2/ #v i?2 pHm2 b = 2R1 X 6Q` HH p`BMi `2T`2b2MiiBQMb Q7  S*J- i?2 bBKmHiBQM Q7 i?2 bi`2bb@Ĝ bi`BM bii2 rb +``B2/ Qmi mbBM; i?2 2H2K2Mi BM i?2 7Q`K Q7  T`HH2H2TBT2/ rBi?  #mBHi@BM QTiB+H }#2` mM/2` /Bz2`2Mi HQ/BM;b #v mMB7Q`K 7Q`+2b TTHB2/ MQ`KHHv iQ i?2 Hi2`H 7+2b Q7 i?2 T`HH2H2TBT2/ U6B;X 8VX >2`2- i?2 bBx2 h = 4 KK M/ +Q``2bTQM/b iQ  bi+F Q7 ky Hv2`b Q7 +`#QM@#b2/ rQp2M 7#`B+ T`2T`2;bX 6m`i?2`- i?2 bBx2 w Bb d iBK2b ;`2i2` i?M i?2 H2M;i? Q7 i?2 `2bBM TQ+F2i 2b M/ T`QpB/2b  mMB7Q`K bi`2bb bii2 BM i?2 KQ/2H Q7  ?QKQ;2M2Qmb +QKTQbBi2 Ki2`BH i  bm{+B2Mi /BbiM+2 7`QK i?2 }#2` U∼ 5bVX JQ/2HBM; rb +``B2/ Qmi mM/2` i?2 7`K2rQ`F Q7 i?2 KQ/2Hb /2b+`B#BM; i?2 HBM2` 2HbiB+ #2?pBQ` Q7 2tKBM2/ Ki2`BHbX jX MHvbBb Q7 bi`2bb +QM+2Mi`iBQM BM i?2 pB+BMBiv Q7 M QTiB+H }#2` 2K#2//2/ BM  KmHiBHv2` +QKTQbBi2 Ki2`BH h?2 b2H2+i2/ +QKTmiiBQMH b+?2K2b /2b+`B#2 i?2 #2?pBQ` Q7 bi`m+im`2b bbQ+Bi2/ rBi? i?2 T`2b2M+2 Q7 bBM;mH` TQBMib S1 M/ S2 U6B;X kVX AM  bKHH M2B;?#Q`?QQ/ Q7 i?2b2 TQBMib- i?2 bi`2bb2b +M #2 /2b+`B#2/ #v i?2 7QHHQrBM; `2HiBQMb?BT (kN- jy), σ ∼ A rα−1 ξ (ϕ) , URV r?2`2 r Bb i?2 /BbiM+2 iQ i?2 TQBMib S1 M/ S2 c M/ ϕ Bb i?2 M;mH` +QQ`@ /BMi2 Q7 i?2 TQH` +QQ`/BMi2 bvbi2Kb rBi? i?2 +2Mi2`b i i?2 TQBMib S1 M/ S2 X i i?2 pHm2b Q7 α biBb7vBM; i?2 +QM/BiBQM α < 1- i?2 bi`2bb2b i i?2 TQBMib S1 M/ S2 +M ?p2 BM}MBi2 pHm2bX h?2 T`Q#H2K rBi? i?2 2K2`;2M+2 Q7 bBM;mH` bQHmiBQMb M/ i?2B` BMi2`T`2iiBQM 7Q`  +QKTQbBi2 Ki2`BH rBi? M 2K#2//2/ QTiB+H }#2` bm``QmM/2/ #v  `2bBM TQ+F2i rb `Bb2/ BM `27b (RRjR)- #mi MQ T`2HBKBM`v +QM+HmbBQMb r2`2 K/2X M /2[mi2 M/ +QKT`2?2MbBp2 /2b+`BTiBQM Q7 i?2 Ki?2KiB+H bT2+ib Q7 +QMbi`m+iBM; bBM;mH` bQHmiBQMb +M #2 7QmM/ BM  MmK#2` Q7 bm`p2vb (jkRR

Homogeneous model without the formation of a resin pocket

Multilayer model without the formation of a resin pocket [0/0]

[90] [0] [0] [90]

Homogeneous model with the formation of a resin pocket

Multilayer model with the formation of a resin pocket [90/90]

[0] [90] [90] [0]

Multilayer model with the formation of a resin pocket [0/90]

[90] [0] [90] [0]

6B;m`2 9, o`BMi `2T`2b2MiiBQMb Q7  TQHvK2` +QKTQbBi2 Ki2`BH rBi? 2K#2//2/ QTiB+H }#2`b

Rk

Pz

h

z

Py x

Px w

Px y

Py

Pz

6B;m`2 8, *QKTmiiBQMH KQ/2H Q7 M 2H2K2Mi Q7 i?2 TQHvK2` +QKTQbBi2 Ki2`BH rBi?  #mBHi@BM QTiB+H }#2`

