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J. Braz. Soc. Mech. Sci. & Eng. vol.29 número3

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(1)

! "

#$ % $&$'( " $ ! !

! "

!" #$%& ' ( ##)*

!+)))*

! ! " !

# ! , !-.* " +

!/

! 0+

$ ! +

% ! & !

' ! 0

1 2 ! $.

+*

( ( ! "

( ! "

(+! 2 "

( ! "

( ! ) -+3× )3"

! -0

1

! %- . . 40! '*

5 !5

) ! '

) ! '

## $ !!% & # # ' ( ) * +

) ! +%% 3 '

* !

* ! ≈

α1

β1

+1 2

(1 "

ε 1

η1

1 "

ν1 +0

ρ1 0

-τ1 "

+ +

6

+ 2

ρ

, !π"+0.* $

+ ) +

ρ

+ (+ $+ + =

" ! *

/

+ %τ

ρ

(2)

 

 !!"

7 , ! *

+

+

1 !+* 7 ρ 1 0, 1

+

+ +

) +

ρ +ρ (+ρ $+ + =

" !-*

ρρρρ

!

"

8 ρ=

+ +

+  +

=

 

!.*

# $

ρρρρ

"

8 ρ= ( '

* )

+ + + + +

+

! *

+

ρ = = = −

( ( (

( ( (

( ' ' ' ( (

( ( ( (

* ) * ) * ) !3*

9 2 )

*

!+)))*

+ +

+

=) )

) !:*

! ( + ∝ ( *

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+ +

+ +

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- 

= = = + −

+

 

( + ( ( ( (

( ( (

( (

+ ( (

!$*

*

( )

9 ! ##)*

#

ρρρρ

! "

+ + +

+

ρ =  

 

$ $

$ $

( '

$ $

* ) !%*

!( '0!* )**+

!+)))*

+ + +

+ + + ! − *

( '

$ $

* ) !#*

;

% &

    

  

! !

+ + + +

+

! *

+ + +

= =

+

+

+ + &

+

" " " ! )*

& +

+ +

+ + +

+ + +

+ + + +

! *

! * )

+ +

  −

+ + − + =

   

( '

' ( ( &

$ $

* ) * ) " ! *

+ +

+ + +

+

+ + + +

! *

! * )

+ +

+ ( ' − + =

' ( ( &

$ $

* ) * ) " ! +*

<

-!+%% 3 ' -+3× )3 " *

+ + + + +

+

+ + . + + +

:

ρ π

= - = ( '

-, " * ) ! -*

' = ' ! .*

' 1 +% #:+3≈+#

0 , ! +* ! .* 9

+ +

+

+ +

+ + 3

! *

3%

! *

.:.

π η

 − 

− −

 

 

=

 

 

 

( $ $

( (

) *

* ) "

-( & ) * ! 3*

8 = ! #%$*

,

! 3* η1 2

0 2

η

) % !+)))* η

) #+ ) #$ 2

) $ = ! #%$*

9 η

+

& η &

(3)

6 ρ =' ( !* ) *

! *

ρ =' ( * ) 2

η

+ + 3

+ +

+ +

+#

! * + ! *

.

π

ρ ρ

 

 

=  − − −

 

"

- ( ( ( $ $

* ) & ! :*

5

+

+ +

+ + + 3

! * + ρ ! *

 − − − 

=  

 

 

( ( ( $ $

- "

& ) * ! $*

+ +

+ +

!( −( * +〉〉 ( ρ !$ −$*

+

+ +

+ 3 +

! *

=  

 

 

( (

- "

& ) * ! %*

?

"

9 ! #3:* =

2

++ 3≈3 :: 5

+ +

+= ′+ !( −(+* 3

- "

& ) * ! #*

+ + +

+ +! * 3

− =

( ( - & ) *

" !+)*

+ +

+

− =

( ( & - !+ *

'

7

@

! * !

*

6 5

ρ-=ρ - =

.

5

-"

ρ π

= !++*

8 ρ =( ' !* ) * * ≈ '≈+#

. +#

5 - (

" )

π

= !+-*

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8 5 + ))

5 + ))

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8

2 ?

/ ? ! ###*

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8 9 ( ! #$%*

&

) 3# ) )3: 5 &

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/ 9 (

! #$%*

+

+ +

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! * ) )))+ ! *

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+ +

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= +

+ !+%*

(4)

 

 !!"

5 + +

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+=

!+#*

+ " ? +B

→ ∞ 5 →:.

# '

! ##%* / " AC

' !+)))*

) + %+3 +

5

 

= − 

 

!-)*

) ) ) ) )+ ) )-) )-). ) )3 ) ):

)- ). )3 ): )$ )%

ε0"1) ))): ε0"1) )))-ε0"1) ))) 3

, !--*

!ε."1) ))):*

, !-)*

, !- *

ε."1) ))):

! " # $ %" % & " '' ( '

( ) "% %% '( " ' " "% % *

? 5

5 ! ##%*

/

< !+)))*

) +

- $ "

ε

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 

1 !- *

, !-)*

9 ! ##)* , !- * 8

5

/ 5 5

5 +

5 ε."

