# Oscilacije Elasticnih Tela

• View
9

4

Embed Size (px)

DESCRIPTION

mehanika

### Text of Oscilacije Elasticnih Tela

• 7.

, , , . . , , , . , , . . . . , , . , , , . . , . , , () , . , . 7.1

, , , . . , , . . , . , , , . A i B tako da u svakom preseku postoji normalni napon =z . , , (.7.1), .

dz dmy

7.1

• F

r F r

zd+= . ( ) , , . , :

zy

) (7.1.1) ,( tzyy = . dm F

r F r ( )FFF == rr :

FFdmarrr +=

Oy :

sin)sin(22

FdFdmty

z += . (7.1.2)

zd , : dz dz

zdda z )(sin)(sinsin)sin(

==+ . ,

y , :

zy= tgsin , dz

zydz 2

2)(sin

= . :

AFAdzdVdm === , , : , A , , (7.1.1) :

==

2

2

22

2

2 0 c

zyc

ty , (7.1.3)

. , .

c

(7.1.3) .

• (7.1.1) , . (7.1.3) : ) , (7.1.4) ()( tTzZy = :

TZdt

TdZtyTZT

dzZd

zy &&==

==

2

2

2

2

2

2

2

2 , .

(7.1.3) : 0 (7.1.5) 2 = TZcTZ &&, :

hTc

TZZ == 2

&&, (7.1.6)

, ,

h

z t . (7.1.5) : (7.1.7) .0 ,0 2 == ThcThZZ && , : h

(7.1.8)

).sin()cos( : 0 3)

),sinh()cosh( : 0 2)

, : 0 1)

2

2

kzDkzCZkh

kzDkzCZkh

DCzZh

+==

+==

(7.1.4) ) , : , 0( lzz == 0)( 0),( ,0)0( 0),0( ==== lZtlyZty . (7.1.9) (7.1.8) 3) , (7.1.7) :

h

(7.1.10) ),( 0 ,0 22222 ckTTZkZ ==+=+ && : ) (7.1.11) sin()cos( kzDkzCZ += )sin()cos( tBtAT += . (7.1.12) (7.1.11) (7.1.9), : (7.1.13) ,0 0)0( == CZ , )0( D , :

• ,0)sin( =kl (7.1.14) :

l

nkn= ),,2,1( = Kn . (7.1.15)

, (7.1.11) (17.1.2), :

n

(7.1.16) )sin( zkDZ nnn =

==+=

lcncktBtAT nnnnnn

n )sin()cos( , (7.1.17) , (7.1.4), [ )sin()sin()cos( zktBtAy nnnnnn ] += , (7.1.18) : nnnnnn DBDAA == B , . (7.1.3) (7.1.18), . :

, (7.1.19) [ )sin()sin()cos(1

zktBtAy nn

nnnn

=+= ]

:

) , (7.1.20) cos()sin(1

nnnn

n tzkRy =

= :

n

nnnn A

BBAR =+= arctg , n22 . (7.1.21)

nn BA , (7.1.19) , nnR , (7.1.20), . ) n- (.7.2) .

sin( zkR nn

. )0( 0 =t , : )( ),()0,( ,0

00 zt

yzfzytt

=

==

=, (7.1.22)

(20) :

)(sin ,)(sin11

zzl

nBzfzl

nAn

nnn

n =

=

=

= . (7.1.23)

nnA B , :

• ==

l

nmnm

ldzz

lmz

ln

0 21 0

sinsin ),...,2,1,( =nm . (7.1.24)

(7.1.23)

zl

msin [ ]l,0 , (7.1.24), :

=

= l lnn dzzlnz

cndzz

lnzf

lA

0 0sin)(2B ,sin)(2

. (7.1.25) (7.1.19) (7.1.20) . . , n , . 7.2 .

7.2

7.1.1 : b, , , . 7.3. .

• 7.3

: , , :

.0)()0,(

2),(

501

20,

50)()0,( ==

== zzy

bzbzb

bzz

zfzy & (1)

(7.1.10) :

bnc

bn

n == . (2) :

0,2

sin25

2sin50

2sin50

2

2/22

2/

0==+= n

b

b

b

n Bn

nbdz

bznzb

bdz

bznz

bA

, (3) :

=

=1

22 cossin2sin1

252),(

nt

bn

bznn

nbtzy

. (4)

7.1.2 l :

lzvzzy

lzyzfzy 5sin)()0,(,2sin)()0,( 00 ==== & . (1)

, A F . : (7.1.24) :

====

===

5,0

5,5sin5sin2

2,02,

sin2sin2

0

5

0

00

0

00

n

nFAlvv

dzlzn

lzv

lB

nny

dzlzn

lzy

lA

l

nn

l

n

(2)

:

• tA

Fll

zFAlvt

AF

llzytzy

5sin5sin5

2cos2sin),( 00 += , (3) , , . 7.2 ()

( ) , . . , :

l

) , , . , ) , ) , , . , , :

Oz

z w

. (7.2.1) lztzww = 0 ),( z z :

zw

z = ,

zwEE zz == , (7.2.2)

E . (7.2.1) , . , (.7.4). dz dm

7.4 F

r F

r

• .

ktwa

rr2

2

= Oz , , :

FFdma

rrr += . (7.2.3) :

)( d22

FFFFddmtw

zz == , (7.2.4)

, , :

Fdzz

dzzwAEdz

zAEdz

2 ,

==

=== , (7.2.5)

: , . (7.2.4) :

A

Ec

zwc

tw ==

2

2

22

2

2 , 0 (7.2.6)

. . .

c

(7.2.6) (7.1.3) , . , , ) , 7.2.7) ()( tTzZw = , (7.2.6), :

===+=+

EkckTTZkZ 222222 0 ,0 && , (7.2.8)

: )sin()cos( ),sin()cos( tBtATkzDkzCZ +=+= . (7.2.9) (7.2.9), (7.2.7).

k

( )

• . , , , . . 1. . .7.5 , .

7.5 : ,0),( ,0),0( == tlwtw (7.2.10) , (7.2.7) (7.2.9) : .0)sin(0)( ,00)0( ==== klDlZCZ (7.2.11) 0D , (7.2.11) :

),,2,1( 0)sin( === Knl

nkkl n . (7.2.13)

, . , :

,sincos ,sin

+

=

= ctl

nBctl

nATzl

nDZ nnnnn (7.2.14)

+

= =

zl

nctl

nBctl

nAwn

nn sinsincos

1, (7.2.15)

: nnnnnn DBDAA == B , . 2. . (.7.6) .

7.6 , , , , , :

• ,0 ,00

=

=

== lzz zw

zw (7.2.16)

, (7.2.7) (7.2.9) : 0)sin(0)( ,00)0( ==== klClZDZ . (7.2.17) )0( C :

),,2,1( 0)sin( === Knl

nkkl n . (7.2.18)

(7.2.9):

+

=

= ctl

nBctl

nATzl

nCZ nnnnn sincos ,cos , (7.2.19)

:

=

+

=1

cossincosn

nn zlnct

lnBct

lnAw . (7.2.20)

3. . .7.7 .

7.7 :

,0 ,0),0( =

=

=lzzwtw (7.2.21)

: ,0)cos(0)( ,00)0( ==== klDlZCZ (7.2.22) :

),,2,1( 2

)12( 0)cos( ,0 === Knl

nkklD n , (7.2.23)

:

=

+

=1 2

)12(sin2

)12(sin2

)12(cosn

nn zlnct

lnBct

lnAw .(7.2.24)

• 4. . A (.7.8) , , .

1m

7.8

A , (7.2.7) (7.2.8),

)()()()( 222

tTlZtTlZtwa

lzA ==

=

=&& , (7.2.25)

, ,

Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents