mencari frekuensi natural (MDOF)2 lantai

diketahui :E : 100000 kg/cm2 1000000000 kg/m2q1 : 2000 kg/mq2 : 1000 kg/m

jawab :> mencari I (Inersia) :

I1 = 1/12.b.h^3 I2 =0.00213333333 m4

> berat (w) :

w1 = q1.L w2 =12000 kg

> massa (m) :

m1 = w1/g m2 =1223.24159021 kg.s2/m

> kekakuan (k) :

k1 = 2.12.E.I1/h1^3 k2 =409600 kg/m

unit m = 10 kg.s2/m unit k => matrik m :

m1 0=

122.32415902 00 m2 0 61.162079510703

> matrik k

k1+k2 (-k2)=

66272.5 -25312.5(-k2) k2 -25312.5 25312.5

> persamaan eigen problem :

(k1+k2)-m1 (-k2)-0=

66272.5 -

(-k2)-0 k2-m2=

-25312.5

> penyederhanaan :

66272.5 - 122.324159021 λ + ( -25312.52.61817283951 - 0.0048325594 λ

> subtitusi persamaaan (6) ke persamaan (5) :

-25312.5 + 25312.5 - 61.162079510703-25312.5 + 66272.5 -122.3241590214

40960 -282.457054404 λ + 0.2955693804 λ^2 = 0

> menentukan akar persaan :

> pers. (7) = -3.54E-06 λ1 = 178.26792649808λ2 = 777.36913597968

244.320810927 rad/s567.204993597 rad/s

mode 1 = 178 m0de 2 = 7771 1

1.75668250116 -1.1385096615

> mencari periode (T) :

1 1.75668250116 x 122.324159021410

122.324159021 107.442354811 x 122.324159021410

1 1.7566825012 x

122.324159021 107.44235481x

(40985312,5-50,96839959λ).φ1 + (-25312,5.φ2) = 0(-25312,5.φ1) + (25312,5-81,54943935λ).φ2 = 0

> misal : φ1 = 1

φ2 =

ω1 =

ω2 =

nilai fungsi φinilai φi

φ1 = 1

φ2 = (2,6182-0,0048λ)

P1 = (φm1)x[m]xm1

M1 = (φm1T)x[m]x(φm1)xm1

x

38050.919095

T= P1/M1 0.39324148368 s

> frekuensi natural 1:

2.54296670494 Hzω =1/T

g : 9.81 m/s2 balok 1 : 40x40 mL : 6 m balok 2 : 30x30 mh1 : 5 mh2 : 4 m

1/12.b.h^30.000675 m4

q2.L6000 kg

w2/g611.620795107 kg.s2/m

2.12.E.I1/h2^3253125 kg/m

10 kg/m

…persamaan (1)

…persamaan (2)

122.324159021 λ ) ( -25312.5x

φ1

) ( 25312.5 - 61.1620795 λx

φ2

…persamaan (4)…persamaan (5)

…persamaan (6)

λ x 2.61817283951 - 0.00483256 λλ -160.13289538 λ + 0.295569… persamaan (7)

1500

0 x 122.32415902161.1620795107 0

= 14963.2

122.324159021 0 x 1 x 122.32420 61.16208 1.756683

1x

122.324159021

).φ2 = 0

λ^2

1.75668250116x

=0 …persamaan (3)

=0