Lat. Am. j. solids struct. vol.11 número6

(1)

(2)

(3)

0 0.2 0.4 0.6 0.8 1 1.2

0 0.05 0.1 0.15 0.2 0.25 0.3

P/P

cr1

w/L

Q=5000 kN Q=30000 kN Q=59897.6 kN Q=59897.7 kN Q=72000 kN Q=78553.7 kN Q=72000 kn Q=78553.7 kN Pcr1 Pcr2 Pu-wu Pc-wc

Q

cr2

Q

cr1

P

cr1

P

cr2

w

c

w

u

฀

√

(4)

√

(5)

0 0.5 1 1.5 2 2.5 3 3.5

3 4 5 6 7 8 9

10x 10

-3

rf

w

(m

)

Large Deformations small Deformations

P0=4500kN q0=Qc B=1 wn=18.32rad/s w(0)=0.0033102 m v(0)=0

alpha = 0.5

0 200 400 600 800 1000 1200 1400 1600 1800 2000

2 2.5 3 3.5 4 4.5

5x 10 -3

t (sec)

w

(m

)

0 20 40 60 80 100 120 140 160 180 200

-4 -2 0 2 4 6 8 10x 10

-3

t (sec)

w

(m

)

(6)

19952 1996 1997 1998 1999 2000

2.5 3 3.5 4 4.5

5x 10

-3

t (sec)

w

(m

)

2 2.5 3 3.5 4 4.5 5

x 10-3 -0.02

-0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

w (m)

v

(m

/s

)

1995 1995.5 19962 1996.5 1997 1997.5 1998 1998.5 1999 1999.5 2000

3 4 5 6 7x 10

6

t (sec)

P

(N

)

1995 1996 1997 1998 1999 2000

1.5085 1.509 1.5095 1.51 1.5105 1.511 1.5115x 10

8

t (sec)

K

(N

/m

)

(7)

0

0.5

1

1.5

2

2.5

3

3.5

0

0.02

0.04

0.06

0.08 rf

w

(m

)

0

0.5

1

1.5

2

2.5

3

3.5

3.3

3.35

3.4

3.45

3.5

3.55 x 10

-3

rf

w

(m

)

0

0.5

1

1.5

2

2.5

3

3.5

3

4

5

6

7 x 10

-3

rf

w

(m

)

0

0.5

1

1.5

2

2.5

3

0

0.01

0.02

0.03

0.04 rf

w

(m

)

0

0.5

1

1.5

2

2.5

3

3.5

0

0.02

0.04

0.06 rf

w

(m

)

0

0.5

1

1.5

2

2.5

3

3.5

0

0.005

0.01

0.015

0.02 rf

w

(m

)

q0=Qc

P0=4500kN

wn=18.3rad/s

w(0)=0.003317

v(0)=0

t=200s

alpha=0.75

alpha=0.5

alpha=0.1

alpha=1

alpha=0.25

(8)

0

0.2

0.4

0.6

0.8

1

1.2

0

0.5

1

1.5

2

2.5

α

r

_f

Min1

Max1

Min2

(9)

195 196 197 198 199 200

2 3 4 5 6 7x 10

6

t (sec)

P

(N

)

195 196 197 198 199 200

0.4 0.6 0.8 1 1.2 1.4 1.6x 10

8

t (sec)

K

(N

/m

)

195 196 197 198 199 200

-0.02 -0.01 0 0.01 0.02 0.03 0.04

t (sec)

w

(m

)

-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 -0.4

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

w (m)

v

(m

/s

)

(10)

195 196 197 198 199 200

-2 0 2 4 6 8 10 12 14x 10

-3

t (sec)

w

(m

)

0 0.005 0.01 0.015 0.02 -0.15 -0.1 -0.05 0 0.05 0.1

w (m)

v

(m

/s

)

1952 196 197 198 199 200

3 4 5 6 7x 10

6

t (sec)

P

(N

)

195 196 197 198 199 200

0.4 0.6 0.8 1 1.2 1.4 1.6x 10

8

t (sec)

K

(N

/m

)

wr = 12.938 rad/s wf = 25.876 rad/s n=2

rf=1.414 alpha=0.5

0 0.5 1 1.5 2 2.5 3

0.305 0.306 0.307 0.308 0.309

rf

w

(m

)

