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RXj

*QMi`B#miBQMb

h?2 KBM +QMi`B#miBQMb K/2 i?`Qm;? i?Bb i?2bBb `2 ?B;?HB;?i2/ #2HQr- 2+? H2/BM; iQ i H2bi QM2 T22` `2pB2r2/ DQm`MH Tm#HB+iBQMX RX JMm7+im`BM; Q7 i`Mb/m+2` Hv2` 7Q` bi`m+im`H ?2Hi? KQMBiQ`BM; Ua>J Hv2`VX h?2 `Q#mbiM2bb Q7 i?Bb M/ Qi?2` +QKK2`+BHHv pBH#H2 i`Mb/m+2`b r2`2 2pHmi2/ r?2M 2tTQb2/ iQ QT2ìBQMH M/ 2MpB`QMK2MiH +QM/BiBQMb `2H2pMi iQ B`#Q`M2 2H2+@ i`QMB+bX Ç aHKMTQm`- JX aX- wX a?`B7 E?Q/2B- M/ JX >X HB#/BX ǴB`#Q`M2 h`Mb@ /m+2` AMi2;`Biv mM/2` PT2ìBQMH 1MpB`QMK2Mi 7Q` ai`m+im`H >2Hi? JQMB@ iQ`BM;XǴ a2MbQ`b ReXRk UkyReV, kRRyX kX .2p2HQTK2Mi Q7 M BMbiMiM2Qmb #b2HBM2 K2i?Q/ HHQrBM; ;2QK2i`B+HHv bBKBH` `2b iQ #2 mb2/ b #b2HBM2b 7Q` M BMi2``Q;iBQM `2X k9

RXj, *QMi`B#miBQMb Ç aHKMTQm`- JXaX- wX a?`B7 E?Q/2B- M/ JX>X HB#/BX ǴAMbiMiM2Qmb "b2HBM2 .K;2 GQ+HBxiBQM lbBM; a2MbQ` JTTBM;XǴ A111 a2MbQ`b CQm`MH RdXk UkyRdV, kN8@jyRX jX i2KT2ìm`2 +QKT2MbiBQM K2i?Q/ r?B+? TTHB2b `M;2 Q7 +Q``2+iBQM 7+iQ`bM/ /Q2b MQi bbmK2 +QMbiMi i2KT2ìm`2X h?Bb rb p2`B}2/ rBi? HQ+HBbiBQM Qp2` M 2ti`2K2 `M;2 Q7 i2KT2ìm`2b rBi? QMHv QM2 #b2HBM2X Ç aHKMTQm`- JXaX- wX a?`B7 E?Q/2B- M/ JX>X HB#/BX Ǵ:mB/2/ rp2 i2KT2ìm`2 +Q``2+iBQM K2i?Q/b BM bi`m+im`H ?2Hi? KQMBiQ`BM;XǴ CQm`MH Q7 AMi2HHB;2Mi Ji2`BH avbi2Kb M/ ai`m+im`2b UkyReVX Ç aHKMTQm`- JXaX- wX a?`B7 E?Q/2B- M/ JX>X HB#/BX ǴAKT+i .K;2 GQ+HBbiBQM lM/2` PT2ìBQMH M/ 1MpB`QMK2MiH *QM/BiBQMbXǴ a2MbQ`b UBM T`2bbVX 9X i`Mb/m+2` TH+2K2Mi QTiBKBbiBQM TT`Q+? mbBM; rp2 T`QT;iBQM 72im`2bX h?Bb rb #H2 iQ BM+Q`TQì2 /Bz2`2Mi /K;2 ivT2b- biBz2M2`b M/ b2MbQ` 7BHm`2X Ç aHKMTQm`- JXaX- wX a?`B7 E?Q/2B- M/ JX>X HB#/BX Ǵh`Mb/m+2` TH+2@ K2Mi QTiBKBbiBQM b+?2K2 7Q` /2Hv M/ bmK /K;2 /2i2+iBQM H;Q`Bi?KXǴ ai`m+im`H *QMi`QH M/ >2Hi? JQMBiQ`BM; UkyReV

k8

*?Ti2` hqP

"+F;`QmM/ kXR

AMi`Q/m+iBQM

a>J TT`Q+?2b `2 BM+`2bBM;Hv #2BM; +QMbB/2`2/ 7Q` TTHB+iBQM BM iM/2K Q` 2p2M b `2TH+2K2Mi 7Q` 2bi#HBb?2/ L.h TT`Q+?2bX h?2b2 7KBHv Q7 TT`Q+?2b ?p2 ii`+i2/ #Qi? BM/mbi`BH M/ +/2KB+ ii2MiBQM (Ry- RR)X lbBM; M2irQ`F b2MbQ`b M/fQ` +imiQ`b- a>J bvbi2Kb +M +QMiBMmQmbHv KQMBiQ` bi`m+im`H BMi2;`Biv r?BH2 i?2 bi`m+im`2 Bb BM QT2ìBQMX h?2b2 +M 7HH BMiQ KMv +i2;Q`B2b BM+Hm/BM; }#`2 QTiB+- KQ/H /i #b2/- +QmbiB+ 2KBbbBQMb- 2H2+i`QK2+?MB+H BKT2/M+2 U1JAV M/ mHi`bQMB+X lHi`bQMB+ ;mB/2/ rp2 U:qV K2i?Q/b rBi? BMi2;ì2/ b2MbQ`b +M QT2ì2 BM M +iBp2 Q` TbbBp2 TT`Q+?2bX SbbBp2 bvbi2Kb +QMiBMmQmbHv KQMBiQ` 7Q` 2p2Mib i?i +QmH/ BMBiBi2 /K;2X 6Q` 2tKTH2- `2+Q`/2/ mHi`bQMB+ rp2b BMBiBi2/ Q` 2t+Bi2/ #v M BKT+i 2p2Mi `2 MH@ vb2/- b+2ìBMBM; r?2i?2` i?2 BKT+i 2p2Mi ?b +mb2/ bB;MB}+Mi /K;2 (Rj- R9)X +iBp2 TT`Q+?2b HHQr bb2bbK2Mi Q7 bi`m+im`H BMi2;`Biv rBi?Qmi FMQrH2/;2 Q7 i?2 /K;2 BMBiBiBM; 2p2Mi (R8ĜRN)X h?i Bb- +imiQ`b `2 mb2/ iQ 2t+Bi2 i?2 `2[mB`2/ /B;MQbiB+ bB;MHb iQ KQMBiQ` i?2 +m``2Mi ?2Hi? Q7 i?2 bi`m+im`2X +iBp2 K2i?Q/b HHQr BM@bBim bb2bbK2Mib Q7 BMi2;`Biv M/ KQMBiQ`BM; Q7 T`2b2Mi /K;2b 7Q` ;`Qri?X h?2 7Q+mb Q7 i?Bb rQ`F Bb QM GK# rp2 #b2/ :q a>J rBi? TB2xQ2H2+i`B+ i`Mb@ /m+2`bX ke

kXk, GK# qp2b

kXk

GK# qp2b

>Q`+2 GK# (ky) T`2/B+i2/ i?2 2tBbi2M+2 Q7 GK# rp2b BM i?BM THi2 HBF2 bi`m+im`2b M/ i?2 TQi2MiBH 7Q` /K;2 /2i2+iBQM rb MQi2/ #v qQ`HiQM (kR)- r?Q rb #H2 iQ 2t+Bi2 GK# rp2b BM bi`m+im`2bX h?2b2 `2 7Q`K2/ #v i?2 bmT2`TQbBiBQM Q7 i`Mbp2`b2 M/ HQM;Bim/BMH rp2b rBi? p2HQ+BiB2b CT M/ CL `2bT2+iBp2Hv CL =

ˆ ı ı Ù

E(1 ≠ v) , fl(1 + v)(1 ≠ 2v)

CT =

Û

E , fl(1 + v)

UkXRV

r?2`2 E, v M/ fl `2 i?2 uQmM;Ƕb KQ/mHmb- SQBbbQMǶb ìBQ M/ /2MbBiv `2bT2+iBp2HvX hQ 7Q`KmHi2 GK# rp2 T`QT;iBQM- Bi Bb mb27mH iQ +QMbB/2` T`QT;iBQM HQM; i?2 x1 /B`2+iBQM BM M BM}MBi2 BbQi`QTB+ k. THi2X SHi2 i?B+FM2bb Bb BM i?2 x3 /B`2+iBQM/BbTH+2K2Mib BM i?2 x2 `2 B;MQ`2/ M/ ?2M+2 ˆ/ˆx2 = 0X h?2 ;Qp2`MBM; 2[miBQMb `2 ;Bp2M b i?2 LpB2`Ƕb 2[miBQM Q7 2HbiB+ KQiBQM 2tT`2bb2/ BM i?2 #b2M+2 Q7 #Q/v 7Q`+2b UkXkV

(⁄ + µ)ÒÒ · u + µÒ2 u = fl¨ u,

r?2`2 i?2 GKĕ +QMbiMib `2 ⁄ M/ µ- M/ r?2`2 Qp2` /Qi BM/B+i2b iBK2 /2`BpiBp2X lbBM; >2HKQHix /2+QKTQbBiBQM rBi? p2+iQ` M/ b+H` TQi2MiBHb UÂ-„V- irQ rp2 2[miBQMb +M #2 Q#iBM2/ BM i2`Kb Q7 i?2 i`Mbp2`b2 CT M/ HQM;Bim/BMH CL rp2 T`QT;iBQM p2HQ+BiB2b ¨ CL2 Ò2 „ = „, ¨ CT2 Ò2 Â = Â.

