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“„Š 532.5

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á«®ï.

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¯®«®¦¥-­¨¥, ¯à¨ ª®â®à®¬ ­¥ ¯à®¨á室¨â § å¢ â  ¦¨¤ª®á⨠¨§ ¤à㣨å á«®¥¢ [1{3].

‚á«ãç ¥, ª®£¤  ¦¨¤ª®áâì § ¡¨à ¥âáï ¨§ ­¨¦­¥£®á«®ï, ªà¨â¨ç¥áª®¥

¯®«®-¦¥­¨¥ ¯®¢¥àå­®á⨠ࠧ¤¥«  ­ §ë¢ ¥âáï ¢¥àå­¨¬ ¯®«®¦¥­¨¥¬ (à¨á. 1),   ¯à¨

§ ¡®à¥ ¨§ ¢¥àå­¥£® á«®ï | ­¨¦­¨¬ ¯®«®¦¥­¨¥¬(à¨á. 2).

‚ ¯àאַ㣮«ì­®© á¨á⥬¥ ª®®à¤¨­ â x0z ç áâì ¯à®áâà ­á⢠,

®£à ­¨ç¥­-­ ïãá«®¢¨ï¬¨ 06x6l,06z 6H

1

, ¯à¥¤áâ ¢«ï¥â ¢¥àå­¨© á«®©­¥á¦¨¬ ¥¬®©

¯à®¢®¤ï饩¦¨¤ª®áâ¨,¤à㣠ïç áâì¯à®áâà ­á⢠|06x6l,,H

2

6z 60|

­¨¦­¨©á«®©(l |¤«¨­  ¢ ­­ë,H

1 ¨ H

2

| £«ã¡¨­ë á«®¥¢,®áì z |

­ ¯à ¢«¥-­  ¢¢¥àå,¯«®áª®áâì z =0 ᮢ¬¥é¥­  á ¯®¢¥àå­®áâìîà §¤¥«  á«®¥¢). Ž¡  á«®ï

¦¨¤ª®á⨠¯®¬¥é¥­ë ¢ áªà¥é¥­­ëå ®¤­®à®¤­ëå í«¥ªâà¨ç¥áª®¬ ¨ ¬ £­¨â­®¬

¯®«ïå. ‘®§¤ ­­ ïí«¥ªâ஬ £­¨â­ë¬¯®«¥¬¯®­¤¥à®¬®â®à­ ïᨫ ­ ¯à ¢«¥­ 

¢¥à⨪ «ì­® ᢥàåã ¢­¨§ ¨ á®§¤ ¥â ¢®§¬®¦­®áâì £à ¢¨â æ¨®­­®£® ¢á¯«ë¢ ­¨ï

ç áâ¨æ ¯à¨¬¥á¨ ¨§ ­¨¦­¥£® á«®ï ¢ ¢¥àå­¨©. Žç¨é¥­­ë© ®â ¯à¨¬¥á¨ ­¨¦­¨©

á«®© ¦¨¤ª®á⨠ç¥à¥§ § ¡®à­®¥ ®ª­® ¢ë⥪ ¥â ¨§ ¢ ­­ë. ‡ ¡®à­®¥ ®ª­®

®£à -­¨ç¥­® ãá«®¢¨ï¬¨ x = 0, ,H

2

6 z 6 ,H

2

+ h, £¤¥ h | ¢ëá®â  ®ª­ . „«ï

á®åà ­¥­¨ï ¯®áâ®ï­­ëåã஢­¥©á«®¥¢¯®« £ ¥âáï,ç⮢­¨¦­¥¬á«®¥¯à¨x =l

(2)

¦¨¤ª®á⨠ç¥à¥§ § ¡®à­®¥ ®ª­®. †¨¤ª®áâì áç¨â ¥âáï ¨¤¥ «ì­®©, ¤¢¨¦¥­¨¥ |

¡¥§¢¨åà¥¢ë¬ (¯®â¥­æ¨ «ì­ë¬).