jj- j9)X h?2 TTHB2/ bB;MB}+M+2 Q7 bBM;mH` bQHmiBQMb Bb [mBi2 2pB/2Mi- bBM+2 i?2v /2}M2 i?2 bi`2bb +QM+2Mi`iBQM xQM2X h?2 KQbi MQi#H2 TTHB+iBQMb Q7 bBM;mH` bQHmiBQMb `2 bbQ+Bi2/ rBi? i?2 K2+?MB+b Q7 #`BiiH2 7`+im`2 (j8- je)- r?B+? QT2`i2 rBi? i?2 7`+im`2 +`Bi2`B HHQrBM; BM}MBi2 pHm2b Q7 bi`2bb2b- BM T`iB+mH`- i i?2 +`+F iBTX hQ i?2 #2bi Q7 Qm` FMQrH2/;2- i?2`2 `2 MQ `272`2M+2b BM i?2 HBi2`im`2 iQ i?2 bi`2M;i? +`Bi2`B HHQrBM; 7Q` BM}MBi2 pHm2b Q7 i?2 bi`2bb2b i i?2 #Qp2@ K2MiBQM2/ bBM;mH` TQBMib S1 M/ S2 X AM i?Bb `2;`/- M/ 7Q` i?2 T`Q#H2Kb mM/2` +QMbB/2`iBQM- Bi Bb BKTQ`iMi iQ 2biBKi2 i?2 pHm2 Q7 i?2 T`K2i2` α- r?B+? +QmH/ #2 mb2/ iQ Dm/;2 i?2 bBx2 Q7 i?2 `2;BQM BM i?2 pB+BMBiv Q7  bBM;mH` TQBMi rBi?  T`QMQmM+2/ bi`2bb ;`/B2MiX h?2 +HQb2` α Bb iQ mMBivi?2 bKHH2` i?Bb `2 BbX M MHvbBb Q7 i?2 HBi2`im`2 b?Qrb i?i 7Q` MBbQi`QTB+ Ki2`BHb- i?2 T`Q#H2K Q7 +H+mHiBM; i?2 bi`2bb bBM;mH`Biv 2tTQM2Mi i i?2 bBM;mH` TQBMib S1 M/ S2 BM i?2 ;2M2`H +b2 +M #2 bQHp2/ QMHv #v MmK2`B+H K2i?Q/b (jdj3- jN)X h?2 bBM;mH`Biv 2tTQM2Mi Q7 i?2 bi`2bb2b i i?2b2 TQBMib Bb /2i2`KBM2/ #v i?2 pHm2b Q7 i?2 K2+?MB+H +?`+i2`BbiB+b Q7 i?2 +QKTQbBi2 Ki2`BH M/ i?2 #QM/BM; /?2bBp2 BM i?2 pB+BMBiv Q7 i?2 TQBMib S1 M/ S2 - M/ i?2 pHm2 Q7 i?2 M;H2 γX h?2 `2bmHib Q7 bm+? +H+mHiBQMb `2 ;Bp2M BM `27X (jN) M/ b?Qr2/ i?i 7Q` γ i2M/BM; iQ x2`Q- i?2 bi`2bb bBM;mH`Biv 2tTQM2Mib i2M/ iQ mMBivX 6Q` Ki2`BHb +QMbB/2`2/ mM/2` i?2 7`K2rQ`F Q7 i?2 ?QKQ;2M2Qmb K2/BmK Rj

KQ/2H- i i?2 KtBKmK pHm2 Q7 i?2 M;H2 γ = 2 arctan (a/b) ≈ 14◦ - i?2 bBM;mH`Biv 2tTQM2Mi rb α = 0.858X h?mb- Bi 7QHHQrb i?i i?2 `2;BQM BM i?2 pB+BMBiv Q7 i?2 bBM;mH` TQBMi S1 rBi? i?2 bi`2bb +QM+2Mi`iBQM Bb p2`v bKHHM/ i i?2 pHm2 Q7 γ +HQb2 iQ x2`Q- Bi T`+iB+HHv /BbTT2`bX h?2b2 +H+mHiBQMb r2`2 +``B2/ Qmi 7Q`  i?`22@/BK2MbBQMH Uj.V 7Q`Km@ HiBQM #v i?2 }MBi2 2H2K2Mi K2i?Q/ mbBM; K2b?2b rBi? ;`/mH `2}M2K2Mib BM i?2 /B`2+iBQM Q7 i?2 xQM2b Q7 bi`2bb +QM+2Mi`iBQM U6B;X eVX h?2 ++m`+v Q7 i?2 +H+mHiBQMb rb 2biBKi2/ #v +QKT`BM; i?2 bQHmiBQMb Q#iBM2/ 7Q` /Bz2`2Mi /Bb+`2iBxiBQM b+?2K2b M/ #v MHvxBM; i?2 +QMp2`;2M+2 Q7 i?2 bQHmiBQM rBi? BM+`2bBM; i?2 MmK#2` Q7 2H2K2MibX

6B;m`2 e, 6BMBi2 2H2K2Mi K2b? 7Q`  KQ/2H Q7 i?2 Ki2`BH rBi? M 2K#2//2/ }#2` M/ `2bBM TQ+F2i

h?2 bBKmHiBQM rb +``B2/ Qmi 7Q`  S*J +QMbBbiBM; Q7 ky Hv2`b Q7 mMB@ /B`2+iBQMH T`2T`2;bX h#H2 R b?Qrb i?2 K2+?MB+H +?`+i2`BbiB+b Q7 i?2 mMB@ /B`2+iBQMH T`2T`2; M/ i?2 2z2+iBp2 K2+?MB+H +?`+i2`BbiB+b Q7 i?2 bi+F Q7 T`2T`2; Hv2`bX h#H2 k b?Qrb i?2 K2+?MB+H +?`+i2`BbiB+b Q7 i?2 }#2` M/ #QM/BM; /?2bBp2X AM i?2 +H+mHiBQMb- i?2 QTiB+H }#2` ?/  `/Bmb R0 = 0.062 KK- M/  TQHvBKB/2 +QiBM; i?B+FM2bb Q7 0.012 KKX MHvbBb Q7 i?2 BK;2b Q7 i?2 Q#iBM2/ b2+iBQMb Q7 i?2 HKBMi2/ +QKTQbBi2 Ki2`BH bm;;2bi2/ i?i HQM; i?2 z@tBb- i |y| > 8R1 HH i?2 Hv2`b ?/ i?2 bK2 i?B+FM2bb M/ r2`2 T`HH2H iQ 2+? Qi?2`X h?Bb K2Mb i?i T`2bbBM; Q7 R9

h#H2 R, J2+?MB+H T`QT2`iB2b Q7 i?2 mMB/B`2+iBQMH T`2T`2; M/ i?2 2z2+iBp2 K2+?MB+H +?`+i2`BbiB+b Q7 i?2 Hv2` bi+F