UkXjV

h?2 /BbTH+2K2Mib u `2 ;Bp2M #v u1 =

ˆ„ ˆÂ + - u2 = 0ˆx1 ˆx3

M/ u3 =

ˆ„ ˆÂ ≠ ˆx3 ˆx1

UkX9V

r?2`2 Â2 Bb `2TH+2/ #v ÂX h?2`27Q`2 7`QK >QQF2Ƕb Hr i?2 bi`2bb2b ‡ `2 û3 û1 + ) ˆx1 ˆx3 ˆ2„ ˆ2Â ˆ2Â = µ( ≠ + ), ˆx1 ˆx3 ˆx21 ˆx23

‡31 = µ(

UkX8V

kd

kXk, GK# qp2b û1 û3 û3 + ) + 2µ ˆx1 ˆx3 ˆx3 2 2 ˆ „ ˆ „ ˆ2„ ˆ2Â = ⁄( 2 2 + 2 ) + 2µ( 2 ≠ ). ˆ x1 ˆ x1 ˆ x3 ˆx1 ˆx3

‡31 = ⁄(

UkXeV

bbmKBM; i`+iBQM 7`22 #QmM/`v +QM/BiBQMb i bm`7+2b x3 = ±h UTHi2 i?B+FM2bb k?V M/ iFBM; ?`KQMB+ bQHmiBQMb rBi? `/BH 7`2[m2M+v Ê- i?2 _vH2B;?@GK# 7`2[m2M+v 2[miBQM +M #2 7QmM/ b tan(qh) 4k 2 qpµ = tan(ph) (⁄k 2 + ⁄p2 + 2µp2 )(k 2 ≠ q 2 ) r?2`2 p2 =

Ê2 Ê2 2 2 ≠ k q = ≠ k2CL2 CT2

M/ k =

UkXdV

Ê . Cp

UkX3V

1[miBQM UkXdV +M #2 bTHBi BMiQ Tìb- `2T`2b2MiBM; i?2 irQ 7KBHB2b Q7 BM}MBi2 GK# rp2 KQ/2b tan(qh) 4k 2 qp =≠ 2 tan(ph) (k ≠ q 2 )2 tan(qh) (k 2 ≠ q 2 )2 =≠ tan(ph) 4k 2 qp

avKK2i`B+ KQ/2bMiB@bvKK2i`B+ KQ/2bX

UkXNV

+iBpiBQM Q7 bvKK2i`B+ M/ MiB@bvKK2i`B+ KQ/2b- Si M/ Ai Ui4y-R- XXXV- /2T2M/ QM i?2 2t+BiiBQM 7`2[m2M+vX Ai KQ/2b ?p2 /QKBMMi Qmi Q7 THM2 KQiBQM rBi? +QMbiMi i?B+FM2bb ~2tBM;X Si KQ/2b ?p2 /QKBMMi BM@THM2 KQiBQMX h?2 7mM/K2MiH S0 T`QT;i2b i Km+? 7bi2` T?b2 Cp M/ ;`QmT p2HQ+Biv Cg - i?M i?2 bHQr2` A0 i ;Bp2M 7`2[m2M+vX qBi? BM+`2bBM; 7`2[m2M+v- i?2 p2HQ+Biv Q7 HH KQ/2b i2M/ iQr`/b i`Mbp2`b2 p2HQ+Biv CT X h?2 T`QT;iBQM p2HQ+Biv +M #2 7QmM/ b i?2 `QQib iQ i?2 b2Tì2/ _vH2B;?@GK# 2[miBQMb UkXNV- i?2b2 `2 T`2b2Mi2/ b /BbT2`bBQM +m`p2bX h?2 /BbT2`bBQM +m`p2b 7Q` M HmKBMBmK THi2 i i2KT2ìm`2 /Bz2`2M+2 Q7 9y ê* `2 b?QrM BM };m`2 kXRX GK# rp2b T`QT;iBM; BM `2H bi`m+im`2b rBHH 2M+QmMi2` #QmM/`B2b r?B+? +mb2 b+ii2`BM;- KQ/2 +QMp2`bBQMb M/ `2~2+iBQMbX hQ 2M?M+2 /2i2+i#BHBiv- /K;2 rp2 72im`2b b?QmH/ #2 `2/BHv /BbiBM;mBb?#H2X 6B`biHv i?2 2t+BiiBQM 7`2[m2M+v b?QmH/ #2 Q7 M``Qr #M/rB/i? iQ ;Bp2 KQ/2 Tm`Biv M/ HbQ iQ KBMBKBb2 /BbT2`bBQM 2z2+ib (kk)X +QMiBMmQmb bBM2 i`BM rBHH ?p2 M 2ti`2K2Hv M``Qr #M/rB/i?X >Qr2p2`/m2 iQ i?2 2t+BiiBQM H2M;i? i?Bb rBHH MQi HHQr /K;2 b+ii2` iQ #2 `2/BHv B/2MiB}2/ k3

kXk, GK# qp2b

9

S2

S1

8

S3

7

Cp km/s

A2

Increased Temperature

6

A1

S0

5

A3

4 3

A0

2 Anti−Symmetric Modes Symmetric Modes

1 0

0

1

2

3 4 5 6 Freduency.Thickness MHz.mm 6`2[m2M+vXh?B+FM2bb J>xXKK

7

8

6B;m`2 kXR, .BbT2`bBQM +m`p2b 7Q` M HmKBMBmK THi2 rBi? i?2 KQ/mHmb `2/m+2/ #v kX8 :S /m2 iQ BM+`2b2/ i2KT2ìm`2X

/m2 iQ Qp2`HT- i?2 +imiBQM bB;MH Kmbi #2 i`mM+i2/X _2+iM;mH` rBM/Qr2/ bB;MH b?QrM BM };m`2 kXk- rBHH H2p2 H`;2 bB/2 HQ#2b- b b?QrM BM };m`2 kXjX >MMBM; rBM/Qr2/ +imiBQM bB;MH A(t) = sin(2fifc t)[1 ≠ cos(

2fifc t )] Nc

UkXRyV

Bb b?QrM BM };m`2 kXk#- M/ i?Bb T`QpB/2b M``Qr #M/rB/i? +imiBQM bB;MH UiV rBi? `2/m+2/ KTHBim/2 bB/2 HQ#2b b /2TB+i2/ BM kXj#X >2`2 fc Bb i?2 +2Mi`H 7`2@ [m2M+v- t Bb iBK2 M/ Nc Bb i?2 MmK#2` Q7 +v+H2bX `2/m+2/ MmK#2` Q7 +v+H2b rBHH BM@im`M BM+`2b2 i?2 #M/rB/i?- r?BH2 ?B;?2` +v+H2 +QmMi rBHH BM2pBi#Hv `2bmHi BM KQ`2 bB;MH Qp2`HT- KFBM; /K;2 b+ii2` H2bb `2/BHv /BbiBM;mBb?#H2 (kk)X S`2pBQmb rQ`Fb ?p2 BMp2biB;i2/ i?2 2z2+ib 7`2[m2M+v M/ MmK#2` Q7 +v+H2b- M/ 7QmM/ 8 +v+H2b iQ #2 bmBi#H2 7Q` /K;2 /2i2+iBQM +`Qbb `M;2 Q7 7`2[m2M+B2b (jN)X h?`Qm;?Qmi i?Bb rQ`F }p2 +v+H2 >MMBM; rBM/Qr2/ iQM2 #m`bi bB;MH rb mb2/- b22 };m`2b kXk#X //BiBQMHHv i?2 T`QT;iBQM b?QmH/ #2 bm+? i?i rp2H2M;i? Bb ?H7 Q7 i?2 /2bB`2/ /2i2+i#H2 /K;2 bBx2X

kN

1

1

0.5

0.5 Amplitude

Amplitude

kXk, GK# qp2b

0

−0.5

−0.5

−1

0

0

2

4 Time(s)

6

−1

8

0

2

−5

x 10

4 Time(s)

6

8 −5

x 10

U#V

UV

6B;m`2 kXk, +imiBQM bB;MH 7Q` Ryy F>x }p2 bB;MH KQ/mHi2/ rBi?- UV a[m`2 rBM/Qr- U#V >MMBM; rBM/QrX

1 Normalised Amplitude

Normalised Amplitude

1 0.8 0.6 0.4

0.6 0.4 0.2

0.2 0

0.8

0

0.5

1 Frequency (kHz)

UV

1.5

2 5

x 10

0

0

0.5

1 Frequency (kHz)

1.5

2 5

x 10

U#V

6B;m`2 kXj, 6`2[m2M+v bT2+i`mK 7Q` Ryy F>x }p2 +v+H2 iQM2 #m`bi bB;MH KQ/mHi2/ rBi?- UV a[m`2 rBM/Qr- U#V >MMBM; rBM/QrX

jy

kXj, a2MbQ` M/ +imiQ`b

kXj

a2MbQ` M/ +imiQ`b

JMv /Bz2`2Mi ivT2b Q7 b2MbQ` M/ +imiQ`b 2tBbi HHQrBM; /B;MQbiB+ bB;MHb iQ #2 ;2M2ì2/ M/ `2+Q`/2/- i?2b2 `2 bmKK`Bb2/ BM i#H2 kXRX 6B#`2 QTiB+ b2MbQ`b HHQr ++mì2 K2bm`2K2Mi Q7 bi`BM- rBi? ?`/r`2 M/ bQ7i@ r`2 bQHmiBQMb +QKK2`+BHHv pBH#H2- b22 };m`2 kX9X M QTiB+H }#`2 Bb B``/Bi2/ rBi? Hb2` bQm`+2- Mv +?M;2 BM i?2 }#`2 +M #2 /2i2+i2/ b b?B7ib BM i?2 `2+2Bp2/ bT2+i`mKX 6B#`2 "`;; ;ìBM; U6":V b2MbQ`b ?p2 `2b Q7 Hi2`2/ `27`+iBp2 BM/2t rBi?BM i?2 }#`2 +Q`2- H2M;i? +?M;2 i i?2b2 HQ+iBQMb `2 /2i2+i#H2 b T2F b?B7i BM i?2 `2~2+i2/ bT2+i`mKX /pM+2b BM }#`2 M/ bT2+i`mK MHvb2` i2+?MQHQ;v ?p2 HHQr2/ }#`2 QTiB+ b2MbQ`b iQ +Tim`2 ?B;? 7`2[m2M+v bi`BM 2p2Mib M/ 2p2M mHi`@ bQMB+ rp2 T`QT;iBQM (kj)X JQ`2 `2+2MiHv GvM+? 2i HX (k9) T`QTQb2/ K2i?Q/b 7Q` 2M?M+BM; i?2 b2MbBiBpBiv Q7 6":b 7Q` /2i2+iBM; GK# rp2bX amM 2i HX (k9) T`Q@ TQb2/ ?v#`B/ Swh@6": bvbi2K 7Q` /2i2+iBM; /K;2- /2i2`KBMBM; rp2 bQm`+2 /B`2+iBQM rBi? M 6": `Qb2ii2X

