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M Ω2
;
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∫
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β
∫
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0
Y (s) =
∞
π
ξ −1Fm (ξ ) J0 (ξs) J0 (ξβ ) dξ ∫
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1
Rm (ζ ,t,s) = ζ [F (ζ ) − 1] 
(m = 1,2) 2
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þµ ζ = ±N º¸É½Ã¶ÍÃÑË
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ÁÄ Ã¶ ·»ÇÀÄûÍÃÄÇȾ Åƾ
r¾Ç
ξ > k1,2 ÈÄ ¾Â»»È »ÇÈÄ Åƾ
Reκ 1,2 (ξ ) ≥ 0 Imκ j(ξ ) > 0 u;ÈѸ¶µÈ¶ÀÄ¿¸Ñ·ÄƸ»È¸»¿Æ¶½Æ»½ÑÌ »
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ÆÄ Reκ 1,2 (ζ ) > 0 fÁµÍ»ÈÀÄÇȾ¾Ã¶¹ÁµºÃÄÇȾÅÆĸ»º»Ã¾µÆ¶½Æ»½Ä¸¾
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½¶Â»ÃµÁ¾ÇÒö N = N − LN ′ ≤ N ′ << N P
L
M
M
W
M
r¶ÇÇÂÄÈƾÂÇÉÂÂɾÃÈ»¹Æ¶Áĸ
m =2
∑ ∫ Rm (ζ ) dζ
m =1Lm
m =2
= 2πi∑ (− 1)
m =1
5HV [Rm (ζ m )]
m −1
¹º»ÀÄÃÈÉÆÑ / ¾ÅÄÁÔǶ ζ = ζ ζ = ζ ÅÄÀ¶½¶ÃÑÃ¶Æ¾Ç ζ §ÀÄÂ
P
ÅÁ»ÀÇÃÑ¿ ÃÉÁÒ ÊÉÃÀ̾¾ H 2(2) (ζa) ¸ ŻƸÄ À¸¶ºÆ¶ÃÈ» qÄÇÁ» ÅÆ»º»Á Ò
ÃÑËŻƻËĺĸ ζ = ε → ζ = r → ∞ N ′ → ¾Åƻķƶ½Ä¸¶Ã¾¿ÅÄÁ É
;ºÁµµºÆ¶
k
∞
1  2
2i 1 2
K (t,s) ts=  ∫ ξ f1(ξ ,t,s) dξ − ∫ ξ f2 (ξ ,t,s) dξ +
a  0
π 0
k2

2i 2

+
ξ f3 (ξ ,t,s) dξ − π Re ζ 02f4 (ζ 0,t,s)  ; (s ≤ t) ,
∫
π k1

¹º»
I (ξ s)K 0 (ξ t) [π I2 (ξ a)C1(ξ ) + K 2 (ξ a)C2 (ξ )]
;
f1(ξ ,t,s) = 0
ξ ξ 2 + k12 K 2 (ξ a) π 2I22 (ξ a) + K 22 (ξ a)
[
f2 (ξ ,t,s) =
f3 (ξ ,t,s) =
]
J0 (ξ s)H 0(2) (ξ t)
ξ
k12
−ξ
H 2 (ξa)
(1)
2
J0 (ξ s)H 0(2) (ξ t)
ξκ 1(ξ ) H 2 (ξa)
(1)
2
[
2
]
C4 (ξ ) ;
C3 (ξ ) ;
J0 (ζ 0s)H 0(1) (ζ 0t)
f4 (ζ 0,t,s) =
C5 (ζ 0 ) ,
κ 1(ζ 0 )
½º»ÇÒ , ([) . ([) § Âĺ¾Ê¾Ì¾Æĸ¶ÃÃÑ» ÊÉÃÀ̾¾ c»ÇÇ»Áµ ÅÄƵºÀ¶ Q
Q
(Q = ) ¾
Q
(
)
(
)
~ (1 + WJ η~ ) (∆
~ + WJ η~ );
C (ξ ) = ∆
C (ξ ) = ∆ (WK η − 1) (∆ + WK η );
C (ξ ) = ∆ (1 + WJ η ) (∆ + WJ η );
~21 WJη~ ∆
~21 + WJ η~ ;
C1(ξ ) = 1 − ∆
2
1
3
1
4
1
2
1
1
C5 (ζ 0 ) = C2\ ∞ (ζ 0 ) ;
¹º»
2
1
2
1
2
1
a a a
∆ = δ δ η~1 = h1κ~1(ξ ) ∆ = δ δ η1 = h1κ 1(ξ )
δ~j = µ jκ~j(ξ ) δ j = µ jκ j(ξ ) κ~j(ξ ) = ξ 2 + kj2 κ j(ξ ) =
ξ 2 − kj2 böÁĹ¾ÍÃÑ»ÀÄÃÈÉÆÃÑ»Åƻķƶ½Ä¸¶Ã¾µºÁµÊÉÃÀ̾¾º¶ÔÈ
i1
π ∞
Y (s) = −
f1(ξ ,β ,s) dξ − ∫ f2 (ξ ,β ,s) dξ +
2a ∫0
a0
k
i2
π2
Re f4 (ζ 0,β ,s) ;
+ ∫ f3 (ξ ,β ,s) dξ −
a k1
2a
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