Ji2`BH

Ex :S

Ey - Ez :S :S

νxy

νyz

lMB/B`2+iBQMH T`2T`2;

R83XR

3XNe

3XNe

yXjk

yX98 yXjk

9Xe

jXy

9Xe

1z2+iBp2 K2+?MB+H +?`+i2`BbiB+b Q7 i?2 Hv2` bi+FBM;

39XR

39XR

RyXd

yXyj8

yX98 yX98

9Xj

jX8

jX8

νxz

Gxy - Gyz - Gxz :S :S :S

h#H2 k, J2+?MB+H +?`+i2`BbiB+b Q7 i?2 QTiB+H }#2` M/ /?2bBp2 Hv2`

Ji2`BH

E- :S

ν

[m`ix UQTiB+H }#2`V TQHvBKB/2 U+QiBM;V 2TQtv U/?2bBp2 Hv2`V

dRX9 kX8 kXN

yXRd yXj8 yXje

i?2 Hv2`b +mb2/  /2+`2b2 BM i?2 i?B+FM2bb Q7 i?2 T`2T`2; Hv2`b BM i?2 xQM2 −8R1 < y < 8R1 /m2 iQ `2bBM Qp2`~QrBM; 7`QK i?2b2 Hv2`bX 6m`i?2`- i?2 p`BiBQM BM i?2 Hv2` i?B+FM2bb /2+`2b2/ rBi? i?2 /BbiM+2 7`QK i?2 QTiB+H }#2`X hQ MHvx2 i?2 bi`2bb bii2 Q7 i?2 2H2K2Mi Q7 i?2 +QKTQbBi2 Ki2`BH rBi? i?2 2K#2//2/ QTiB+H }#2`- r2 +QMbB/2`2/ i?`22 p`BMib Q7 HQ/BM; `2;BK2X _2;`/BM; i?2 H2p2H Q7 bi`2bb +QM+2Mi`iBQM- i?2 KQbi mM7pQ`#H2 rb i?2 p`BMi Py = P0 - Px = Pz = 0- BM r?B+? i?2 HQ/ rb TTHB2/ T`HH2H iQ i?2 Hv2`b Q7 i?2 +QKTQbBi2 Ki2`BH M/ T2`T2M/B+mH` iQ i?2 QTiB+H }#2`X h?2`27Q`2- i?2 `2bmHib 7`QK i?2 MmK2`B+H bBKmHiBQM `2 T`2b2Mi2/ ?2`2BM KBMHv 7Q` i?Bb p`BMi Q7 HQ/BM;X 6B;m`2 d b?Qrb i?2 /Bbi`B#miBQMb Q7 bi`2bb σy HQM; i?2 y@tBb i x = z = 0r?BH2 6B;m`2 3 b?Qrb i?2 /Bbi`B#miBQM Q7 bi`2bb σy HQM; i?2 z@tBb i x = y = 0X h?Bb +QKTQM2Mi Q7 i?2 bi`2bb i2MbQ` Bb bB;MB}+MiHv H`;2` i?M i?2 Qi?2`bX HH i?2 ;`T?b- HQM; rBi? i?2 `2bmHib 7`QK i?2 KmHiBHv2` S*J KQ/2H- /BbTHv i?2 `2bmHib 7Q`  ?QKQ;2M2Qmb KQ/2H BM i?2 T`2b2M+2 Q` #b2M+2 Q7  `2bBM R8

TQ+F2i- r?B+? Bb /2MQi2/ #v i?2 +Q``2bTQM/BM; BMb+`BTiBQM i i?2 iQT Q7 i?2 ;`T?X AM i?2 MHvbBb Q7 i?2 bi`2bb bii2- r2 mb2 i?2 pHm2 i?i /2i2`KBM2b i?2 bi`2bb +QM+2Mi`iBQM +Q2{+B2Mi 7Q` i?2 +Q``2bTQM/BM; +QKTQM2Mi Q7 i?2 bi`2bb i2MbQ`X [0/0] without a resin pocket

[90/90] with a resin pocket

2

2

1.5

1.5


y 1 P0


y 1 P0

0.5

0.5

0

0

0.5

1 y (mm)

1.5

a

0

2

0

0.5

1 y (mm)

1.5

b

[0/90] with a resin pocket 2 layer [90]

1.5
y 1 P0 0.5 layer [0]

0

0

0.5

1 y (mm)

1.5

2

c 6B;m`2 d, Sii2`Mb Q7 bi`2bb /Bbi`B#miBQM σy /P0 BM i?2 pB+BMBiv Q7 i?2 QTiB+H }#2`, Ĝ Ĝ Ĝ Ĝ Ĝ Ĝ Ĝ ?QKQ;2M2Qmb KQ/2H- ěěěěěĜ KmHiBHv2` KQ/2H

h#H2 j b?Qrb i?2 H`;2bi bi`2bb +QM+2Mi`iBQM +Q2{+B2Mib 7Q` i?2 /Bz2`2Mi ivT2b Q7 HQ/BM; Q7 i?2 KQ/2H bvbi2KX h?2 `2bmHib Q#iBM2/ HHQr mb iQ /`r  b2`B2b Q7 +QM+HmbBQMbX 6Q` HKB@ Mi2/ +QKTQbBi2 Ki2`BHb +QKT`BbBM; b2p2`H mMB/B`2+iBQMH T`2T`2; Hv2`bBi Bb TQbbB#H2 iQ +?QQb2  p`BMi Q7 i?2 Hv2` ``M;2K2Mi i?i 2HBKBMi2b i?2 TQbbB#BHBiv Q7 7Q`KBM;  `2bBM TQ+F2i M/ bi`2bb +QM+2Mi`iBQM BM Bib pB+BM@ Re

2

[0/0] without a resin pocket

[90/90] with a resin pocket

4.5

4.5

3.5

3.5


y 2.5 P0 1.5


y 2.5 P0 1.5

0.5

0.5

-0.5

-0.5 0

0.5

1 z (mm)

1.5

a

2

0

0.5

1 z (mm)

1.5

b

[0/90] with a resin pocket 4.5 3.5


y 2.5 P0 1.5 0.5 -0.5 0

0.5

1 z (mm)

1.5

2

c 6B;m`2 3, ai`2bb /Bbi`B#miBQM σy /P0 HQM; i?2 z@tBb i y = 0, Ĝ Ĝ Ĝ Ĝ Ĝ Ĝ Ĝ ?QKQ;2M2Qmb KQ/2H- ěěěěěĜ KmHiBHv2` KQ/2H

BivX h?Bb QTiBQM Bb /2i2`KBM2/ #v irQ +QM/BiBQMb, RV i?2 /B`2+iBQM Q7 i?2 `2BM7Q`+2K2Mi Q7 mMB/B`2+iBQMH Hv2`b- rBi? M QTiB+H }#2` +QM}M2/ #2ir22M i?2K- Kmbi +QBM+B/2 rBi? i?2 /B`2+iBQM Q7 i?2 }#2`c kV i?2 /BK2i2` Q7 i?2 QTiB+H }#2` Kmbi #2 H2bb i?M i?2 i?B+FM2bb Q7 i?2 T`2T`2; Hv2`X h?Bb +QM@ +HmbBQM 7QHHQrb 7`QK i?2 `2bmHib T`2b2Mi2/ BM 6B;X 3 7Q`  KmHiBHv2` S*J KQ/2HX h?2 +H+mHiBQMb 7Q` i?2 ?QKQ;2M2Qmb S*J KQ/2H 7BH2/ iQ Q#iBM i?Bb `2bmHi M/ T`2/B+i2/  bB;MB}+Mi bi`2bb +QM+2Mi`iBQM BM i?2 pB+BMBiv Q7 i?2 }#2`X KQM; i?2 KQ/2Hb +QMbB/2`2/-  p2`bBQM Q7  ?QKQ;2M2Qmb KQ/2H rBi? M 2K#2//2/ QTiB+H }#2` rBi?Qmi i?2 7Q`KiBQM Q7  `2bBM TQ+F2i rb [mBi2 +QMbBbi2Mi rBi? i?i Q7  HKBMi2/ +QKTQbBi2 Ki2`BH #b2/ QM rQp2M 7#`B+ T`2T`2;b rBi? M 2K#2//2/ QTiB+H }#2`X b rb T`2pBQmbHv b?QrMRd

2

h#H2 j, JtBKmK pHm2b Q7 i?2 bi`2bb +QM+2Mi`iBQM +Q2{+B2Mi

JQ/2H bvbi2K JmHiBHv2` +QKTQbBi2 KQ/2H BM i?2 #b2M+2 Q7  `2bBM TQ+F2i (yfy) >QKQ;2M2Qmb KQ/2H BM i?2 #b2M+2 Q7  `2bBM TQ+F2i JmHiBHv2` +QKTQbBi2 KQ/2H BM i?2 T`2b2M+2 Q7  `2bBM TQ+F2i (NyfNy) >QKQ;2M2Qmb KQ/2H BM i?2 T`2b2M+2 Q7  `2bBM TQ+F2i JmHiBHv2` +QKTQbBi2 KQ/2H BM i?2 T`2b2M+2 Q7  `2bBM TQ+F2i (yfNy)

o`BMib Q7 HQ/BM; Px = P0 Py = P0 Pz = P0 Py = Pz = 0- Px = Pz = 0- Px = Py = 0:S :S :S RXNR

RXNy

RXk3

RXyR

jXd3

RXjd

RXNR

9X88

RXek

RXyR

kXRy

RXey

RXNR

9Xjj

RXe3

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b1 /R0 9 3 Rk 3 3 3

b2 /R0 9 3 Rk 9 3 3

δ/R0 yXR yXR yXR yXR yXy yXj

ky kXNN kXyN RX3j kX8y jXjk kXjj

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b1

b2

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6B;m`2 Ry, h?2 b+?2K2 Q7 Hv2` ``M;2K2Mi