6B;m`2 kX9, 6B#`2 "`;; ;ìBM; QTiB+H b2MbQ`b mb2/ 7Q` K2bm`BM; bi`BMX

Gb2` BMi2`72`QK2i2`b `2 pHm#H2 iQQH BM /2i2`KBMBM; 7mHH rp2 }2H/ T`QT;iBQMHi?Qm;? MQi +m``2MiHv bmBi#H2 7Q` BM@bBim QT2ìBQM /m2 iQ #mHFv 2[mBTK2Mi M/ ?B;? TQr2` `2[mB`2K2Mi- b22 };m`2 kX8X h?2b2 ;Bp2 r2Hi? Q7 BM7Q`KiBQM- HHQrBM; 2ti`+iBQM Q7 F2v rp2 T`QT;iBQM 72im`2bX AM Km+? i?2 bK2 rv b Q#bi+H2b BM b?HHQr ri2` rp2b- i?2 7mHH rp2 }2H/ +M ;Bp2 pBbmHBbiBQM Q7 ~rb (k8- ke)X

jR


6B;m`2 kX8, j. Hb2` pB#`QK2i2`- `2+Q`/BM; 7mHH }2H/ GK# rp2 T`QT;iBQMX

lHi`bQMB+ S`Q#2b `2 #H2 iQ ;2M2ì2 TìB+mH` mHi`bQMB+ rp2 ivT2 rBi?BM bi`m+im`2X h?2b2 +M #2 +QmTH2/ iQ i?2 bi`m+im`2 rBi? ;Hbb +QK#b- +QmTHBM; D2HH Q` 2p2M T2`KM2MiHv #QM/2/ B7 +Qbib HHQrX rB/2 `M;2 Q7 KQ/mH2b `2 pBH#H2 r?B+? `2 M BKTQìMi Tì Q7 mHi`bQMB+ L.h bvbi2Kb- b22 };m`2 kXeX

6B;m`2 kXe, aT2+BHBb2/ mHi`bQMB+ i`Mb/m+2` T`Q#2b (kd)X

SB2xQ2H2i`B+ i`Mb/m+2`b `2 Q7 ;`2i BMi2`2bi /m2 iQ i?2B` bKHH bBx2- #BHBiv iQ b2Mb2 M/ +imi2 rB/2 `M;2 Q7 bB;MHb 7`QK m/B#H2 iQ mHi`bQMB+b- HQr +Qbi M/ TQr2` +QMbmKTiBQMX SB2xQ2H2+i`B+ Ki2`BH +M ;2M2ì2 M 2H2+i`B+ }2H/ r?2M bm#D2+i2/ iQ K2+?MB+H bi`BMX h?2 /BTQH2 KQK2Mib `2Q`B2Mii2 mM/2` K2+?MB+H HQ/BM;- BM/m+BM; bm`7+2 +?`;2 /2MbBiv BM r?i Bb FMQrM b i?2 /B`2+i TB2xQ2H2+i`B+ 2z2+iX h?Bb Bb 2tTHQBi2/ 7Q` b2MbBM; bi`BM M/ HbQ ?b TTHB+iBQMb BM 2M2`;v ?`p2biBM; (k3- kN)X aBKBH`Hv jk

kXj, a2MbQ` M/ +imiQ`b BM i?2 BMp2`b2 2z2+i- pQHi;2 BMTmi ;2M2ì2b K2+?MB+H bi`BM rBi?BM i?2 Ki2`BH HHQrBM; Bi iQ +i b M +imiQ`X AM i?2 7QHHQrBM; b2+iBQM SB2xQ2H2i`B+ i`Mb/m+2`b `2 /2b+`B#2/ BM i?`22 bm#@+i2;Q`B2b, SQHvK2` SB2xQ2H2i`B+- THBM G2/ wB`+QMi2 hBiMi2 USwhV Ti+?2b M/ Swh Hv2`bX

kXjXR

SQHvK2` M/ *QKTQbBi2 Si+?2b

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AM i?Bb BKTH2K2MiiBQM k9 i`Mb/m+2`b r2`2 mb2/ QM 8yy t 8yy KK THi2 h?2 /2Hv@M/@bmK K2i?Q/ (Rd) mb2b #b2HBM2 +QKT`BbQM M/ i?2 iBK2 Q7 ~B;?i iQ T`Q/m+2 M BK;2 ?B;?HB;?iBM; i?2 HQ+iBQM Q7 /K;2- b22 };m`2 kXRjX h?Bb K2i?Q/ Bb mb2/ 2ti2MbBp2Hv BM i?Bb i?2bBbX h?2 +m``2Mi bB;MH Cij [t] Bb bm#i`+i2/ 7`QK i?2 T`BbiBM2 #b2HBM2 bB;MH Bij [t]- 7Q` HH N b2MbQ`b M/ +imiQ`b Ui, j = 1, 2, ..., N VX h?Bb ;Bp2b `2bB/mH bB;MH Rij [t]- +QMiBMBM; rp2 72im`2b /m2 iQ i?2 +m``2Mi bii2 QMHv- 2X;X /K;2, UkXR9V Rij [t] = Cij [t] ≠ Bij [t]. h?2 2Mp2HQT2 Eij [t] Q7 i?2 `2bB/mH bB;MH Bb i?2M 7QmM/ b i?2 K;MBim/2 Q7 i?2 MHviB+H bB;MH, UkXR8V Eij [t] = |Rij [t] + iH(Rij [t])| r?2`2 H Bb i?2 >BH#2ì i`Mb7Q`K (8k)X lbBM; i?2 ;`QmT rp2 T`QT;iBQM p2HQ+Biv Cg - i 2+? TQBMi x = (x, y) QM i?2 bi`m+im`2 i?2 iBK2 Q7 ~B;?i Bb +H+mHi2/ 7Q` jN


UV

U#V

6B;m`2 kXRk, GQ+HBbBM; M/ bBxBM; /K;2 mbBM; +QMp2t ?mHH Q7 hP6 HQ+BX /Ti2/ 7`QK (8R)X

;Bp2M i`Mb/m+2` Ti? ij T OFij (x) = (|x ≠ xi | + |x ≠ xj |)/Cg .

UkXReV

h?2 pHm2 Q7 i?2 `2bB/mH 2Mp2HQT2 Bb 7QmM/ 7Q` 2+? BMi2``Q;iBQM TQBMi rBi? i?2 +H+mHi2/ hP6X A7 /K;2 Bb T`2b2Mi i i?i TQBMi- i?2 +Q``2bTQM/BM; `2bB/mH K;MBim/2 rBHH #2 ?B;?2` +QKT`2/ iQ TQBMi rBi? MQ /K;2X h?2 `2+Q`/2/ pHm2b 7Q` HH BMi2``Q;iBQM TQBMib 7`QK 2+? i`Mb/m+2` Ti?b `2 i?2M 7mb2/ iQ 7Q`K k. BK;2 I(x, y) r?B+? ?B;?HB;?ib i?2 KQbi T`Q##H2 HQ+iBQM Q7 /K;2- b22 UkXRdVX I(x) =

N ÿ

N ÿ

i=1 j=1,j”=i

Eij (T OFij (x)).

UkXRdV

9y


Baseline signals for each transducer path 𝒊𝒋

Baseline Signal

Difference envelope containing damage features 𝑬𝒊𝒋

-

TOF

Current signals for each transducer path 𝒊𝒋

Damage

x TOF

Fuse transducer data 𝑵𝒂𝒄𝒕 𝑵𝒔𝒆𝒏𝒔

𝑬𝒊𝒋 [𝑻𝑶𝑭]

𝑰 𝒙, 𝒚 = 𝒋=𝟏 𝒊=𝟏 𝒊≠𝒋

x

6B;m`2 kXRj, PmiHBM2 Q7 i?2 /2Hv M/ bmK K2i?Q/X

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9R


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kX9, .K;2 .2i2+iBQM M/ GQ+HBbiBQM /B`2+iBQMH GK# rp2 T`QT;iBQMX

kX9Xj

LQM@HBM2` J2i?Q/b

h?2b2 K2i?Q/b /2i2+i /K;2 b MQM@HBM2` b+ii2`b Q7 Qi?2`rBb2 HBM2` rp2 T`QT@ ;iBQM- M/ `2 /pMi;2Qmb b `272`2M+2 #b2HBM2b `2 MQi ivTB+HHv `2[mB`2/X LQM@ HBM2` 72im`2b +M #2 BbQHi2/ #v b+HBM;- iBK2 `2p2`bBM; Q` bmKKBM; ;mB/2/ rp2 bB;MHb (8NĜeR)X h?2 iBK2 `2p2`bH K2i?Q/ mb2b TBi+?@+i+? b2MbQ` +QM};mìBQM BM irQ bi2T +imiBQM M/ b2MbBM; T`Q+2bbX 6B`bi- ivTB+H TBi+?@+i+? bB;MHb `2 `2+Q`/2/X h?2M i?2 `2+Q`/2/ bB;MH Bb iBK2 `2p2`b2/ M/ TTHB2/ b i?2 +imiBQM bB;MH BM `2p2`bH Q7 `QH2b #v i?2 Q`B;BMH i`Mb/m+2` TB`- b22 };m`2 kXR9X h?2 i`Mb/m+2` +iBM; b i?2 b2MbQ` BM i?2 }`bi BMbiMi +M #2 i?Qm;?i Q7 b bB;MH KB``Q`X S`F 2i HX (ey) mb2/ iBK2 `2p2`b2/ iQ /2i2+i /K;2 2z2+i2/ Ti?b #v +QMb2+miBp2 QmiHB2` MHvbBbX *B 2i HX (ek) mb2/ pBìmH iBK2 `2p2`bH K2i?Q/- `2@ [mB`BM; #b2HBM2 BMTmi- iQ HQ+HBb2 /K;2 rBi? ?B;? bTiBH `2bQHmiBQMX CmM M/ G22 (ej) mb2/ ?v#`B/ iBK2 `2p2`bH K2i?Q/ iQ HQ+HBb2 //2/ Kbb QM THi2X _2+2MiHv M 2M?M+2/ /K;2 BM/2t U.AV ?b #22M mb2/ iQ }M/ /K;2/ Ti?b (e9)- M/ iBK2 `2p2`bH rb mb2/ iQ /2i2+i bBKmHi2/ TBT2HBM2 +Q``QbBQM TBi (9e)X

