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地盤災害システム論 前田研究室 maedalab Pendulum

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(1)

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IIISSSAAASSSTTTEEERRR

P

P

P

RRREEEVVVEEENNNTTTIIIOOONNN

S

S

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YYYSSSTTTEEEMMM 1/3

G

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EEEOOOTTTEEECCCHHHNNNIIICCCAAALLL

E

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NNNGGGIIINNNEEEEEERRRIIINNNGGG

L

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AAABBB... How to use ‘Pendulum.for’ : free pendulum and swing

Pendulum.for

Input file: Pendulum.idt Output files:

Pendulum.thd

aext: amplitude of supporting point

xl: length of string

xmass: mass of spindle

Origin of arch displacement Origin of angle displacement

(counter-clockwise)

roeo0: ratio of external omega (omegae) to natural

omega (omega0)

コメント [A1]: Time history of

(2)

G

G

G

EEEOOO---

D

D

D

IIISSSAAASSSTTTEEERRR

P

P

P

RRREEEVVVEEENNNTTTIIIOOONNN

S

S

S

YYYSSSTTTEEEMMM 2/3

G

G

G

EEEOOOTTTEEECCCHHHNNNIIICCCAAALLL

E

E

E

NNNGGGIIINNNEEEEEERRRIIINNNGGG

L

L

L

AAABBB... Pendulum.idt

c

c xl : length of string c xmass : mass of obejects winging

c viscc : coefficient of viscocity -> vicoscity force = -viscc*vel c theata0 : initial angle displacement

c tinc : time increment for calculation c nstep : number of calculation steps c iprint : skip number of output

c results will be output at step = (j-1)*iprint j=1, nstep c deltan : delta in Newmark's beta method

c betan : beta in Newmark's beta method c aext : amplitude of supporting point c roeo0 : ratio omegae / omega0

/parameter/ 10.0 5.0 0.0 30.0 0.001 100000 1 0.5 0.5 0.5 2.0

Note:

1. To hold stability condition for numerical analysis by Newmark’s method

If betan < 0.25 tinc must be smaller than 2.d0/( dsqrt(1.d0-4.d0*betan)*dsqrt(grav/xl) )

2. omega0=

2

π

T

N, omegae: angle frequency of vibration of supporting point with amplitude aext

g

xl

T

N

=

2

π

roeo0= omegae/ omega0 2 is best: refer to note in lecture.

3. if theata0 is small and viscc is zero, the period of pendulum analyzed must be coincident with TN.

4. if aext is set to be zero, it is free swing.

(3)

G

G

G

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D

D

D

IIISSSAAASSSTTTEEERRR

P

P

P

RRREEEVVVEEENNNTTTIIIOOONNN

S

S

S

YYYSSSTTTEEEMMM 3/3

G

G

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EEEOOOTTTEEECCCHHHNNNIIICCCAAALLL

E

E

E

NNNGGGIIINNNEEEEEERRRIIINNNGGG

L

L

L

AAABBB... ‘thd’ files: Pendulum.thd

istep, time, disp, theata, vel, acc

0 0.0000000E+00, 0.5235988E+01, 0.3000000E+02, 0.0000000E+00, -0.4900000E+01

1 0.1000000E-02, 0.5235985E+01, 0.2999998E+02, -0.5155674E-02, -0.5411348E+01

2 0.2000000E-02, 0.5235977E+01, 0.2999994E+02, -0.1082265E-01, -0.5922608E+01

---

aext=0: free vibration of pendulum

0 20 40 60 80 100

-60 -30 0 30 60

time (s)

an

g

le (

d

eg

.)

aext=0.5: forced vibration of pendulum (roeo0=2.0)

0 20 40 60 80 100

-60 -30 0 30 60

time (s)

an

g

le (d

eg

.)

コメント [A3]: Step number,

duration time, displacement

from xl*theata0 which is arch

displacement, angle

参照

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