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Ji2`BH :`T?Bi2f1TQtv

Ex - Ey - Ez - νxy :S :S :S

νyz

νxz

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yX9

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jXy

9X8

6Q` i?2 p`BMi rBi? M QTiB+H }#2` HQ+i2/ HQM; i?2 /B`2+iBQM Q7 `2BM@ 7Q`+2K2Mi- i?2 2tT2`BK2MiH pHm2 Q7 i?2 +Q2{+B2Mi Q7 i?2 KtBKmK +QK@ TQM2Mi Q7 i?2 bi`BM i2MbQ` Bb 9- r?2`2b i?2 pHm2 Q7 i?Bb [mMiBiv Q#iBM2/ 7`QK i?2 MmK2`B+H 2tT2`BK2Mi BM i?2 7`K2rQ`F Q7 i?2 Hv2`2/ KQ/2H Bb RX9X 6Q` i?2 p`BMi rBi? M QTiB+H }#2` HQ+i2/ #2ir22M i?2 Hv2`b rBi? i?2 `2BM7Q`+2K2Mi /B`2+iBQM +`Qbb i?2 }#2`- i?2b2 pHm2b `2 jXe M/ kXe`2bT2+iBp2HvX  +QKT`BbQM b?Qrb i?2 /Bb+`2TM+v #2ir22M i?2 2tT2`BK2MiH M/ Mm@ K2`B+H `2bmHib Bb rBi?BM e8WX h?mb- i?2b2 `2bmHib im`M iQ #2 //BiBQMH `;mK2Mib BM 7pQ` Q7 mbBM; i?2 `2bmHib Q7 MmK2`B+H bBKmHiBQM 7Q` i?2 b@ b2bbK2Mi Q7 i?2 bi`2bb M/ bi`BM +QM+2Mi`iBQMb BM i?2 pB+BMBiv Q7 i?2 QTiB+H }#2` #mBHi BMiQ i?2 S*JX 9X LmK2`B+H MHvbBb Q7 i?2 `2HB#BHBiv Q7 bi`BM pHm2b /2i2`KBM2/ QM i?2 #bBb Q7 /i 7`QK  }#2` "`;; ;`iBM; b2MbQ`  #HQ+F /B;`K Q7 i?2 T`Q+2bb Q7 bi`BM `2;Bbi`iBQM mbBM; i?2 }#2`QTiB+ "`;; ;`iBM; U6":V b2MbQ` Bb b?QrM BM 6B;m`2 RRX h?2 KBM T`QT2`iv Q7 i?2 "`;; ;`iBM; Bb i?2 ;2M2`iBQM Q7  `2~2+i2/ bB;MHX h?2 rp2H2M;i? Q7 i?2 `2~2+i2/ bB;MH λ∗ /2T2M/b QM i?2 `27`+iBp2 BM/2t Q7 i?2 QTiB+H }#2` M M/ i?2 H2M;i? Q7 i?2 T2`BQ/ Q7 i?2 "`;; ;`iBM; L (kR) λ∗ = 2nL. kk

UkV

I

Reflected signal

Quarz cladding fiber core

Bragg grating





*

L I

Input signal

I

Transmitted signal


*







6B;m`2 RR, "HQ+F /B;`K Q7 i?2 "`;; ;`iBM;

h?2 BMi2`+iBQM Q7  }#2`@QTiB+ b2MbQ` rBi?  /27Q`K#H2 Ki2`BH +?M;2b i?2 H2M;i? Q7 i?2 "`;; ;`iBM;- r?B+? H2/b iQ  +?M;2 BM i?2 rp2H2M;i? Q7 i?2 `2~2+i2/ bB;MH ∆λ `2+Q`/2/ #v i?2 BMi2``Q;iQ`X h?2 p`BiBQM Q7 i?2 rp2H2M;i? Q7 i?2 `2~2+i2/ bT2+i`mK rBi? i?2 bi`BM Q7 i?2 }#2` BM i?2 "`;; ;`iBM; xQM2 +M #2 /2i2`KBM2/ #v i?2 7QHHQrBM; `2HiBQMb (kR) ∆λ1 λ∗

= ε3 − 21 n2 (p11 ε1 + p12 (ε2 + ε3 )),

∆λ2 λ∗

= ε3 − 21 n2 (p11 ε2 + p12 (ε1 + ε3 )),

UjV

r?2`2 ε3 Bb i?2 bi`BM HQM; i?2 }#2`c ε1 - ε2 `2 i?2 T`BM+BTH bi`BMb BM i?2 THM2 T2`T2M/B+mH` iQ i?2 QTiB+H }#2`c ∆λ1 = λ1 − λ∗ - ∆λ2 = λ2 − λ∗ `2 i?2 /Bz2`2M+2b BM i?2 `2bQMM+2 rp2H2M;i?b Q7 i?2 `2~2+i2/ bT2+i`mK i i?2 +m``2Mi Uλ1 - λ2 V M/ BMBiBH Uλ∗ V BMbiMib Q7 iBK2- M/ p11 - p12 `2 i?2 SQ+F2Hb +Q2{+B2MibX lM/2` M mMBtBH bi`2bb bii2 Q7 i?2 QTiB+H }#2`- r?B+? Bb 7`22 7`QK i?2 BMi2`+iBQM rBi? i?2 2MpB`QMK2Mi- ε1 = ε2 = −νε3 - r?2`2 ν Bb SQBbbQMǶb `iBQ 7Q` i?2 QTiB+H }#2`X AM i?Bb +b2- ∆λ1 = ∆λ2 = ∆λ M/   n21 ∆λ = 1− (p12 − ν(p11 + p12 )) ε3 , U9V λ 2 Q` kj