6B;m`2 kXR9, a+?2KiB+ QmiHBM2 Q7 i?2 iBK2 `2p2`bH TT`Q+?- /Ti2/ 7`QK (ej)X

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9j


6B;m`2 kXR8, .2i2+iBM; i`Mb/m+2` /Bb@#QM/BM; i?`Qm;? i?2 TT2`M+2 T2Fb bbQ+Bi2 iQ 7`22 `2bQMM+2 (e3)X

kX9X9

1H2+i`Q@J2+?MB+H AKT2/M+2 U1JAV

h?2 2H2+i`B+H BKT2/M+2 Q7 TB2xQ2H2+i`B+ i`Mb/m+2` Bb +QmTH2/ iQ Bib K2+?MB+H `2bTQMb2X h?2 ?B;?Hv +QmTH2/ Mim`2 HHQrb i?2 K2+?MB+H bii2 iQ #2 BMi2`T`2i2/ i?Q`Qm;? MHvbBb Q7 i?2 2H2+i`B+H BKT2/M+2 T`Q}H2X 6`QK 2ti2MbBQM Q7 P?KǶb Hr iQ bvbi2K rBi? * BMTmi i 7`2[m2M+v Ê- BKT2/M+2 Z Bb ;Bp2M b, V (Ê) Z(Ê) = = R + iX(Ê) UkXR3V I(Ê) r?2`2 V M/ I `2 i?2 pQHi;2 M/ +m``2Mi- R M/ X `2 i?2 `2H M/ BK;BM`v Tì Q7 BKT2/M+2X /KBiiM+2 Bb ;Bp2M b i?2 BMp2`b2 Q7 BKT2/M+2 M/ /KBiiM+2X "v MHvbBM; i?2 /KBiiM+2 T`Q}H2 Bi Bb TQbbB#H2 iQ }M/ i?2 `2bQMi2 7`2[m2M+B2b Q7 TB2xQ2H2+i`B+ Ti+?X q?2M i`Mb/m+2`b `2 #QM/2/ iQ ?Qbi bi`m+im`2- i?2 Ti+?Ƕb K2+?MB+H M/ ?2M+2 i?2 2H2+i`B+H BKT2/M+2 T`Q}H2 Bb Hi2`2/X h?Bb ?b #22M 2tTHQBi2/ iQ /B;MQb2 i?2 i`Mb/m+2` #QM/BM; bii2 (ee)- HHQrBM; B/2MiB}+iBQM Q7 /Bb@#QM/BM; rBi? i?2 2K2`;2M+2 Q7 `2bQMMi T2Fb bbQ+Bi2/ iQ 7`22 i`Mb/m+2`bb22 };m`2 kXR8X h?2 H2p2H Q7 /Bb@#QM/BM; +M HbQ #2 [mMiB}2/ #v +QKT`BM; i?2 BKT2/M+2 T`Q}H2 (ed)X AM //BiBQM iQ /2i2`KBMBM; i?2 #QM/BM; bii2- 1JA +M HbQ B/2MiB7v /K;2 BM i?2 ?Qbi bi`m+im`2X h?i Bb i?2 T`BbiBM2 1JA `2bTQMb2 +M #2 +QKT`2/ iQ i?2 /K;2 bii2 iQ B/2MiB7v i?2 T`2b2M+2 Q7 /K;2X 1JA ?b #22M mb2/ iQ /2i2+i /K;2 BM B`+`7i bi`m+im`2b (eN)X >Qr2p2` i?2b2 K2i?Q/b `2 MQi 2z2+iBp2 7Q` B/2MiB7vBM; 7`@ }2H/ /K;2bX h?Bb HQM; `M;2 BMb2MbBiBpBiv @ Q` ì?2` b2MbBiBpBiv HBKBi2/ iQ +HQb2 99

kX9, .K;2 .2i2+iBQM M/ GQ+HBbiBQM T`QtBKBiv @ HHQrb 1JA iQ ;Bp2 `Qm;? Q` BMBiBH 2biBKi2 Q7 /K;2 HQ+iBQM #v B/2MiB7vBM; i`Mb/m+2`b 2z2+i2/ #v /K;2 (dy)X JmHiB@H2p2H /2+BbBQM 7mbBQM +M ;Bp2 ?B;? bT+BH ++m`+v /K;2 HQ+HBbiBQM BM +QKTQbBi2 B`+`7i +QKTQM2Mib (R3)X

kX9X8

Pi?2` J2i?Q/b

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UV

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6B;m`2 kXRe, hQKQ;`T?B+ K2i?Q/ Q7 HQ+HBbBM; /K;2 mbBM; M2r mHi`bQMB+ 1Jhb (d8)X

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amKK`v

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kX8, amKK`v

h#H2 kXk, amKK`v Q7 /2i2+iBQM K2i?Q/b /Bb+mbb2/ BM i?2bBbX

J2i?Q/

ai`2M;i?

+QmbiB+ 2KBbbBQMb

#H2 iQ HQ+HBb2 /K;2 BM H`;2 `2b- 2p2M QM +QKTH2t ;2QK2i`B2bX

S?b2/ ``v

AMi2``Q;i2 H`;2 `2X GQr MmK#2` Q7 i`Mb/m+2`b `2[mB`2/X

LQM@GBM2` J2i?Q/b

*M #2 #b2HBM2 7`22X .2i2+i /K;2 T`2b2M+2 BM H`;2 BMi2``Q;iBQM `2

1JA aT`b2 ``v .K;2 AK;BM;

a2H7@BMi2``Q;iBQM 7Q` /2i2+iBM; 7mHiv i`Mb/m+2`bX :QQ/ /2i2+iBQM +HQb2 iQ i`Mb/m+2` pB+BMBiv AMi2``Q;i2 H`;2 `2b M/ +QKTH2t ;2QK2i`B2bX LQ "HBM/ bTQibX :QQ/ bT+BH `2bQHmiBQMX

q2FM2bb S`QM2 iQ 2MpB`QMK2MiH +QMiKBMiBQMbX .K;2 2p2Mi Kmbi #2 +Tim`2/X _M;2 Bb HBKBi2/ #v Ki2`BH /KTBM;X "HBM/ bTQi +HQb2 iQ i`Mb/m+2` ``vX _2[mB`2b #b2HBM2X .B{+mHiv BMi2``Q;iBM; +QKTH2t ;2QK2i`B2bX Jv `2[mB`2 H`;2 MmK#2` Q7 i`Mb/m+2`b iQ HQ+HBb2 /K;2X .B{+mHiv BMi2``Q;iBM; +QKTH2t b?T2bX a?Qì BMi2``Q;iBQM `;2 7Q` 2+? i`Mb/m+2`X GQr bT+BH `2bQHmiBQMX HKQbi Hrvb `2[mB`2b #b2HBM2X

9d

*?Ti2` h>_11

h`Mb/m+2` AMi2;`Biv jXR

AMi`Q/m+iBQM

GK# rp2 T`QT;iBQM mb2/ 7Q` a>J /K;2 /2i2+iBQM Bb b2MbBiBp2 iQ i?2 bi`m+@ im`2Ƕb Ki2`BH M/ ;2QK2i`B+ T`QT2ìB2b (3R)X h?Bb Bb 2tTHQBi2/ iQ /2i2+i2/ bi`m+@ im`H /K;2 M/ ~rb (Rd- RN)X qp2 T`QT;iBQM +M #2 p`B2/ #v 2MpB`QMK2MiH +QM/BiBQMb- 7Q` BMbiM+2 BM+`2b2/ p2HQ+Biv i `2/m+2/ i2KT2ìm`2X JQ`2 BKTQ`@ iMiHv- +2ìBM +QM/BiBQMb +M +mb2 B``2p2`bB#H2 +?M;2b BM i?2 a>J bvbi2K Bib2H7X 6Q` BMbiM+2 TB2xQ2H2+i`B+ i`Mb/m+2`b +M #2 /2@TQH`Bb2/ r?2M 2tTQb2/ iQ BMi2Mb2 2H2+i`B+ }2H/b Q` i2KT2ìm`2b #2vQM/ i?2 *m`B2 i2KT2ìm`2X h?Bb +?Ti2` BMp2biB@ ;i2b BMi2;`Biv M/ `Q#mbiM2bb Q7 B`#Q`M2 +QKTQM2Mib mb2/ BM ;mB/2/ rp2 a>JX h?2 2MpB`QMK2MiH i2bi T`Q}H2b `2 b2H2+i2/ #b2/ QM B`+`7i 2tT2+i2/ QT2ìBM; +QM/BiBQMb M/ i?2 T2`7Q`KM+2 bb2bb2/ #b2/ QM Tbbf7BH +`Bi2`BQMX

jXk

"+F;`QmM/

Ai Bb BKTQìMi iQ `2+Q;MBb2 i?i M a>J bvbi2K Bb +QKT`Bb2/ Q7 ;`QmM/ #b2/ +QKTQM2Mib- B`#Q`M2 +QKTQM2Mib M/ +QKTQM2Mib i?i Kv #2 B`#Q`M2 Q` ;`QmM/ #b2/ /2T2M/BM; QM i?2 ivT2 Q7 a>J bvbi2K b b?QrM BM };m`2 jXRX a>J +Qp2`b 93

jXk, "+F;`QmM/ rB/2 `M;2 Q7 TT`Q+?2b 2KTHQvBM; p`BQmb b2MbQ`- +imiQ`- bB;MH ;2M2ìQ` M/ /B;BiBx2` ivT2bX h?2 AMi2`MiBQMH JBMi2MM+2 _2pB2r "Q`/ SQHB+v "Q`/ UAJ_"S"V (3k) b2i Qmi /2}MBiBQMb 7Q` a+?2/mH2/@a>J- (3j) K/2 7mì?2` //BiBQMb rBi? miQKi2/@a>J /2}M2/ BM ;2M2`H i2`KbX h?2 /BbiBM+iBQM #2BM; @a>J Bb Mv a>J i2+?MQHQ;v rBi?Qmi T`2@/2i2`KBM2/ BMi2`pH 7Q` bi`m+im`2 KBMi2MM+2 +iBQMb- BMbi2/ `2HvBM; QM i?2 bvbi2K iQ BM7Q`K r?2M +iBQM Kmbi iF2 TH+2X q?BH2 MQ b2i 7`K2rQ`F 2tBbi 7Q` +2ìB}+iBQM M/ i2biBM; Q7 a>J bvbi2Kb- 6 `2+QK@ K2M/iBQMb (39- 38) M/ 2tBbiBM; biM/`/b (38) +M T`QpB/2 7QmM/iBQMX