0 0.5 1 1.5 2 2.5

0.3 0.305 0.31 0.315 0.32

rf

w

(m

)

0 0.5 1 1.5 2 2.5

0.35 0.4 0.45 0.5

rf

w

(m

)

0 0.5 1 1.5 2 2.5

0 0.5 1 1.5

rf

w

(m

)

0 0.5 1 1.5 2 2.5

rf

w

(m

)

0 0.5 1 1.5 2 2.5

0 0.5 1 1.5 2 2.5 3

rf

w

(m)

(11)

0 0.5 1 1.5 2

1.4 1.6 1.8 2 2.2 2.4 2.6

t (sec)

w

(m

)

0 0.5 1 1.5 2

-1 0 1 2 3 4 5 6 7 8

t (sec)

v

(m

/s

)

1.4 1.6 1.8 2 2.2

-1 0 1 2 3 4 5 6 7

w (m)

v

(m

/s

)

0 0.5 1 1.5 2

0 1 2 3 4 5 6x 10

7

t (sec)

K

(N

/m

)

P0=0.65pcr1 q0=72000kN w(0)=1.3498m v(0)=0 wn=10.89rad/s t=1.759s

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5

0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98

rf

w

(m

)

(12)

495

496

497

498

499

500

0.75

0.8

0.85

0.9

0.95

1 t (sec)

w

(m

)

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1 -1.5

-1

-0.5

0

0.5

1

1.5 w (m)

v

(m

/s

)

495

496

497

498

499

500

1.105

1.11

1.115

1.12

1.125

1.13

1.135 x 10

9

t (sec)

P

(N

)

495

496

497

498

499

500

7.9

8

8.1

8.2

8.3

8.4

8.5 x 10

7

t (sec)

K(N

/m

)

P0= 0.45 Pcr1

alpha = 0.01

rf = 0.905

(13)

495 496 497 498 499 500

0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91

t (sec)

w

(m

)

0.84 0.86 0.88 0.9 0.92 0.94 -0.6 -0.4 -0.2 0 0.2 0.4

w (m)

v

(m

/s

)

495 496 497 498 499 500

1.105 1.11 1.115 1.12 1.125 1.13 1.135x 10

9

t (sec)

P

(N

)

495 496 497 498 499 500 8.3 8.32 8.34 8.36 8.38 8.4 8.42 8.44x 10

7

t (sec)

K

(N

/m

)

P0 = 0.45pcr1 alpha=0.01 rf = 1.993 wf=27.184rad/s wr=13.6 rad/s n=2

495 496 497 498 499 500

0.8 0.82 0.84 0.86 0.88 0.9 t (sec)

w

(m

)

0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 w (m)

v

(

m

/s

)

495 496 497 498 499 500

1.105 1.11 1.115 1.12 1.125 1.13 1.135x 10

9

t (sec)

P

(N

)

495 496 497 498 499 500

8.3 8.32 8.34 8.36 8.38 8.4 8.42 8.44x 10

7 t (sec)

K

(N

/m

)

(14)

B

l

3

_l

3

[

B B {

g_L g_L3

}

]

0 0.5 1 1.5 2 2.5

0 0.02 0.04 0.06

rf

w

(m

)

0 0.5 1 1.5 2 2.5 3

0 0.01 0.02 0.03 0.04

rf

w

(m

)

0 0.5 1 1.5 2 2.5

3.3 3.34

3.38x 10

-3

rf

w

(m

)

0 0.5 1 1.5 2 2.5 3

3 3.5 4 4.5

5x 10

-3

rf

w

(m

)

0 0.5 1 1.5 2 2.5 3

2 4 6 8

10x 10

-3

rf

w

(m

)

0 0.5 1 1.5 2 2.5 3

0 0.005 0.01 0.015 0.02 0.025

rf

w

(m

)

q0=Qc Pa1=4500kN wn=18.3rad/s w(0)=0.003317 v(0)=0 t=200s

alpha=0.75 xi=0.03

alpha=1.0 xi=0.03 alpha=0.5 xi=0.03 alpha=0.25

xi=0.03

alpha=0.1 xi=0.03 alpha=0.01

(15)