1 ∆λ . U8V · k λ∗ 6Q` i?2 QTiB+H }#2`b mb2/ BM i?2 HKBMi2/ +QKTQbBi2 KQ/2H- k = 0.78X q?2M i?2 }#2`@QTiB+ b2MbQ` Bb 2K#2//2/ BM  S*J Q` bQK2?Qr +QM@ M2+i2/ rBi? i?2 bm`7+2 Q7 i?2 Ki2`BH- 7Q` 2tKTH2 #v /?2bBp2 #QM/BM;-  +QKTH2t bi`2bb bii2 Bb `2HBx2/ BM i?2 b2MbQ` b  `2bmHi Q7 BMi2`+iBQM rBi? i?2 Ki2`BH- BX2X- i?2 b2MbQ` Bb bm#D2+i2/ iQ /27Q`KiBQM- r?B+? +M #2 B/2M@ 1 M/ iB}2/ QM i?2 #bBb Q7 i?2 2tT2`BK2MiH /i- MK2Hv- i?2 pHm2b ∆λ λ∗ ∆λ2 X h?2 T`2b2M+2 Q7 irQ `2bQMM+2 rp2H2M;i?b BM i?2 `2~2+i2/ bT2+i`mK λ∗ Q7  bBM;H2@KQ/2 "`;; ;`iBM; /m2 iQ Bib BMi2`+iBQM rBi? i?2 bm``QmM/BM; Ki2`BH rb /2b+`B#2/ 7`QK i?2 `2bmHi Q7 2tT2`BK2Mib BM `27X (k8)X 6`QK i?2 MHvbBb Q7 1[X UjV- Bi 7QHHQrb i?i i ε1 6= ε2 - r2 ?p2 irQ 2[miBQMb rBi? i?`22 mMFMQrMb- M/ i ε1 = ε2 - QM2 2[miBQM rBi? irQ mMFMQrMbX h?mb- M mMK#B;mQmb `2HiBQMb?BT #2ir22M i?2 2tT2`BK2MiH /i QM ∆λ/λ∗ M/ QM2 Q7 i?2 +QKTQM2Mib Q7 i?2 bi`BM i2MbQ` ε3 Bb 2bi#HBb?2/ QMHv mM/2` mMBtBH /27Q`KiBQM Q7 i?2 "`;; ;`iBM;X AM ;2M2`H- MmK2`B+H bBKmHiBQMb HHQr mb iQ 2biBKi2 i?2 TTHB+#BHBiv `M;2 Q7 1[X U8VX b BM T`2pBQmb 2tT2`BK2Mib- 7Q` M Q#D2+i Q7 bim/v- r2 +?Qb2  T`HH2H2TBT2/ rBi? M 2K#2//2/ QTiB+H }#2` U6B;X 8VX q2 T2`7Q`K2/ i?2 bim/v rBi?  72r p`BMib Q7 HQ/BM;- /m`BM; r?B+? /Bz2`2Mi 7Q`+2b r2`2 TTHB2/ MQ`KHHv iQ i?2 Hi2`H 7+2b Q7 i?2 T`HH2H2TBT2/ Px = P0 - Py = Pz = 0c Py = P0 - Px = Pz = 0c Pz = P0 - Px = Py = 0X 6Q` i?2 KQ/2HBM; HKBMi2/ +QKTQbBi2 rb +QMbB/2`2/ b  ?QKQ;2M2Qmb K2/BmK- rBi? i?2 2z2+iBp2 K2+?MB+H +?`+i2`BbiB+b b?QrM BM h#H2 RX q2 2tKBM2/ irQ p`BMib Q7 i?2 +QKTQbBi2 KQ/2H, QM2 rBi? M/ rBi?Qmi  `2bBM TQ+F2iX h?2 QTiB+H }#2` ?/ i?2 bK2 K2+?MB+H +?`+i2`BbiB+b M/ /BK2MbBQMb b i?2 }#2` mb2/ BM i?2 T`2pBQmb MmK2`B+H 2tT2`BK2MibX h?2 MmK2`B+H 2tT2`BK2Mib r2`2 T2`7Q`K2/ rBi? i?2 BK iQ 2pHmi2 i?2 bi`BMb ε1 - ε2 - ε3 BM i?2 }#2` 7Q` i?2 /Bz2`2Mi p`BMib Q7 HQ/BM; M/ iQ +H+mHi2 i?2 pHm2b Q7 ∆λ1 /λ∗ M/ ∆λ2 /λ∗ mbBM; 1[X UjVX q?BH2 /QBM; i?Bb- +`2 rb iF2M iQ +QMi`QH i?2 +Q``2HiBQM #2ir22M i?2 bi`BM ε3 M/ i?2 +Q``2bTQM/BM; bi`BM BM i?2 Ki2`BH BM i?2 pB+BMBiv Q7 i?2 }#2`X 6m`i?2`- i?2 pHm2b Q7 ∆λ1 /λ∗ M/ ∆λ2 /λ∗ rb iF2M b i?2 2tT2`BK2MiH /i 7Q` +H+mHiBM; i?2 pHm2b Q7 bi`BM εE 3 HQM; i?2 }#2` #b2/ QM 1[X U8VX b i?2 M2ti bi2T-  +QKT`iBp2 MHvbBb rb K/2 iQ 2biBKi2 i?2 /Bz2`2M+2b #2ir22M i?2 pHm2b Q7 i?2 bi`BM ε3 M/ bi`BM εE 3 Q#iBM2/ QM i?2 #bBb Q7 i?2 bBKmHi2/ 2tT2`BK2MiH /i ∆λ1 /λ∗ M/ ∆λ2 /λ∗ - r?B+? r2`2 2pHmi2/ #v MmK2`B+H 2tT2`BK2Mib mM/2` ε3 =

k9

i?2 bbmKTiBQM i?i i?2 QTiB+H }#2` rb mM/2` mMBtBH /27Q`KiBQMX h#H2 e /BbTHvb i?2 pHm2b Q7 bi`BMb ε01 - ε02 - ε03 - i?2 pHm2b Q7 (∆λ1 /λ∗ )0 - (∆λ2 /λ∗ )0 M/ i?2 K;MBim/2b Q7 i?2 2``Q`b δ1 M/ δ2 X >2`2 ε01 = ε1 /P0 - ε02 = ε2 /P0 - ε03 = ε3 /P0 - M/ i?2 [mMiBiB2b (∆λ1 /λ∗ )0 (∆λ2 /λ∗ )0 r2`2 2pHmi2/ #v 1[X UjV M/ BM i?2 7QHHQrBM; `2 iF2M b i?2 2tT2`BK2MiH /iX AM i?Bb +b2- i?2 bi`BM ε3 Bb i?2 bi`BM εx HQM; i?2 }#2` H2M;i?- M/ i?2 biBMb ε1 M/ ε2 `2 2[mH iQ εy ) M/ εz - iFBM; BMiQ ++QmMi i?2 7+i i?i ε1 M/ ε2 `2 i?2 T`BM+BTH bi`BMb Uε1 > ε2 VX h?2 2``Q` BM i?2 bi`BM +H+mHiBQM K/2 rBi? i?2 mb2 Q7 1[X U8V Bb /2i2`KBM2/ b 7QHHQrb, δ1 =

εE1 3 − ε3 , ε3

δ2 =

εE2 3 − ε3 , ε3

UeV

1 ∆λ2 1 ∆λ1 E2 r?2`2 εE1 3 = k λ∗ - ε3 = k λ∗ X h#H2 e HbQ b?Qrb i?2 pHm2b Q7 k1 M/ k2 - r?B+? T`QpB/2 `2HB#H2 bi`BM pHm2b +H+mHi2/ #v 7Q`KmHb ∆λ1 /λ∗ = k1 ε3 - ∆λ2 /λ∗ = k2 ε3 X 6Q` BHHmbi`iBQM Tm`TQb2b- 6B;X Rk T`2b2Mib i?2 /2T2M/2M+2b k1 M/ k2 QM i?2 +QKTQM2Mib Q7 i?2 bi`BM i2MbQ` `2HiBp2 iQ i?2 THM2 k = 0.78 7Q` i?2 +QQ`/BMi2b ln(ε2 /ε3 - ln(ε1 /ε3 )X h?2 Q#iBM2/ `2bmHib HHQr mb iQ +QM+Hm/2 i?i i?2 mb2 Q7 i?2 "`;; ;`i@ BM; BM  bBM;H2@KQ/2 QTiB+H }#2` T`QpB/2b ++2Ti#H2 BM7Q`KiBQM #Qmi i?2 +QKTQM2Mi Q7 i?2 bi`BM i2MbQ` HQM; i?2 }#2`- T`QpB/2/ i?2 b2MbQ` Bb HQ+i2/ BM i?2 xQM2 r?2`2 i?Bb bi`BM +QKTQM2Mi T`2/QKBMi2bX h?Bb +QM+HmbBQM +M #2 bmTTQ`i2/ #v i?2 `2bmHib Q7 i?2 M2ti 2tT2`BK2Mi (9j)X h?2 bim/v rb +``B2/ Qmi 7Q`  `2+iM;mH` S*J THi2 U50 × 300 × 5 KKV +QMiBMBM; BM i?2 7Q`K Q7  +B`+mH` `+ U6B;X RjVX AM +QMi`bi iQ i?2 FMQrM 2tT2`BK2Mib- /2KQMbi`iBM; i?2 TQbbB#BHBiv Q7 K2bm`BM; bi`BMb rBi? i?2 6Paa BMi2;`i2/ BMiQ i?2 Ki2`BH- i?Bb bT2+BK2M /2KQMbi`i2b  bB;MB}+Mi bi`BM BM?QKQ;2MmBiv mM/2` +QM/BiBQMb Q7 mMBtBH HQ/BM;X h?2 QTiB+H }#2`b 2K#2//2/ BM i?2 bT2+BK2Mb `2 mb2/ iQ HQ+i2 "`;; ;`iBM; b2MbQ`b rBi?  H2M;i? Q7 8 KKX S*Jb `2 T`2T`2/ QM i?2 #bBb Q7 }#2`;Hbb T`2T`2; ?pBM; i?2 7QH@ HQrBM; K2+?MB+H +?`+i2`BbiB+b, 2HbiB+ KQ/mHmb BM #b2 i2MbBQM Bb E11 = 26.5 :Sc 2HbiB+ KQ/mHmb BM r27i i2MbBQM Bb E22 = 26.1 :Sc 2HbiB+ KQ/m@ Hmb BM i2MbBQM MQ`KH iQ i?2 THM2 Q7 i?2 Hv2` Bb E33 = 6 :Sc b?2` KQ/mHB G12 = 4 :S- G13 = 3 :S- G23 = 3 :Sc SQBbbQMǶb `iBQb, ν12 = 0.144ν13 = 0.138- ν23 = 0.18X h?2 QTiB+H }#2` K/2 Q7 [m`ix ?b i?2 7QHHQr@ BM; K2+?MB+H +?`+i2`BbiB+b, EK = 71.4 :Sc νK = 0.17- i?2 /BK2i2`

k8

k1 k = 0.78

1.2 1 0.8 k1 0.6 0.4 0.2 1

1 0.5 0 ln(
2/
3)

-0.5

-1

-1

0 ln(
1/
3)

k2 k = 0.78

1.2 1 0.8 k2 0.6 0.4 0.2 1

1 0.5 0 ln(
2/
3)

-0.5

-1

-1

0 ln(
1/
3)