Airborne Components Sensor Transducer

Connection Network

Actuator

Ground-Based Components Ground database

Ground Station

Airborne or Ground-Based Components Power Components

Signal Conditioning

Signal Processing

Communication

Data stores and Interface devices

6B;m`2 jXR, a>J +QKTQM2Mib- /Ti2/ 7`QK (38)X

a1 AMi2`MiBQMH 1Se9eR (38) K/2 `272`2M+2b iQ i`Mb/m+2` M/ +QMM2+iBQM M2i@ rQ`F BMi2;`Biv bb2bbK2Mib i?`Qm;? _h*f.P@Rey 1MpB`QMK2MiH *QM/BiBQMb M/ h2bi S`Q+2/m`2b 7Q` B`#Q`M2 1[mBTK2Mi M/ JAG@ah. 3Ry i2bi T`Q+2/m`2b (3e- 3d)X AM i?Bb rQ`F Bi Bb bbmK2/ i`Mb/m+2`b M/ i?2 +QMM2+iBQM M2irQ`F `2 T2`KM2MiHv ii+?2/ iQ ?Qbi bi`m+im`2- i?2v rBHH #2+QK2 B`#Q`M2 i bQK2 Tì Q7 i?2B` QT@ 2ìBQMH HB72X Ai Bb bbmK2/ i?i a@a>J rQmH/ i?2M #2 T2`7Q`K2/ QM i?2 ;`QmM/X bb2bbBM; i?2 T2`7Q`KM+2 Q7 M @a>J bvbi2K r?BH2 B`#Q`M2 Bb MQi i?2 7Q+mb Q7 i?Bb +?Ti2`X Ai Bb bbmK2/ i?i rBi? bm`7+2 KQmMi2/ /2pB+2b i?2 ?Qbi +M T2`7Q`K bi`m+im`HHv b /2bB;M2/X h?Bb Bb 2Mbm`2/ #v mbBM; M /?2bBp2 i?i Bb H`2/v mb2/ BM 2`QbT+2 U_2/mt }HK /?2bBp2 bmTTHB2/ #v >2t+2HV- i?2 mb2 Q7 r?B+? /Q2b MQi /2;`/2 i?2 ?QbiǶb T`QT2ìB2bX *QKTQM2Mib BMp2biB;i2/ `2 MQi 2K#2//2/ rBi?BM i?2 Ki2`BH Q` +Q@+m`2/ r?B+? +M H2/ iQ }#`2 mM/mHiBQM (33)X h?Bb +?Ti2` BMp2biB;i2b BMi2;`Biv M/ `Q#mbiM2bb `2[mB`2K2Mib 7Q` T2`KM2MiHv ii+?2/ +QKTQM2Mib 7Q` #b2HBM2 +QKT`BbQM ;mB/2/ rp2 a>JX aT2+B}+HHv i?2 9N

jXk, "+F;`QmM/ BMi2;`Biv Q7 i?2 i`Mb/m+2`b M/ i?2 +QMM2+iBQM M2irQ`F Bb bb2bb2/ 7Q` .m`+i.m`+i rBi? E2pH` +QiBM;- aKì Gv2` M/ KMm7+im`2/ a>J Hv2`X h?2 7QHHQrBM; bbmKTiBQMb #Qmi i?2 B`+`7i rBHH b2`p2 b F2v 7+iQ`b BM /2i2`KBMBM; i?2 QT2ìBQM 2MpB`QMK2Mi M/ ?2M+2 i?2 `2[mB`2/ i2bi T`Q}H2, Ç 6Bt2/ rBM; bm#bQMB+ Ç hm`#Q7M T`QTmHbBQM Ç JtBKmK QT2ìBM; HiBim/2 Q7 8y-yyy 7i Ç _2;BQMH B`+`7i QT2ìBM; BM 1m`QT2

AM //BiBQM Bi rBHH #2 bbmK2/ i?i i`Mb/m+2`b M/ +QMM2+iBQM M2irQ`F rBHH #2, Ç AMi2`MHHv KQmMi2/ Ç AM MQM@i2KT2ìm`2 +QMi`QHH2/ `2 Ç AM MQM@T`2bbm`2 +QMi`QHH2/ `2 Ai Bb MQi 2MpBb;2/ i?i i`Mb/m+2`b rBHH #2 KQmMi2/ 2ti2`MHHv b i?Bb +QmH/ BMi`Q@ /m+2 //BiBQMH +?HH2M;2b BM i2`Kb Q7 i?2 +QMM2+iBQM M2irQ`F M/ rB`BM;X h?2b2 rBHH ?p2 /p2`b2 BMi2`+iBQM 2z2+ib rBi? i?2 ~Qr `QmM/ i?2 B`+`7iX

jXkXR

S`2HBKBM`v h2bib

AM i?Bb b2+iBQM- T`2HBKBM`v i2bib `2 T`2b2Mi2/ +QKT`BM; irQ /Bz2`2Mi ivT2b Q7 /@ ?2bBp2b mb2/ 7Q` i`Mb/m+2` #QM/BM;X *vMQ+`vHi2 U*V /?2bBp2 ?b #22M mb2/ 7Q` i`Mb/m+2` #QM/BM; #v KMv `2b2`+?2`b 7Q` a>J TTHB+iBQMb (k3- 8k- 8j)X >Qr2p2ì?2 T2`7Q`KM+2 Q7 i?Bb ivT2 Q7 #QM/BM; Bb [m2biBQM#H2- 2bT2+BHHv mM/2` +?M;BM; 2MpB`QMK2MiH +QM/BiBQMX 6BHK /?2bBp2b i?i `2 +m``2MiHv mb2/ 7Q` 2`QbT+2 TTHB@ +iBQMb `2 bmBi#H2 Hi2`MiBp2X h?Bb b2+iBQM BMp2biB;i2b i?2 i2KT2ìm`2 bi#BHBiv Q7 * /?2bBp2 +QKT`2/ iQ >2t+2H _2/mt jRk }HK /?2bBp2X aT2+B}+HHv `2T2i@ #BHBiv Q7 rp2 T`QT;iBQM ;2M2ì2/ rBi? i`Mb/m+2`b #QM/2/ mbBM; i?2b2 /?2bBp2b `2 bb2bb2/X

8y

jXk, "+F;`QmM/ jXkXRXR S`2HBKBM`v h2bi a2i@mT hrQ bKTH2b r2`2 T`2T`2/ #v #QM/BM; /BbF b?T2/ Swhb Ti+?2b URtRyKKV iQ *6_S ?Qbi THi2X h?2 Ti+? /BK2i2` Bb BMp2`b2Hv T`QTQìBQMH iQ i?2 `2bQMM+2 7`2[m2M+v (3N)X R +K /BK2i2` Ti+? rb 7QmM/ iQ ?p2 `2bQMM+2 7`2[m2M+v i `QmM/ jyy F>x- ?2M+2 ;QQ/ +?QB+2 7Q` /K;2 /2i2+iBQM BM i?Bb 7`2[m2M+v `M;2X bKHH2` /BK2i2` Ti+? rQmH/ ?p2 ?/ ?B;?2` `2bQMi2 7`2[m2M+v ?2M+2 /2i2`BQì2/ bB;MH KTHBim/2 BM i?2 7`2[m2M+v `M;2 mT iQ jyy F>x- r?B+? Bb ivTB+HHv mb2/ 7Q` ;mB/2/ rp2 /2i2+iBQMX h?2 ?Qbi THi2b r2`2 +mi 7`QK i?2 bK2 *6_S HKBMi2 rBi? HvmT (y-98-@98-Ny)2s >2tTHv NR9@ha@8@Rj9 THB2b rBi? i?B+FM2bb kKKX h?2 irQ bKTH2b r2`2 B/2MiB+H Tì 7`QK i?2 /?2bBp2 mb2/- GQ+iBi2 * /?2bBp2 Q` >2t+2H _2/mt jRk- b22 };m`2 jXkX

#

5

10

22.5 cm

5

5

11.25

+ 6B;m`2 jXk, S`2HBKBM`v bKTH2- UV _2/mt U#V *vMQ+`vHi2 /?2bBp2X "Qi? bKTH2 ?p2 B/2MiB+H ;2QK2i`v b+?2KiB+ U+VX

h?2 bKTH2b r2`2 bm#D2+i2/ iQ +v+HB+ +?M;2 BM i2KT2ìm`2 M/ i?2 i`Mb/m+2` bB;MHb `2+Q`/2/ i i?2 2M/ Q7 2+? +v+H2- b22 };m`2 jXjX h?2 i2KT2ìm`2 `M;2 8R

jXk, "+F;`QmM/ rb b2i i @jd iQ 38 ê*- i?Bb 2t+22/2/ i?2 QT2ìBM; ?B;? i2KT2ìm`2 Q7 i?2 _h* .y@Rey (3e) QT2ìBQM `2[mB`2K2Mib- #mi rb HBKBi2/ #v i?2 KBMBKmK i2KT2ìm`2 Q7 i?2 i2bi +?K#2` mb2/ U1*P h*G Rj8VX h?2 THi2b r2`2 +v+H2/ Ry iBK2b M/ bB;MHb r2`2 `2+Q`/2/ 7i2` 2+? +v+H2 r?2M i?2 i2KT2ìm`2 ?/ bi#BHBb2/ i kj ê*X hQ p2`B7v i?i T?b2 i`MbBiBQMb r2`2 MQi iFBM; TH+2 rBi?BM i?2 /?2bBp2- bK@ TH2b r2`2 i2bi2/ rBi? /Bz2`2MiBH b+MMBM; +HQ`BK2i2` U.a*VX h?2b2 i2bib r2`2 T2`7Q`K2/ QM +m`2/ _2/mt mbBM; h .Bb+Qp2`v .a* K+?BM2X LQM@?2`K2iB+HHv b2H2/ HmKBMBmK TQib r2`2 mb2/ b i?2 /?2bBp2 Bb FMQrM iQ #2 MQM@pQHiBH2 BM i?2 i2bi i2KT2ìm`2b `M;2X .vMKB+ K2+?MB+H i?2`KH MHvbBb U.JhV +QmH/ HbQ ?p2 #22M T2`7Q`K2/- i?Bb rQmH/ ?p2 HbQ T`QpB/2/ /KTBM; T`K2i2`b iQ #2 mb2/ BM MmK2`B+H bBKmHiBQMbX >Qr2p2`- i?2 Q#D2+iBp2 Q7 i?Bb b2+iBQM rb iQ p2`B7v i?2 bmBi#BHBiv Q7 i?2 b2i@mT- M/ i?2 `Q#mbiM2bb iQ i2KT2ìm`2X