h

z

0

x

H

1

ρ , σ

H

2

1

1

ρ , σ

2

2

Ðèñ. 1.

l

‚¡¥§¨­¤ãªæ¨®­­®¬¨«¨­¥©­®¬¯à¨¡«¨¦¥­¨¨áä®à¬ã«¨à®¢ ­­ ï

ª®­â ªâ-­ ï§ ¤ ç ¬ £­¨â­®©£¨¤à®¤¨­ ¬¨ª¨á¢®¤¨âáïªà¥è¥­¨î¤¨ää¥à¥­æ¨ «ì­ëå

ãà ¢­¥­¨© ‹ ¯« á 

l

z

0

x

H

ρ , σ

1

H

2

1

1

ρ , σ

2

2

Ðèñ. 2.

@ 2

'

1

@x 2

+ @

2

'

1

@z 2

=0 ¯à¨ 06z 6H

1

; (1)

@ 2

'

2

@x 2

+ @

2

'

2

@z 2

=0 ¯à¨ ,H

2

6z 60 (2)

¯à¨ á«¥¤ãîé¨å ­ ç «ì­ëå ¨ £à ­¨ç­ëå ãá«®¢¨ïå:

'

1 j

t=0 =

@'

1

@t

t=0

=0; '

2 j

t=0 =

@'

2

@t

t=0 =0;

(3)

@'

1

@x

x=0 =0;

@'

1

@x

x=l

=0; (4)

@'

2

@x

x=0

=,V(z)=

,V

0

¯à¨ ,H

2

6z 6,H

2 +h;

0 ¯à¨ ,H

2

+h <z 60;

@'

2

@x

=,V

l =,

V

0 h

H

2 ;

(3)

1 @'

1

@t +

1 B

2

0 '

1 +g

1

1 H

1

=0 ¯à¨ z =H

1

; (6)

@'

1

@z =

@'

2

@z

¯à¨ z =0; (7)

1

@ 2

'

1

@t 2

+

1

1 B

2

0 '

1 +g

1 @'

1

@z

=

2

@ 2

'

2

@t 2

+

2

2 B

2

0 '

2 +g

2 @'

2

@z

¯à¨ z =0; (8)

@'

2

@z

z=,H2

=0; (9)

£¤¥ ¯à¨­ïâë á«¥¤ãî騥 ®¡®§­ ç¥­¨ï: '

1

(x;z;t) ¨ '

2

(x;z;t) | ¯®â¥­æ¨ «ë

᪮à®á⥩ ¢ ¢¥àå­¥¬ ¨ ­¨¦­¥¬ á«®ïå ᮮ⢥âá⢥­­®,

1 ¨

2

| ¯«®â­®áâ¨,

1

¨

2

| í«¥ªâய஢®¤­®á⨠¢ ¢¥àå­¥¬ ¨ ­¨¦­¥¬ á«®ïå ¦¨¤ª®áâ¨,

g

1

=g+

1

1 E

0 B

0 ; g

2

=g+

2

2 E

0 B

0

; (10)

E

0 = E

y

| ­ ¯à殮­­®áâì í«¥ªâà¨ç¥áª®£® ¯®«ï, B

0 = B

x

| ¨­¤ãªæ¨ï

¬ £-­¨â­®£® ¯®«ï.

Žâ­®á¨â¥«ì­® £à ­¨ç­®£® ãá«®¢¨ï (6) ®â¬¥â¨¬, çâ® ¢®«­®®¡à §®¢ ­¨¥ ­ 

᢮¡®¤­®© ¯®¢¥àå­®á⨠¢¥àå­¥£® á«®ï ­¥ ãç¨â뢠¥âáï.

