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(1)
(2)

2

Aq Bq C D q 0

1 2

i

N

q z

q z

q z

q z

q

1, 2,...,

i

q iN

i i

q p z

0 0

0 i i

i i

q q

for z

q q

0 0

0 ,

l

i i i i

q z s z p d q z q

s s

,

(3)

z ,

0 z

s z

z

i

p z qi0

0 i

q

i

q z

0

0 ,

l

i i i

q z s z p d q

1 z ,

0 s z

z

i

p z

ik

p

0 M

i k ik

k

p z z p

k

0 i

p p zi

0 2 1 2

i i i

(4)

Fig. 2:

p

ik

i

0 0

0

,

M

i k ik i i

k

q z S z p q z q

0

, ,

l

k k

(5)

1, 2,..., M j

0 0

0 M

ij jk ik i j i

k

q S p q z q

,

ij i j

jk j k

q q z

S S z

2

2

6 j = k 0 j < k

j > k

jk

S

j k

0 2 1 2

i i i

p p p

2 2 1 k 1 3 1 1 2 2 3 jk j S j k 0 0 M

ij jk ik i

k

q S p q

2 j = k 0 j < k j > k

jk

S

1 2 2

(6)

0

Q SP LQ

11 11 12

1

21 21 22 22

2

3 31 31 32 32 33

1 1 2 2 3

1 1 2 2 3

j j j j j j jj

M M M M M M Mj MM

S S S

S S S S

S S S S S

S S S S S S

S S S S S S S

I I

q

I I

q

q I I I

q I I I I

q I I I I I

Q

0 0 0 1 1 2 2 3 3 j M z z j M z z z

p I I

p I I

p I I

q q

p I I

p I I

Q

P

L

S

j

q pj

0

Q S P L Q

Q P

0

2 +

* * * *

A Q B Q C D Q

1 2 1 2

1 2

M M

M 1 1 2 2 1 2 M M M * * * * A B A B A B A B C D C D C D C D

1 2

M

1

2

(7)

* *

0

2 2

* * * * *

A B S C D S P B L C D L Q 0

1 0

P K LQ

2

2

* * *

* * *

K A B S C D S

L B L C D L

1 2 3

1 1 2 2 3

1 1 2 2 3

M

M M M M M Mj MM

M

M M M M M M Mj MM

j M

M

S S S S S S S

S S S S S S S

p p p

I I I I I

q

q I I I I I

p p

Q

S

0 0 0 l q I 0 q I I

T

Q

P

0 M M

Q S P TQ

1

0

M M

Q S K L T Q

0 0 0 M M M q q R R r r 0

(8)

0 0

R EQ

M M

R EQ

1 1

0

M M

R E S K L T E R

0 M

R FR

1 1

M

F E S K L T E

2 2

0

0

EI kGF V I

kGF V m V

0 v

0 EI

0 kGF v

(9)

m F

1 2

q V z

q z

q

1 1

EI kGF kGF I

kGF kGF m

kFG kFG

EI

A B C D

E

0 0 0

0

M M

V

Q M

kg m3

2 4

200 GPa 77.5 GPa

7830

0.0097389 m

0.0001171 m

1.0 m 0.53066 E

G

F

I

L k

(10)

2 2

2

0

0

0

y y

s

EI kGF V K I

kGF V m V

K GJ I

,

V zzz

0 v

0

y

EI K

0 kGF v

0

K GJ

1 2 3

q V z

q z

q z

q

y y

s

EI K kGF kGF I

kGF kGF m

K GJ I

A B C D

1 1

1

y

kFG kFG

EI K

K GJ

(11)

8

4.584 10 kgm

y

I

(12)
(13)

Imagem

Fig. 2: p ik  i 0 0 0 ,Mi k ik i ikqzS zpq zq 0, ,lk kS zs z d

Referências

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