Temperature (oC)

80 Sample Temperature Recording

60 40 20 0 −20 −40

0

2

4

6

8 10 Time minutes

12

14

16 4

x 10

6B;m`2 jXj, /?2bBp2 BMp2biB;iBQM bKTH2 i2KT2ìm`2b rBi? bB;MHb `2+Q`/2/ i kj ê*X

jXkXRXk S`2HBKBM`v _2bmHib M/ *QM+HmbBQMb h?2 bB;MH `2+Q`/2/ 7i2` i?2 Hbi i2KT2ìm`2 +v+H2 UHbi /i b2iV rb +QKT`2/ iQ i?2 bB;MH `2+Q`/2/ 7i2` i?2 }`bi i2KT2ìm`2 +v+H2 U}`bi /i b2iV mbBM; i?2 MQ`KHBb2/ T`K2i2` H2p2H QmiHBM2/ BM b2+iBQM jXjX8X HQr2` pHm2 Q7 MQ`KHBb2/ T`K2i2` BM/B+i2b `2/m+2/ `2bB/mH H2p2H #2ir22M i?2 irQ /i b2ib #2BM; +QK@ T`2/- ?2M+2 ?B;?2` T`K2i2` rQmH/ BM/B+i2 bB;MB}+Mi +?M;2b BM i?2 bi`m+im`2X AM i?Bb +b2 Mv +?M;2b `2 bbQ+Bi2/ iQ i?2 #QM/BM; Hv2`X aB;MHb `2+Q`/2/ 7i2` bm#b2[m2Mi ?2iBM; +v+H2b `2 +QKT`2/ iQ i?2 Hbi /i b2iX Ai +M #2 Q#b2`p2/ i?i i kyy F>x i?2 _2/mt }HK /?2bBp2 ?b #2ii2` i2KT2ìm`2 bi#BHBiv +QKT`2/ iQ i?2 *vMQ+`vHi2 ;Hm2- b22 };m`2 jX9X 6Q` i?2 _2/mt /?2bBp2 8k

jXk, "+F;`QmM/

2

2

1

1

Amplitude \v

Amplitude /v

i?2 KTHBim/2 Q7 i?2 }`bi M/ b2+QM/ rp2 T+F2ib r2`2 bi#H2 7i2` i?2 i2KT2`@ im`2 +v+H2b- rBi? KBMQ` +?M;2b BM i?2 7QHHQrBM; rp2 T+F2ibX >Qr2p2`- 7Q` i?2 *vMQ+`vHi2 ;Hm2 i?2`2 Bb bKHH KTHBim/2 /Bb+`2TM+v BM i?2 }`bi rp2 T+F2i#mi i?2 `2bi Q7 i?2 rp27Q`K Bb bB;MB}+MiHv Hi2`2/ 7i2` i2KT2ìm`2 +v+HBM;X

0 −1

0 −1

First Set −2

Last Set 0

1 Time /s

UV

−2 2 −4

x 10

0

1 Time \s

2 −4

x 10

U#V

6B;m`2 jX9, aKTH2 GK# rp2 `2bTQMb2 i kyy F>x #27Q`2 7i2` 2tTQbm`2 iQ ?2iBM; +v+H2X UV *vMQ+`vHi2 M/ U#V _2/mt /?2bBp2X

h?2 rp27Q`K /Bb+`2TM+v +mb2/ #v i2KT2ìm`2 +v+HBM; rb HbQ T2`bBbi2Mi Qp2` i?2 ivTB+H `M;2 Q7 +imiBQM 7`2[m2M+B2b mb2/ 7Q` ;mB/2/ rp2 a>J- b b?QrM #v i?2 `2bB/mH H2p2Hb BM };m`2 jX8X h?Bb Bb ?B;?HB;?i2/ #v THQiiBM; i?2 KtBKmK `2bB/mH #2ir22M 2+? /i b2i M/ i?2 }MH /i b2i b T2`+2Mi;2 Q7 i?2 bB;MH KTHBim/2X h?2 `2bB/mH 7Q` i?2 _2/mt /?2bBp2 bi#BHBb2/ iQ #2HQr RyW 7Q` HH 7`2[m2M+B2b 7i2` d +v+H2b r?BH2 i?2 *vMQ+`vHi2 /B/ MQi bi#BHBb2 iQ i?Bb H2p2H 2p2M 7i2` Ry +v+H2bX h?2 `2bB/mH #2ir22M i?2 Ryi? `2+Q`/BM; M/ i?2 }MH b2i rb #Qp2 ky W 7Q` 7`2[m2M+B2b #2ir22M kyy M/ jyy F>xX Ai Bb `2+Q;MBb2/ i?i ?2iBM; *6_S THi2b `2/m+2b i?2B` KQBbim`2 +QMi2MiX >Qr2p2ì?Bb +QmH/ MQi ++QmMi 7Q` i?2 ?B;? H2p2H Q7 `2bB/mH BM i?2 *vMQ+`vHi2 bKTH2 +QKT`2/ iQ i?2 _2/mt bKTH2 b i?2 *6_S ?Qbi 7Q` #Qi? bKTH2b r2`2 B/2MiB+HX h?2 MQ`KHBb2/ ?2i ~Qr BM irQ bKTH2b Q7 +m`2/ _2/mt /?2bBp2- b?Qr i?i #2ir22M @88 M/ Ryy * i?2`2 rb MQ bB;MB}+Mi +?M;2 Q` i`MbBiBQMX 7i2` Ryy ê* i?2`2 rb M 2M/Qi?2`KB+ /`QT rBi? KBMBKmK TQBMi i RReX9 M/ RRdX3 ê*X h?Bb +Q``2bTQM/2/ iQ i?2 Rky ê* `2+QKK2M/2/ +m`BM; i2KT2ìm`2 7Q` `2/mt /?2bBp2X >Qr2p2` i?2`2 rb MQ b?`T i`MbBiBQM bbQ+Bi2/ rBi? K2HiBM; TQBMi b i?2 i?2`KQb2i `2/mt bKTH2b r2`2 H`2/v +m`2/X Ai +M #2 +QM+Hm/2/ i?i BM 2ti`2K2 i2KT2ìm`2 ~m+imiBQMb 8j

jXj, 1MpB`QMK2MiH h2biBM; S`Q}H2b 30 Normalised Residual (% of first arrivals)

Normalised Residual (% of first arrivals)

50 50 kHz 100 kHz 150 kHz 200 kHz 250 kHz 300 kHz

40

30

20

10

0

1

2

3

4

5 6 Record Index

7

8

9

10

50 kHz 100 kHz 150 kHz 200 kHz 250 kHz 300 kHz

25 20 15 10 5 0

1

2

3

4

5 6 Record Index

UV

7

8

9

10

U#V

6B;m`2 jX8, aKTH2 GK# rp2 `2bB/mH 7Q` i?2 }`bi 9 ``BpHb 7i2` 2+? ?2iBM; +v+H2- UV *vMQ+`vHi2 M/ U#V _2/mt /?2bBp2X

`2/mt }HK /?2bBp2 Bb KQ`2 bmBi#H2 7Q` i`Mb/m+2` ii+?K2Mi i?M *vMQ+`vHi2X JQ`2Qp2` `2/mt /?2bBp2 /Q2b MQi /BbTHv i`MbBiBQM BM i?2 i2KT2ìm`2 @88 M/ Ryy *X

6B;m`2 jXe, >2i ~Qr@i2KT2ìm`2 THQi 7Q` irQ bKTH2b Q7 +m`2/ _2/mt /?2bBp2X

jXj

1MpB`QMK2MiH h2biBM; S`Q}H2b

1+? Q7 i?2 bKTH2b rBi? /Bz2`2Mi i`Mb/m+2` ivT2b r2`2 bm#D2+i2/ iQ 2MpB`QMK2MiH T`Q}H2b ++Q`/BM; iQ i?2 _h*f.P@Rey* (3e)X h?2 2MpB`QMK2MiH i2bib T2`7Q`K2/ `2 bmKK`Bb2/ BM i#H2 jXR M/ /2b+`B#2/ BM KQ`2 /2iBH BM bm#b2+iBQMb jXjXR iQ jXjX9X

89

jXj, 1MpB`QMK2MiH h2biBM; S`Q}H2b

h#H2 jXR, 1MpB`QMK2MiH i2bi Ki`BtX aKTH2 ivT2 /2}MBiBQMb BM a2+iBQM jX9XjX

h2bi *i2;Q`v

1MpB`QMK2Mi

*2ìB}+iBQM *i2;Q`v

aKTH2b hvT2b

GQr h2KT2ìm`2 >B;? h2KT2ìm`2

≠88 ê* dy ê* ≠88 iQ dy ê* i 8 ê*/KBM 8y-yyy 7i URRXe FSV _M/QK Sa. Ry@kyyy >x

.P@Rey * 9X8XR .P@Rey * 9X8Xj

9 9

.P@Rey * 8

9

.P@Rey * 9Xe

9

.P@Rey * 3

9

h?2`KH a?Q+F HiBim/2 oB#ìBQM

h?2 i2bi T`Q}H2 BMBiBH +QM/BiBQMb `2 T`2b+`B#2/ b MQ`KH K#B2Mi +QM/BiBQMb_h*f.P@Rey* HHQrb rB/2 K`;BM 7Q` K#B2Mi +QM/BiBQMb, Ç h2KT2ìm`2, k8 ± Ryê*Ç >mKB/Biv, Ç S`2bbm`2, 39 iQ Ryd FSX q?BH2 i?2 bKTH2b `2 2tTQb2/ iQ i?2 i2bi T`Q}H2b- +QM/BiBQMb +M #2 rBi?BM `M;2 Q7 i?2 i`;2i T`Q}H2 pHm2b, Ç S`2bbm`2, ± 8WÇ h2KT2ìm`2, ± j ê*Ç oB#ìBQM, Ĝ #Qp2 8yy F>x ± j /"-