‚®«­®¢ ï¯®¢¥àå­®áâì à §¤¥«  á«®¥¢ ¯à¨ z =0

(x;t)=

1

2 g

2 ,

1 g

1 @'

1

@t ,

2

2 g

2 ,

1 g

1 @'

2

@t

+

1 B

2

0

2 g

2 ,

1 g

1 '

1 ,

2 B

2

0

2 g

2 ,

1 g

1 '

2

(11)

¨«¨

@(x;t)

@t =

@'

1

(x;z;t)

@z

z=0 =

@'

2

(x;z;t)

@z

z=0

: (12)

„«ï ­¥¯à®¢®¤ï饩 ¦¨¤ª®á⨠íâ  § ¤ ç  ¯®áâ ¢«¥­  ¨ à¥è¥­  ¢ [4].

à¨áâ㯠ïªà¥è¥­¨î¯®áâ ¢«¥­­®©­ ç «ì­®-ªà ¥¢®©§ ¤ ç¨(1){(9),

¯à¨-¬¥­¨¬ ¨­â¥£à «ì­®¥ ¯à¥®¡à §®¢ ­¨¥ ‹ ¯« á  ®â­®á¨â¥«ì­® ¢à¥¬¥­¨ t.

~ '

1;2

(x;z;p)= +1

Z

0 '

1;2

(x;z;t)e ,pt

dt: (13)

‚ १ã«ìâ â¥ ¯à¥®¡à §®¢ ­¨ï (13) ¢ëà ¦¥­¨ï (1){(9) ¢ ¨§®¡à ¦¥­¨ïå

§ -¯¨èãâáï á«¥¤ãî騬 ®¡à §®¬

(4)

'~

(5)
(6)

ãá«®¢¨-£¤¥

(p)cosa

n (t)cos

n

sin r sin

q cos

q

sin r sin

q cos

(7)

s

n =

2 B

2

0

2

1+

2 th(a

n H

1 )th(a

n H

2 )

1+

1

2 th(a

n H

1 )th(a

n H

2 )

;

th(a

n H

1 )=

1,e ,2a

n H

1

1+e ,2a

n H

1

; th(a

n H

2 )=

1,e ,2a

n H

2

1+e ,2a

n H

2 ;

sh(a

n h)

ch(a

n H

2 )

= e

,an(H2,h)

,e

,an(H2+h)

1+e ,2a

n H

2

; h<H

2 :

‹¨â¥à âãà 

1. ®¢åˆ.‹. ’¥å­¨ç¥áª ï£¨¤à®¬¥å ­¨ª .|‹.: Œ è¨­®áâ஥­¨¥,1976.|501á.

2. ®¢åˆ.‹,Š ¯ãá⠀.,—¥ª¨­.‚. Œ £­¨â­ ï£¨¤à®¤¨­ ¬¨ª ¢¬¥â ««ãࣨ¨.|Œ.:

Œ¥â ««ãࣨï,1974.|240á.

3. ‘¯à ¢®ç­¨ª ¯® £¨¤à ¢«¨ª¥ ¯®¤ । ªæ¨¥© ‚. €. ®«ìè ª®¢ .|Ѝ¥¢: ‚¨é  誮« ,

1977.|278á.

4. ‘®§ ­®¢ ‚. ƒ, Œã§ ¥¢ ˆ. „, ’ã ¥¢  †. „., Œã§ ¥¢  ’. ‚. ®áâ ­®¢ª  ¨ à¥è¥­¨¥

­ ç «ì­®-ªà ¥¢®© § ¤ ç¨ ¢­ãâ७­¨å ¢®«­ ¯à¨ ᥫ¥ªâ¨¢­®¬ ¢®¤®§ ¡®à¥ ¨§

áâà â¨ä¨-æ¨à®¢ ­­®£® ¢®¤®¥¬  // ˆ§¢. ¢ã§®¢. ‘¥¢¥à®-Š ¢ª §áª¨© ॣ¨®­, ¥áâ¥á⢥­­ë¥ ­ ãª¨.

®á⮢-­ -„®­ã.|2001.|ü1.|‘.104{106.

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