9

)-#

5 =-3 +-3 ! 0ε "*− !-+*

9 ! ##)*

6 A? + %+3

+ 3

)

+ %+3 +

- $ 5

" ε

 

= −  + 

 

!--*

εεεε)

)

-)A:

).

)3

):

)$

)%

)A3 )A. )A- )A+ )A

, !- *

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2

2 5

, !-+*

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0+/ .3.%) .:)+# %%

--0./ :%++ $+) . +:% %

/ #)#: #%#-+ .+3$3

+/ % #++ + +:.) %$)%#

./ -:-%.. .3$)-$ %-3%:

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%/ $+$:%$ #%+---

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.%#3--8

5 5

2

5

) ).:

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±-)E*

2

* +

, ! 3*

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) ):%.- ! *

= − (

# $ $

) * !-.*

+

+ + + 3

+

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=  

 

 

) ( ( # "

-( & ) * !-3*

3) + +

+

( −(

= ! #%$*

+ +

+ ! +* + ! +* 0 +

− = − +

( ( ( ( ( ( !-:*

+

!(+(* 0 +1(′ !-$*

(

+ +

+

( ( 1!(−(+* +⋅ (′ !-%*

+ + 3 +

! * +

- +#%:  − ′ − 

=  

 

 

( ( ( #

) "

-( & ) * !-#*

( (+

8

D

8

5 β

α

= !.)*

5

. +#

5 - (

" )

π

= !+-*

, ! 3*

! + 3 *

! *

! ) 3 * ! * ! *

) 3

+ + ! *

+ ! + * ! * ! *

:

! *

+

β β

β β β

β

β β

β β

α π

− − −

− −

− −

 

=

 

 

 

 

-) ( ( #

"

( & ) *

!. *

2

8 9

,

-#

# - .

) )$-)3 - .-: 5

= !.+*

α1 - .-: β1 ) )$-)3 5 , !. *

" 8 9

) 3-#.

+ +

+ : %+ +

) )$%% ) %3-#

! *

.) +#$)  − − 

=  

 

 

) ( ( #

- "

( & ) * !.-*

8

!+)))* 1

). 3× )A3"

) 3-#.

+ +

+ : %+ +

) %3-#

! *

## 3+  − − 

=  

 

 

) ( ( #

- "

( & ) * !..*

. . #

8 F 8

" A ' 2

) + %+3 +

5

 

= − 

  !-)*

, !. *

) 3

+ +

+ 3 +

)

! * + %+3

- +#%: +

5

) ( ( #

- "

( & ) *

 

 − −   

=   − 

 

   

   

(6)

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B) +.E A- +-E 5

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7 !+)) * ? 2

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(

)

+3

)5 )+

= !.:*

? , !.:* , !. *

(

)

) 3

+ +

+3 + 3 +

)

! *

- +#%: 5

)+

0 0

) ( ( #

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=  

 

  !.$*

-" 8 8F8 ? 8

" 8 5

9 !+)) * 8

8F8 ! " A ' *

?

! " ( ' ' - )% . / 0 )

1 2" '

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# - /

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) 3 )

+ +

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) ( ( #

- "

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G 1 )$3%× )A3"

) 3 )

+ +

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) #:)%

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-3 %:##  − − 

=  

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- "

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$

-8 !+))+*

2

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5 , !. *

+

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<

2 , !- *

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ε

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) 3

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)

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- +#%: +

- $

ε

 − −    

=   − 

 

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 

) ( ( # "

- "

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* 0

$-! +))+*

; !9 ##)& F +)))*

6 A? + 3

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5 !F +))) *

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ε

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 

(7)

6 A?

) 3

+ +

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)

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- +#%: +

- $ 5

) ( ( # "

- "

( & ) *

ε

 

 − −   

=   −  + 

 

   

   

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1

F,5F !F

, 5 F H * #:

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?

2

5

F !+)))*

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⋅ ⋅

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) #.+

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+

+ 3 )

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-( & ) *

"

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ε

⋅ ⋅

=  

 

 

  

 

+  

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 

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 

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η

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"

1

6 A?

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A A A A A A8F8

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=

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) 3$.$

+ +

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*

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M N 3 +33

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3 . 5

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(

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) %

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(

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9

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5

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π ρ =

 

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!$%*

, !$$*

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ν ν

ρ ρ

= = ≅ !$#*

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(

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)

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3 3 3

+:

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− − −

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×× ×

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    !%)*

6 , !$3* !$:*

2

, !$:* , !$3*

(

+ +

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+

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  !% *

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.)%% )$3$ )

ρ −

×

× !%+*

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.)%% + + ρ

 

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 

   

!%-*

, !$3* !$:* D

, !$3* , !$:*

, !$ *

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+ +

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%+ . %+

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8 1 )$3$× )A3"

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+%% 3 ' ( 1 ) -+3× )3" * 1

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+ %+

) %+

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&

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=

  !%3*

( (′ 1( B -#) O" P !

* 9

+ +

+

( −( !(−(+*+(′ , !$.* !$:*

5 ) #

+&

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) ( ( #

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(′ 1( B -#) O" P

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= !%%*

3

"1 ./

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3

2 8F8

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