Ĝ "2HQr 8yy F>x @ RX8 Y j /"X Ai b?QmH/ #2 MQi2/ i?i i2bi +QmH/ ?p2 #22M BMi2``mTi2/ i?2M `2bmK2/ i i?2 bK2 b2;K2Mi- #mi i?Bb rb MQi `2[mB`2/X

jXjXR

GQr M/ h2KT2ìm`2

JAG@ah. R3y: (3d) ;Bp2b HQr i2KT2ìm`2 BM KQbi Q7 1m`QT2 b Ƕ"bB+ +QH/ *RǶ- rBi? /BHv B` i2KT2ìm`2 `M;BM; #2ir22M @jk iQ @kR ê*- U@jj iQ @k8 ê* BM/m+2/VX Sìb 88

jXj, 1MpB`QMK2MiH h2biBM; S`Q}H2b Q7 MQì?2`M 1m`QT2 `2 +HbbB}2/ b Ƕ*QH/ *kǶ r?2`2 BM/m+2/ i2KT2ìm`2b `M;2 #2ir22M @9e M/ @jd ê*X Ai b?QmH/ #2 K2MiBQM2/ i?i i?2 2ti`2K2 HQr i2KT2ìm`2 BM 1m`QT2 Bb ;Bp2M b @88 ê* BM _mbbB Q++m``BM; BM R8 v2` T2`BQ/ (3d)X //BiBQMHHvi?2 _h* /2}M2b i?2 HQr i2KT2ìm`2 bm`pBpH b @88 ê*X h?2 bKTH2 i2KT2ìm`2 Kmbi #2 ?2H/ +QMbiMi 7Q` i H2bi j ?Qm`b- b22 };m`2 jXdX

23

≠55

h2KT2ìm`2 ê*

h2KT2ìm`2 ê*

JAG@ah. R3y ;Bp2b ?B;? i2KT2ìm`2 BM 1m`QT2 b Ƕ"bB+ >Qi kǶ iQ ǶAMi2`K2/Bi2 jǶ- rBi? M B` i2KT2ìm`2 Q7 jy iQ 9j ê* Ujy iQ ej ê* BM/m+2/V M/ k3 iQ jN ê* Uk3 iQ 83 ê* BM/m+2/V `2bT2+iBp2Hv (3d)X h?2 ?B;?2bi i2KT2ìm`2 2p2` `2+Q`/2/ BM 1m`QT2 Bb ;Bp2M b 88 ê* a2pBHH2- aTBM BM 9 m;mbi R33RX h?2 _h* .P@Rey (3e) b?Qì QT2ìBM; ?B;? i2KT2ìm`2 Q7 dy ê* Bb mb2/X Ai Kmbi #2 bi`2bb2/ i?i Bi Bb MQi 2MpBb;2/ 7Q` i?2b2 ivT2b Q7 a>J bvbi2Kb iQ QT2ì2 Q` #2 BMbiHH2/ BM HQ+iBQMb 2tTQb2/ iQ 2ti`2K2 i2KT2ìm`2b- 2X;X 2M;BM2 +QrHBM;- Sl ?QmbBM; Q` 2t?mbi QmiH2ibX h?2 ?B;? i2KT2ìm`2 T`Q}H2 Bb BHHmbiì2/ BM };m`2 jXd#X

0

T1 + 3 T2

T1

hBK2 >Qm`b UV

70

23

0

T1 + 3 T2

T1

hBK2 >Qm`b U#V

6B;m`2 jXd, UV GQr i2KT2ìm`2 T`Q}H2- U#V ?B;? i2KT2ìm`2 T`Q}H2X

jXjXk


*QKTQM2Mib Kv 2tT2`B2M+2 i2KT2ìm`2 p`BiBQMb /m`BM; MQ`KH QT2ìBQMX h?2b2 `2Hi2 iQ i?2 bi22T i2KT2ìm`2 ;`/B2Mi 2tT2`B2M+2/ /m`BM; iF2@Qz M/ HM/BM;X 6Q` BMi2`MHHv KQmMi2/ 2[mBTK2Mi BM MQM@i2KT2ìm`2 +QMi`QHH2/ b2+iBQMb Q7 i?2 B`+`7i `KT ì2 Q7 8 ê*fKBM Bb `2[mB`2/ #v _h*X h?Bb rBHH #2 #2ir22M i?2 ?B;? M/ HQr i2KT2ìm`2b UBM b2+iBQM jXjXRVX h?2 i2KT2ìm`2 Kmbi #2 `KT2/ #2ir22M i?2 KBMBKmK M/ KtBKmK i2KT2ìm`2b- #2ir22M i?2 KtBKmK M/ KBMBKmK M/ i?2M +v+H2/ irB+2 b b?QrM BM };m`2 jX3X

8e

jXj, 1MpB`QMK2MiH h2biBM; S`Q}H2b

h2KT2ìm`2 ê*

70 23

≠55

0

100

200 300 400 hBK2 JBMmi2b

500

6B;m`2 jX3, h?2`KH b?Q+F i2KT2ìm`2 T`Q}H2- `KT ì2 ±8 ê*fKBMX

jXjXj

HiBim/2

S`2bbm`2 FS

.m`BM; MQ`KH QT2ìBQM i?2 +QKTQM2Mib rBHH 2M+QmMi2` +?M;2b BM K#B2Mi T`2bbm`2 7`QK b2f;`QmM/ H2p2H iQ +`mBb2 H2p2HX h?Bb +QmH/ BKT+i i?2 #QM/BM;- #mi KQ`2 BKTQìMiHv T`2b2M+2 Q7 b2H2/ B` TQ+F2ib Kv +mb2 /2i2`BQìBQMb BM i?2 i`Mb/m+2` T+F;BM;X h?2 KtBKmK QT2ìBQM HiBim/2 ?b #22M b2i b 8y-yyy 722i rBi? T`2bbm`2 Q7 RRXe FS U#bQHmi2VX 6B;m`2 jXN /2TB+ib i?2 T`2bbm`2 T`Q}H2b mb2/ BM i?2 i2bibX 101

11.6

y

T1

T1 + 2 T2

hBK2 >Qm`b 6B;m`2 jXN, HiBim/2 i2bi T`Q}H2X

jXjX9

oB#ìBQM

.2T2M/BM; QM 2[mBTK2Mi HQ+iBQM _h* .P@Rey* bT2+B}2b +2ìBM pB#ìBQM `2;BK2 M/ H2p2HX 6Q` im`#QD2i UM/ im`#Q7MV bBMmbQB/H i2bib `2 `2[mB`2/ 7Q` 2M@ 8d

jXj, 1MpB`QMK2MiH h2biBM; S`Q}H2b ;BM2 HQ+iBQMb- BM //BiBQM `M/QK i2bib `2 `2[mB`2/ 7Q` HH Qi?2` HQ+iBQMbX aiM/`/ `M/QK i2bi Kmbi #2 T2`7Q`K2/ rBi? i?2 bKTH2 }tim`2 `2T`2b2MiiBp2 Q7 i?2 +@ imH QT2ìBQMH bi`m+im`2X h?2 `M/QK ++2H2ìBQM TQr2` bT2+i`H /2MbBiv USa.V `2H2pMi iQ MQ`KH B`+`7i QT2ìBQM rb +?Qb2MX

++2H2ìQBM SQr2` aT2+i`H .2MbBiv g 2 /Hz

h?2 `M/QK pB#ìBQM T`Q}H2 biì2/ i Ry F>x `BbBM; rBi? bHQT2 Q7 e /" T2` Q+ip2 mMiBH 9y F>x- i?2 T`Q}H2 rb +QMbiMi #2ir22M 9y @ 8yy F>x- 7i2` r?B+? Bi `2/m+2/ rBi? bHQT2 Q7 e /" T2` Q+ip2X h?2 pB#ìBQM T`Q}H2 QM i?2 bKTH2 rb +QMi`QHH2/ rBi? +HQb2/ 722/#+F HQQT M/ KBMiBM2/ BM HBKBib b?QrM BM };m`2 jXRyX h?2 #Qì HBKBib r2`2 ±j /" 7Q` HH 7`2[m2M+B2b 2t+2Ti Ry @ 8yy F>x r?2`2 i?2 HQr2` HBKBi rb @RX8 /"X 0.1 0.02 0.01

0.001 101

oB#ìBQM T`Q}H2 #Qì HBKBi 102 6`2[m2M+v >x

103

6B;m`2 jXRy, _M/QK pB#ìBQM T`Q}H2- Sa. T`Q}H2 bHQTb ±e /"/P*hX

jXjX8

AMi2;`Biv M/ _Q#mbiM2bb S`K2i2`

qp2 T`QT;iBQM Bb b2MbBiBp2 iQ +QM/BiBQMb Q7 i?2 i`Mb/m+2` M/ +QMM2+iBQM M2i@ rQ`FX AM i?2 #b2M+2 Q7 +?M;2b iQ i?2 ?Qbi Ki2`BH T`QT2ìB2b- Mv /2;`/iBQM BM i?2 +QKTQM2Mib rBHH #2 TT`2Mi b `2bB/mH #2ir22M bB;MHb Q#iBM2/ #27Q`2 M/ 7i2` i?2 /2;`/iBQMX AM iQiH- }p2 b2ib Q7 i2bib r2`2 T2`7Q`K2/ QM i?2 7Qm` bKTH2b QmiHBM2/ BM i#H2 jXRX h`Mb/m+2` BMi2;`Biv mM/2` 2+? 2MpB`QMK2MiH T`Q}H2 rBHH #2 bb2bb2/ #v +QKT`BM; bB;MHb B[t] Q#iBM2/ #27Q`2 i?2 i2bib- rBi? i?Qb2 7i2` i?2 i2bi C[t]X hQ #2 `2H2pMi 7Q` #b2HBM2 +QKT`BbQM TT`Q+?2b i?2 `2bB/mH bB;MH Bb +H+mHi2/ 7`QK 2[miBQM UkXR8VX PMHv i?2 }`bi b2;K2Mi Q7 i?2 `2bB/mH bB;MH Bb +QMbB/2`2/ +QMbBbiBM; Q7 i?2 }`bi 7Qm` 83

