simulasi getaran m

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TUGAS GETARAN SISTEM MEKANIS

SIMULASI GETARAN M-DOF DENGAN ODE23 MATLAB

Oleh :

MUHAMMAD FADLIL ADHIM

2110100703

TEKNIK MESIN

INSTITUT TEKNOLOGI SEPULUH NOPEMBER

SURABAYA

2013



Si !l"#i $e%"&"' M-()* (e'$"' )(e23 MATLAB

1. Model Sistemk k k

c

m 1 m 2 m 3

x1 x2 x3

Fsin( wt)

gambar 1. Sistem yang dianalisa

x1 (0)=

0.1 x2 (

0)=

0.1 x3 (

0)=

0.1

x1 (0 )= 0.2 ´ x1 (0 )= 0.2 x1 (0 )= 0.2

M1=1kgM2=1kgM3=1kgF=50NK=100N/k C=10kg/sω=5s 1

2. Model Matematik m1

x1

kx1

c x1 m x1

k(m2-m1)



∑ F = m1 ´ x1 k ( x2 − x1 )− k x1 − c ´ x1 = m1 x1 m1 x1 = 2 k x1 − k x2 +c ´ x1

m2

x2

k(x2-x1)

mx2

k(m3-m2)

∑ F = m3 ´ x3

k ( x3 − x2 )− k ( x2 − x1 )= m2 x2

m2 x

2+2 k x

2− k x

3− k x

1= 0

m3

x3

k(x3-x2)

mx3

Fsin(wt)



∑ F = m3 ´ x3

3 − ¿ x2

x¿¿

(ωt )− k ¿ F sin ¿

m3 ´ x3 +k x3 − k x2 F sin (ωt )= 0

3. !ersia"an Model Matematik dengan #$nge K$ttaModel matematik r$nge k$tta %ar$s berbent$k di&erensial orde "er tama' maka dari it$'sem$a "ersamaan di atas di mani"$lasi agar da"at diselesaikan dengan metode r$ng k$ttaata$ ode23 di M()*(+.

x4 = x1

m1 x4 +C x4 +2 k x1 − k x2 = 0

x4 =− C x 4 − 2 k x1 +k x2

m1

x5 = x2

m2 x5 +2 k x2 − k x3 − k x1 = 0

x5 =− 2 k x2 − k x3 − k x1

m

x6 = x3

m3 x6 +k x3 − k x2 − F sin

ωt =0

x6 =k (− x3 + x2 )+ F sin ωt

m

,. Synta- di M()*(+di editor



function fv = funsys(t,x)fv=[x(4);x(5);x(6);((-10*x(4)-200*x(1)+100*x(2))/1);((-200*x(2)+100*(x(3)+x(1)))/1);((100*(-x(3)+x(2))+50*sin(5*t))/1)]

di ommand indo

[t,x] = od 23(!funsys,[0 20],[0"1;0"1;0"1;0"2;0"2;0"2]);#$ot(t,x(%,3), &-&,t,x(%,6), &--& )tit$ ( &'o$ution of v n d o$ u tion, .u = 1& );x$ $( &ti. t& );y$ $( &so$ution x& );$ nd( &x 3&, &x 6&)

5. ra&ik - dan x s t

grafik x 1 (t )

0 1 2 3 4 5 6-4

-3

-2

-1

0

1

2

3

4Solution o f van der Pol Equation, µ = 1

time t

s o l u t i o n

x

x1

grafik x 2 (t )



0 1 2 3 4 5 6-5

0

5


time t

s o l u t i o n

x

x2

grafik x 3 (t )

0 1 2 3 4 5 6-6

-4

-2

0

2

4

6


time t

s o l u t i o n

x

x3



grafik ´ x1 (t )

0 1 2 3 4 5 6-50

-40

-30

-20

-10

0

10

20

30

40


time t

s o l u t i o n

x

xdot 1

grafik ´ x2 (t )



0 1 2 3 4 5 6-150

-100

-50

0

50


time t

s o l u t i o n

x

xdot 2

grafik ´ x3 (t )

0 1 2 3 4 5 6-80

-60

-40

-20

0

20

40

60


time t

s o l u t i o n

x

xdot3

simulasi getaran m

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