3

0

0.5

1

1.5

2

2.5

3

3.5

0

0.01

0.02

0.03

0.04 rf

w

(m

)

0

0.5

1

1.5

2

2.5

3

4

5

6

7 x 10

-3

rf

w

(m

)

0

0.5

1

1.5

2

2.5

3

0.005

0.01

0.015

0.02 rf

w

(m

)

0

0.5

1

1.5

2

2.5

3

3.5

0

0.02

0.04

0.06

0.08 rf

w

(m

)

0

0.5

1

1.5

2

2.5

3

3.5

0

0.02

0.04

0.06 rf

w

(m

)

0

0.5

1

1.5

2

2.5

3

3.3

3.35

3.4

3.45 x 10

-3

rf

w

(m

)

alpha = 0.1

P0 = 4500kN

q0=Qc

w(0)=0.0033m

v(0)=0

wn=17.335rad/s

t=200s

alpha =0.25

alpha = 0.01

alpha = 0.75

alpha = 1

(16)

0 0.2 0.4 0.6 0.8 1 1.2

0 0.5 1 1.5 2 2.5

α

r

f

Min1

Max1

Min2

(17)

195 196 197 198 199 200

-0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08

t (sec)

w

(m

)

-0.05 -0.025 0 0.025 0.05 0.075 0.1 0.125 0.15 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

w (m)

v

(m

/s

)

195 196 197 198 199 200 0

2 4 6 8 10x 10

6

t (sec)

P

(N

)

1952 196 197 198 199 200

4 6 8 10 12 14 16x 10

7

t (sec)

K

(N

/m

)

rf=0.554

wf = wr = 9.6rad/s

P0=4500kN

q0=Qc

alpha=1

195 196 197 198 199 200

0 2 4 6 8 10x 10

6

t (sec)

P

(N

)

1952 196 197 198 199 200 4 6 8 10 12 14 16x 10

7

t (sec)

K

(N

/m

)

195 196 197 198 199 200

-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

t (sec)

w

(m

)

(18)

1950 196 197 198 199 200

1 2 3 4 5 6 7x 10

-3

t (sec)

w

(m

)

0 1 2 3 4 5 6 7 8 9

x 10-3 -0.05 -0.025 0 0.025 0.05

w (m)

v

(m

/s

)

195 196 197 198 199 200

-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

t (sec)

w

(m

)

-0.02 0 0.02 0.04 0.06

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

w (m)

v

(m

/s

)

rf=1.294 w(0)=0.0037 m v(0)=0 rf=1.294 w(0)=0.0036 m v(0)=0

1951 196 197 198 199 200

2 3 4 5

6x 10

-3

t (sec)

w

(m

)

1 2 3 4 5 6 7 8

x 10-3

-0.05 -0.025 0 0.025 0.05

w (m)

v

(m

/s

)

195 196 197 198 199 200

-0.02 0 0.02 0.04 0.06

t (sec)

w

(m

)

-0.02 0 0.02 0.04 0.06

-0.4 -0.2 0 0.2 0.4

w (m)

v

(m

/s

)

1952 196 197 198 199 200

3 4 5

6x 10

-3

t (sec)

w

(m

)

2 3 4 5 6 7 8

x 10-3

(19)

0 0.5 1 1.5 2 2.5 3 3.5

0 0.02 0.04 0.06

rf

w

(m

)

0 0.5 1 1.5 2 2.5 3 3.5

0 0.01 0.02 0.03 0.04

rf

w

(m

)

0 0.5 1 1.5 2 2.5 3

3.3 3.31 3.32

3.33x 10

-3

rf

w

(m

)

0 0.5 1 1.5 2 2.5 3

3 3.5 4 4.5

5x 10

-3

rf

w

(m

)

0 0.5 1 1.5 2 2.5 3 3.5

0 0.01 0.02 0.03

rf

w

(m

)

0 0.5 1 1.5 2 2.5 3 3.5

2 4 6 8

10x 10

-3

rf

w

(m

)

P=4500kN q0=Qc wn=18.3352rad/s w(0)=0.0033093 v(0)=0 xi=0.03 alpha = 0.01

alpha = 0.1

alpha = 0.25 alpha = 0.5

(20)

(21)