jX9, 1tT2`BK2MiH a2i@mT rp2 T+F2ib U0 6 t 6 t4 VX h?2 BMBiBH b2;K2Mi rb +?Qb2M b i?Bb Tì Q7 i?2 bB;MH Bb +`BiB+H 7Q` /K;2 HQ+HBbiBQM M/ HbQ iQ ?2HT KBiB;i2 Mv 2z2+ib Q7 #QmM/`v +QM/BiBQMb i?i Kv +?M;2 /m`BM; i?2 i2bi (RN- Ny)X h?2 T2`7Q`KM+2 Q7 M a>J bvbi2K rQmH/ #2 +HQb2Hv HBMF iQ i?2 `2[mB`2/ /K;2 bBx2fivT2 M/ Mv +QMbi`BMib QM 7Hb2 H`K M/ KBb@/2i2+iBQM ì2bX h?2 bKHH2` i?2 /2i2+i#H2 /K;2 bBx2 i?2 KQ`2 i?2 `Q#mbi i?2 +imH +QKTQM2Mib M/ +[mBbBiBQM bvbi2K Kmbi #2 iQ 2MpB`QMK2Mib M/ QT2ìBM; +QMbiBimiBQMbX h?2 BMi2;`Biv Tbb i?`2b?QH/ Bb +HQb2Hv `2Hi2/ iQ i?2 7Hb2 H`K ì2b- T`Q##BHBiv Q7 /2i2+iBQM M/ /2i2+i#H2 /K;2 bBx2X h?2 bBx2 Bb +?Qb2M bm+? i?i i?2 KBMBKmK /K;2 b+ii2` iQ #b2HBM2 ìBQ Bb Ry W Q` @ky /"bBKBH` iQ bim/v #v L; M/ o2B/i rBi? KBHHBK2i`2 bBx2 /K;2 BM *6_S THi2b (NR)X h?2 bKTH2 rBHH #2 /22K2/ iQ ?p2 KBMiBM2/ BMi2;`Biv B7 i?2 2Mp2HQT2 T2F Bb mM/2` QM2 i2Mi? Q7 i?2 KtBKmK bB;MH KTHBim/2 2X;X `2bB/mH BM/2t RI Bb H2bb i?M Ry W, RI =

jX9

max(E(t)) ◊ 100, max(B(t))

f or 0 6 t 6 t4

UjXRV

1tT2`BK2MiH a2i@mT

1tT2`BK2Mib r2`2 +QM/m+i2/ iQ bb2bb i?2 BMi2;`Biv M/ `Q#mbiM2bb Q7 i?2 B`#Q`M2 a>J +QKTQM2Mib mM/2` 2+? Q7 i?2 i2bi T`Q}H2b QmiHBM2/X h?Bb rb /QM2 #v `2+Q`/@ BM; mHi`bQMB+b bB;MHb T`BQ`- /m`BM; M/ 7i2` 2+? i2biX aB;MHb r2`2 ;2M2ì2/ M/ `2+Q`/2/ mbBM; LiBQMH AMbi`mK2Mib THi7Q`KX h?Bb +QMbBbi2/ Q7 SsA2 89Rk bBM;H2 +?MM2H `#Bi``v pQHi;2 ;2M2ìQ`- SsA2 8Ry8 /B;B@ iH Qb+BHHQb+QT2 +`/ M/ SB+F2`BM; 9y@dke brBi+?BM; +`/ rBi? KtBKmK QmiTmi pQHi;2 KTHBim/2 Q7 Rk pQHibX *QtBH +#H2b r2`2 mb2/ i?`Qm;?Qmi- KBMBKBbBM; Mv bB;MH MQBb2 Q` +`Qbb iHFX *`Qbb iHF rb bB;MB}+Mi Bbbm2 b i?2 +imiBQM bB;MH ;2M2ì2/ #v i?2 `#Bi``v pQHi;2 ;2M2ì2/ rb KMv Q`/2`b Q7 K;MBim/2 H`;2` i?M i?2 bB;MHb #2BM; `2+Q`/2/X h?Bb rb KBMBKBb2/ 7mì?2` #v 2tTHQBiBM; i?2 `+?Bi2+im`2 Q7 i?2 brBi+?BM; +`/X h?2 bB;MHb r2`2 +Tim`2/ rBi? `2+Q`/BM; `M;2 Q7 e pQHib- rBi? i?2 Rk #Bi SsA2 8Ry8 +`/X h?Bb ;p2 `2bQHmiBQM Q7 RX9e Kp;BpBM; MQBb2 H2p2H Q7 `Qm;?Hv yX9e Kp rBi? Ry p2`;2bX h`Mb/m+2`b r2`2 mb2/ iQ +imi2 M/ b2Mb2 GK# rp2b BM 2+? bKTH2- B/2MiB+H iQ i?2 T`Q+2bb mb2/ 7Q` BKT+i /K;2 /2i2+iBQMX GK# rp2b r2`2 2t+Bi2/ rBi? }p2 +v+H2 >MMBM; iQM2@#m`bi rBi? +2Mi`H 7`2[m2M+v br2Ti BM i?2 `M;2 8y iQ jyy F>xX h?Bb 2Mbm`2/ bB;MHb r2`2 pBH#H2 i #Qi? HQr U8y F>xV M/ ?B;? Ujyy 8N

jX9, 1tT2`BK2MiH a2i@mT F>xV 7`2[m2M+B2b rBi? /QKBMMi A0 M/ S0 KQ/2b `2bT2+iBp2HvX h?2 `2bTQMb2 rb bKTH2/ i ey Jafb 7Q` yXyyR b2+QM/bX 1+? `2+Q`/BM; rb `2T2i2/ Ry iBK2b#M/Tbb }Hi2`2/ M/ p2`;2/X

jX9XR

oB#ìBQM a2i@mT

h?2 pB#ìBQM b2i@mT +QMbBbi2/ Q7 hJa kRRy1 b?F2` /`Bp2M rBi? ky8y1yN@6a TQr2` KTHB}2`X h?Bb rb +QMi`QHH2/ rBi? *`vbiH AMbi`mK2Mib aTB/2` 3R@" +QMi`QH M/ +[mBbBiBQM mMBiX j8k*jj ?B;? b2MbBiBpBiv- +2`KB+ b?2` A*S ++2H2`QK2i2` rb mb2/ 7Q` +QMi`QH K2bm`2K2Mib QM i?2 bKTH2X h?`22 }tim`2 +HKTb- R8 +K Tì `2THB+i2/ biBz2M2` #vb- rBi? i?2 b?F2` +QMM2+i2/ i i?2 +2Mi`2`X bT2+B}+ 7`2[m2M+v `2bTQMb2 7mM+iBQM rb `2+Q`/2/ 7Q` 2+? bKTH2 r?B+? rb mb2/ BM +HQb2/ 722/#+F HQQT iQ +?B2p2 i?2 `2[mB`2/ Sa. T`Q}H2X

F

A

G B

E C

D 6B;m`2 jXRR, oB#ìBQM b2i@mT UV +QMi`QHH2`- U"V b?F2` TQr2` KTHB}2`- U*V +QMi`QH ++2H2`QK2i2`- U.V b?F2`- U1V }tim`2- U6V bB;MH ;2M2ìBQM M/ b2MbBM; bvbi2K U:V rQ`FbiiBQMX

ey

jX9, 1tT2`BK2MiH a2i@mT

jX9Xk

h?2`KH M/ HiBim/2 a2i@mT

h?2 bKTH2b r2`2 2tTQb2/ iQ i?2 2MpB`QMK2MiH T`Q}H2b rBi? ha a2`B2b j i2K@ T2ìm`2- +HBKiB+ M/ T`2bbm`2 +?K#2` BM };m`2 jXRkX h?2 +?K#2` i2KT2ìm`2 rb K2bm`2/ rBi? S_h T`Q#2- M/ QM 2+? bKTH2 rBi? E@ivT2 i?2`KQ+QmTH2bX aKTH2 i2KT2ìm`2b r2`2 `2+Q`/2/ mbBM; M LA *QKT+i .Z NRdk M/ rBi? M LA NkRR i?2`KQ+QmTH2 KQ/mH2X h2KT2ìm`2 M/ ?mKB/Biv QmiTmi `2/BM;b Q7 i?2 +?K#2` r2`2 +QMiBMmHHv `2+Q`/2/ /m`BM; i?2 i2bibX Ai rb 7QmM/ i?i i 2ti`2K2 HQr i2KT2ìm`2b- i?2 +?K#2` i2KT2ìm`2b `2/BM; rb 8 ê* #2HQr i?2 bKTH2 i2KT2ìm`2bX h?Bb rb /m2 iQ i?2 +?K#2` S_h T`Q#2 #2BM; TQbBiBQM2/ rv 7`QK i?2 i2bi b2+iBQM- i?2 +imH bKTH2 i2KT2ìm`2 rb mb2/ b i?2 i`;2i 7Q` i?2 i2KT2ìm`2 T`Q}H2bX Ai rb 7QmM/ i?i r?2M i?2 T`2bbm`2 rb `2/m+2/- i?2 +?K#2` i2KT2ìm`2 +QmH/ MQi #2 +QMi`QHH2/ iQ i?2 bK2 2ti2Mi b mM/2` K#B2Mi T`2bbm`2X h?Bb rb b `2bmHi Q7 i?2 +QQHBM; M/ ?2iBM; bvbi2K #2BM; H2bb 2z2+iBp2 i HQr T`2bbm`2- ?Qr2p2` i?2 bKTH2 i2KT2ìm`2b r2`2 bi#H2 iQ rBi?BM j ê*X 1+? bKTH2 rb +QM/BiBQM2/ rBi? 2tTQbm`2 M/ /r2HH #2ir22M KtBKmK M/ KBM@ BKmK i2KT2ìm`2b iQ `2HBp2 Mv `2bB/mH- i?Bb rb `2T2i2/ i H2bi Ry iBK2bX 1+? bKTH2 rb i?2M KBMiBM2/ i dy ê* 7Q` i?`22 ?Qm`b iQ `2KQp2 Mv `2bB/mH KQBb@ im`2X

eR

!"#"$%&'"()*++),-.)/0-123-40-1))))))5"6789"()*++),-.)/0-123-40/:) +),-.)/0-123-40//)))))))!"#$%&'(#%)(*+#(%+,-./-01''''!!!!!"""#$%&'$(#)*#+,!

!""#$%&'()*+,-%./0% !12%314%!""#$% 5)*+,-%314%"6#78"78%

+ + + + + + + + + + + + + + + UV

jX9, 1tT2`BK2MiH a2i@mT

U#V

91:;')9! @Qr2p2`- i?Bb rb HBKBi2/ #v i?2 pBH#BHBiv 19! @