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(W V )GV = . (W β ) β = E − D ½º»ÇÒ E §Æ¶º¾ÉÇÎȶÂŶ D§Æ¶º¾ÉÇÅÄÁÄÇȾ ∞ . (W V ) = WV ∫ ξ [) (ξ ) − ]- (ξ V )- (ξ W )Gξ ± ± Lπ ∑ 5HV ξ P [)P (ξ P ) − ]- (ξ P V ) - (ξ P W ) P − ) (ξ ) = & ∞ (ξ )πDκ (ξ ) + ( ) (ξD ) 1 + ∆1WKη C2\ ∞ (ξ ) = ∆1 WKη µ κ (ξ ) η 1 = h1κ 1(ξ ) κ j(ξ ) = ξ 2 − kj2 ∆ = µ κ (ξ ) ? ¹º» kj = ω ρ j µ j M = § ÇÁÄ¿ M = § ÅÄÁÉÅÆÄÇÈƶÃÇÈ¸Ä ρ µ § M M ÅÁÄÈÃÄÇÈÒ ¾ ÂĺÉÁÒ Çº¸¾¹¶ ÇÄÄȸ»ÈÇȸ»ÃÃÄ K § ÈÄÁϾö ÇÁĵ d - ([) + ( ) ([) §Ì¾Á¾ÃºÆ¾Í»ÇÀ¾»ÊÉÃÀ̾¾¹Ä¾¹ÄÆĺ¶ÃÉÁ»¸Ä¹Ä ¾ ¹Ä ÅÄƵºÀĸ d µºÆ» . (W V) § ¸ÈÄÆÄ» ÇÁ¶¹¶»ÂÄ» ÅƾÇÉÈÇÈ¸É»È ¸ ÇÁÉͶ»ÀĹº¶¸½¶¾ÂÃѻǸĿÇȸ¶ÇÁĵ¾ÅÄÁÉÅÆÄÇÈƶÃÇȸ¶È¶ÀĸÑÍÈÄ N < N ÈĹº¶ ö ÅÆÄ»¼ÉÈÀ» N < ξ < N ÊÉÃÀ̾µ ¾Â»»È ÀÄûÍÃÄ» ;ÇÁĸ»Ï»Çȸ»ÃÃÑËÅÄÁÔÇĸ ξ µ¸ÁµÔϾËǵ¸»Ï»Çȸ»ÃÃѾÃÉÁµÂ¾ ÈƶÃÇ̻ú»ÃÈÃĹÄÉƶ¸Ã»Ã¾µ WK η = −∆ ¸ÅÆÄȾ¸ÃÄÂÇÁÉͶ» N > N § Éƶ¸Ã»Ã¾»¸»Ï»Çȸ»ÃÃÑËÀÄÆû¿Ã»¾Â»»È¾¸ÈÄÆÄ»ÇÁ¶¹¶»ÂÄ»¸¾ Ç Í»½¶»ÈdŻƸÄÂÇÁÉͶ»¾ÃÈ»¹Æ¶ÁÅÄþ¶»Èǵ¸ÇÂÑÇÁ»lÄξ nĺÉÁÒ ÀÄÂÅÁ»ÀÇÃÄ¿ ¶ÂÅÁ¾ÈÉºÑ É¹Á¶ ÅĸÄÆÄȶ ÎȶÂŶ ¶ÇÇÑ P ¸Ñƶ¼¶»Èǵͻƻ½Æ»Î»Ã¾» ω (W) ¾ÃÈ»¹Æ¶ÁÒÃĹÄÉƶ¸Ã»Ã¾µÈ¶À¼» P À¶À¾¸Æ¶·ÄÈ¶Ë >§@¾¾Â»»È¸¾º Φ = ( Θ(Ω ) = M 0 πµ1b3 g ) −1 Φ (Ω ) (1 − λ Re g )2 + (λ Im g )2 , λ= M Ω2 ; 2π ¹º» 0 = P SE §Åƾ¸»º»ÃöµÂ¶ÇǶÎȶÂŶ S = E D Ω = ωE ρ µ § Åƾ¸»º»Ãöµ ͶÇÈÄȶ ¸ÑÃɼº»ÃÃÑË ÀÄÁ»·¶Ã¾¿ ω § ̾ÀÁ¾Í»ÇÀ¶µ Ͷ Ç ÈÄȶ dÊÉÃÀ̾µ J = J(Ω) ¾Â»»ÈÇÂÑÇÁÀÄÂÅÁ»ÀÇÃÄ¿¶ÂÅÁ¾ÈɺÑÉ ¹ Á¶ÅĸÄÆÄȶ·»½ÑûÆ̾ÄÃÃĹÄÎȶÂŶ¾¸Ñƶ¼¶»Èǵ β 2p3 g(Ω ) = 2 π ∫ sω (s)Y (s) ds − β Y (β ) 0 β ∫ sω (s) ds − β 0 Y (s) = ∞ π ξ −1Fm (ξ ) J0 (ξs) J0 (ξβ ) dξ ∫ 20 y¾ÇÁ»ÃöµÆ»¶Á¾½¶Ì¾µ½¶º¶Í¾ jÃÈ»¹Æ¶ÁÒÃÄ»Éƶ¸Ã»Ã¾»½¶Â » ÃÄ¿¾ÃÈ»¹Æ¶Á¶ÅÄÀ¸¶ºÆ¶ÈÉÆÃÄ¿ÊÄÆÂÉÁ»ÈƶŻ̾¿Ç¸Äº¾ÁÄÇÒÀÁ¾Ã» ¿ ÃÄ¿ ¶Á¹»·Æ¶¾Í»ÇÀÄ¿ ǾÇȻ» Éƶ¸Ã»Ã¾¿ s Ì»ÁÒÔ ÓÊÊ»ÀȾ¸ÃÄ¹Ä ¸ Ñ Í¾ÇÁ»Ã¾µ ¶ÈƾÌÑ Ç¾ÇÈ»ÂÑ ¾ ÊÉÃÀ̾¾ J(Ω) ¶ ȶÀ¼» Ä·»ÇŻͻþµ »º¾ÃÇȸ»ÃÃÄÇȾ ƻλþµ ½¶º¶Í¾ ÍÈÄ Ç¸µ½¶ÃÄ Ç Ã»ÄºÃĽöÍÃÄÇÈÒÔ Æ¶º¾À¶Áĸ κ j(ξ ) ¸ ÅÆĸĺ¾ÁÄÇÒ ÀÄÃÈÉÆÃÄ» Åƻķƶ½Ä¸¶Ã¾» ¾ÃÈ » ¹Æ¶Áĸ ¸ ÀÄÂÅÁ»ÀÇÃÄ¿ ÅÁÄÇÀÄÇȾ ζ cɺ»Â ƶÇǶÈƾ¸¶ÈÒ ÇÁ É Í¶¿ N > N ÈĹº¶¸¸ÑÍ»ÈÑÄÈÇÉÈÇȸÉÔÈr¶ÇÇÂÄÈƾ¾ÃÈ»¹Æ¶Á qĺÑÃÈ»¹Æ¶ÁÒÃÄ» ¸Ñƶ¼»Ã¾» ÅÆ»ºÇȶ¸¾Â À¶À ÊÉÃÀÌ¾Ô ÀÄÂÅÁ»ÀÇÃÄ¿ Żƻ»ÃÃÄ¿ ζ = ξ + Lη ½¶Å¾Ç¶ÃÃÉÔ¸¸¾º» 5(ζ W V) = 5(ζ W V) + 5 (ζ W V) J0 (ζ t) H 0(m ) (ζs) ,t ≤ s, 1 Rm (ζ ,t,s) = ζ [F (ζ ) − 1] (m = 1,2) 2 J0 (ζ s) H 0(m ) (ζ t) ,t > s. r¶½Á¾Í¾» ¸ ÅÆ»ºÇȶ¸Á»Ã¾¾ 5 (ζ W V ) (P = ) Ǹµ½¶ÃÄ Ç ÅÄÇÁ»ºÉÔÏ»¿ ÄÌ»ÃÀÄ¿ ¾ÃÈ»¹Æ¶Á¶ ¸ ÀÄ Â ÅÁ»ÀÇÃÄ¿ ÅÁÄÇÀÄÇȾ ÅÄ Ä À ÆɼÃÄÇȵ ·ÄÁÒÎÄ¹Ä Æ¶º¾ É Ç¶ vÉÃÀ̾µ ÄÅÆ»º»Á»Ã¶ ö Í»ÈÑÆ»ËÁ¾ÇÈÃÄ¿ Æ¾Â¶Ã Ä ¸Ä¿ Åĸ»ÆËÃÄÇȾ fÁµ »» Å Ä ÇÈÆĻþµÅÆĸĺµÈǵƶ½Æ»½Ñ ¸ÑËĺµÏ¾» ¾½ ÈÄÍ»À ¸»È¸Á » þµ ζ = ±N º¸É½Ã¶ÍÃÑË ÊÉÃÀ̾¿ κ 1,2 (ξ ) d»È¸¾ ƶº¾ À¶Áĸ κ (ξ ) ÇÁ»ºÉ»È ¸Ñ·¾ ƶÈÒ È¶À¾Â ķƶ½Ä ÍÈÄ·Ñ Ç ÉÍ»ÈÄ ¸Æ»Â»ÃÃÄ¹Ä ÂÃļ¾È » Áµ H ω ƻλþ» 8 (U ]) Åƾ ] → ∞ ɺĸÁ»È¸ÄƵÁÄ ÉÇÁ Ä ¸¾Ô¾½ÁÉͻþµiÄ»ÆÊ»ÁÒº¶ >@»ÇÁ¾ < ξ < N ¾½¶ÈÉ˶ 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 » Á»ÇÄķƶ½ÃÄÅÆĸĺ¾ÈÒ¸ºÄÁÒ Reκ 1,2 (ζ ) = 0 ¾¸Ñ·¾Æ¶ÈÒÁ¾ÇÈöÀÄÈ Ä ÆÄ Reκ 1,2 (ζ ) > 0 fÁµÍ»ÈÀÄÇȾ¾Ã¶¹ÁµºÃÄÇȾÅÆĸ»º»Ã¾µÆ¶½Æ»½Ä¸¾ ÀÄÃÈÉÆĸ ¾ÇÅÄÁҽĸ¶Áǵ »Èĺ ÅÆ»º»ÁÒÃÄ¹Ä ÅĹÁÄϻþµ >@ È» N 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 §ÀÄ 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 Í¾ÂºÁµµºÆ¶ 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 k (s ≤ β ) nļÃÄÅÄÀ¶½¶ÈÒÍÈÄÅĺÑÃÈ»¹Æ¶ÁÒÃÑ»ÊÉÃÀ̾¾¸ §Ä¹ ƶþͻÃÑ ¸ ÃÉÁ» ¶ ¸ ¾ÃÈ»¹Æ¶Á¶Ë ö ÅÄÁÉ·»ÇÀÄûÍÃÑË ÅÆÄ»¼ÉÈÀ¶Ë ÓÀÇÅÄûÃ̾¶ÁÒÃÄ É·Ñ¸¶ÔÈ Ã¶ ·»ÇÀÄûÍÃÄÇȾ t¶À¾Â ķƶ½Ä ÅÄÁ É Í»ÃÃÑ»ÅÆ»ºÇȶ¸Á»Ã¾µ¾ÃÈ»¹Æ¶ÁĸºÁµ . (W V) ¾ < (V) §µ¸ÁµÔÈǵÓÊÊ»À Ⱦ¸ÃѾºÁµ¸Ñ;ÇÁ»Ã¾µÃ¶dn fÁµÍ¾ÇÁ»ÃÃÄ¿Æ»¶Á¾½¶Ì¾¾½¶º¶Í¾ÄÈŻƻ»ÃÃÑË W V ¾ ξ §Å» Æ»Ëĺ¾Á¾ À ·»½Æ¶½Â»ÆÃÑ Żƻ»ÃÃÑ τ σ ¾ [ Çĸ»Æζµ ½¶Â»ÃÑ V = βσ W = βτ ≤ σ τ ≤ ξ = N [ d¸Äº¾Á¾ÇÒ È¶À¼» ·»½Æ¶½Â»ÆÃÑ» ¸»Á¾Í¾ÃÑ ε = N D β = β D + = K E P = µ µ α = N N (α ≤ ) pÈ»ȾÂÍÈÄÅƾ α = ¾ P = ¸Ñƶ¼»Ã¾µºÁµµºÆ¶ . 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