6B;m`2 Rk, .2T2M/2M+2b Q7 k1 M/ k2 QM i?2 +QKTQM2Mib Q7 i?2 bi`BM i2MbQ`

Q7 0.124 KK M/ i?2 T`Qi2+iBp2 b?2HH 0.012 KK i?B+F- r?B+? Bb K/2 Q7 TQHvKB/2 rBi? EO = 2.7 :Sc νO = 0.31X h?2 T`Q+2bb Q7 ǴS`2T`2; i2+?MQH@ Q;v M/ /B`2+i T`2bbBM;Ǵ BM+Hm/2b i?2 7QHHQrBM; #bB+ QT2`iBQMb, HvBM; mT Q7 ky T`2T`2; THB2b QM  KQH/c 2K#2/K2Mi Q7 }#2` QTiB+ b2MbQ`b #2ir22M Ry M/ RR THB2bc bb2K#Hv Q7 i?2 i2+?MQHQ;B+H T+F;2 7Q` Ki2`BH T`2KQH/BM;c `2HBxiBQM Q7 TQHvK2`BxiBQM KQ/2c /Bbbb2K#HBM; Q7 i?2 i2+?MQHQ;B+H T+F@ ;2X h?2 TQHvK2`BxiBQM M/ +m`BM; Q7 i?2 S*J T+F;2 rBi? i?2 BK#2//2/ 6Paa rb +``B2/ Qmi BM i?2 GM;xmM2` T`2bbX J2bm`2K2Mi Q7 BM?QKQ;2M2Qmb /27Q`KiBQM }2H/b Q7 i?2 6Paa #mBHi BMiQ i?2 S*J rb +``B2/ Qmi /m`BM; mMBtBH i2MbBH2 i2bib QM i?2 mMBp2`bH 2H2+@ i`QK2+?MB+H AMbi`QM 8N3k K+?BM2X hQ MHvx2 i?2 Q#iBM2/ 2tT2`BK2MiH ke

y x 10

6B;m`2 Rj, h?2 b?T2 Q7 i?2 bT2+BK2M K/2 Q7 TQHvK2` +QKTQbBi2 Ki2`BH

`2bmHib BM i?2 7`K2rQ`F Q7 i?2 HBM2` i?2Q`v Q7 2HbiB+Biv- r2 T2`7Q`K2/ i?2 MmK2`B+H +H+mHiBQMb Q7 i?2 bi`2bbĜbi`BM bii2 Q7 i?2 bT2+BK2Mb 7Q`  i?`22@ /BK2MbBQMH 7Q`KmHiBQM Q7 i?2 T`Q#H2K mbBM; i?2 }MBi2 2H2K2Mi K2i?Q/X h?2 +QKTmiiBQM Q7 bi`BMb QM i?2 #bBb Q7 /B;BiH 6Paa BM7Q`KiBQM QM +?M;2b BM i?2 `2bQMM+2 rp2H2M;i? Q7 i?2 `2~2+i2/ bT2+i`mK rb K/2 7Q` 2+? i@i? b2MbQ` BM i2`Kb Q7 1[X U8VX 6B;m`2 R9 b?Qrb i?2 `2bmHib Q7 i?2 /Bbi`B#miBQM Q7 bi`BMb HQM; i?2 tBH HBM2 Q7 i?2 bT2+BK2M mM/2` i?2 7Q`+2 Q7 F = 7 FL UF = P · S- r?2`2 S Bb i?2 +`Qbb@b2+iBQMH `2 Q7 i?2 bT2+BK2MV Q#iBM2/ QM i?2 #bBb Q7 i?2 6Paa `2/BM;b- i?2 oB+@j. QTiB+H bvbi2K /i- M/ i?2 `2bmHib Q7 MmK2`B+H bBKmHiBQM #v i?2 }MBi2 2H2K2Mi K2i?Q/X h?2 /Bz2`2M+2 #2ir22M i?2 `2bmHib Q#iBM2/ rBi? 6Paa M/ i?Qb2 Q#iBM2/ rBi? i?2 B/ Q7 i?2 QTiB+H K2bm`BM; bvbi2K M/ MmK2`B+H bBKmHiBQM /Q2b MQi 2t+22/ eWX 0.45 FEM Vic-3D FOSS

0.4


(%)

0.35 0.3 0.25 0.2 0.15 0.1 -80

-60

-40

-20

0

20

40

60

80

x (mm)

a 6B;m`2 R9, ai`BM /Bbi`B#miBQM BM  bT2+BK2M rBi? b2KB+B`+mH` MQi+?2b

kd

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h#H2 e, _2bmHib 7`QK 2pHmiBM; i?2 TTHB+#BHBiv `M;2 Q7 1[X U9V 7Q` i?2 KQ/2H Q7  T`HH2H2TBT2/ rBi? M 2K#2//2/ QTiB+H }#2`

ε01 −12

Px = P0 Py = 0Pz = 0 Px = 0Py = P0 Pz = 0 Px = 0Py = 0Pz = P0

Px = P0 Py = 0Pz = 0 Px = 0Py = P0 Pz = 0 Px = 0Py = 0Pz = P0

×10

>QKQ;2M2Qmb KQ/2H Q7  bvbi2K rBi?  `2bBM TQ+F2i ε02 ε03 (∆λ1 /λ∗ )0 (∆λ2 /λ∗ )0 k1 δ1 - W −12 −12 ×10 ×10 ×10−12 ×10−12

k2

δ2 - W

−2.25

−1.77

11.91

9.35

9.42

0.78

0.31

0.79

1.12

2.21

−1.28

−0.48

−0.81

−0.26

1.68

114.76

0.55

30.11

20.46

1.94

−5.73

−7.26

−10.15

1.27

62.32

1.77 127.12

ε01 ×10−12

>QKQ;2M2Qmb KQ/2H Q7  bvbi2K rBi?Qmi  `2bBM TQ+F2i ε02 ε03 (∆λ1 /λ∗ )0 (∆λ2 /λ∗ )0 k1 δ1 - W −12 −12 −12 −12 ×10 ×10 ×10 ×10

k2

δ2 - W

−2.26

−1.76

11.91

9.31

9.39

0.78

0.33

0.79

1.17

−3.51

9.64

−0.44

−2.60

−0.55

5.87

652.85

1.23

58.08

19.46

−2.62

−5.35

−5.57

−9.02

1.04 −33.35 1.69 116.05

je