Ujian Semester Gempaa.xlsx
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LEONARDUS MALINO
6
m6 K6
5
m6= 1.962 m5= 0.981 m4= 1.962 m3= 19.62 m2= 9.81 m1= 10.3005 K6= 2000 K5= 1800 K4= 1200 K3= 800 K2= 700 K1= 500
m5 K5
4
m4 K4
3
m3 K3
2
m2 K2
1
m1 K1
(K1+K2 -K2 0 0 0 0
[K]=
[K]=
1200 -700 0 0 0 0
-K2 (K2+K3) -K3 0 0 0 -700 1500 -800 0 0 0
0 -800 2000 -1200 0 0
0 0 -1200 3000 -1800 -2000
0 -K3 (K3+K4) -K4 0 0 0 0 0 -1800 3800 -2000
0 0 -K4 (K4+K5) -K5 0 0 0 0 0 -2000 2000
=
500
(bawah)
(atas) (bawah)
(atas)
0 0 0 -K5 (K5+K6) -K6 2.4 -1.4 0 0 0 0
-1.4 3 -1.6 0 0 0
0 -1.6 4 -2.4 0 0
0 0 0 0 -K6 K6 0 0 -2.4 6 -3.6 -4
[ [K] - ω
2
[M] ] {фn} = 0
500
2.4 -1.4 0 0 0 0
-1.4 3 -1.6 0 0 0
0 -1.6 4 -2.4 0 0
0 0 -2.4 6 -3.6 -4
ω2 500
jadi,
ω2
=
500
λ
500
2.4 -1.4 0 0 0 0
-1.4 3 -1.6 0 0 0
0 -1.6 4 -2.4 0 0
0 0 -2.4 6 -3.6 -4
0 0 0 -3.6 7.6 -4
0 0 0 0 -4 4
500
2.40 -1.40 0.00 0.00 0.00 0.00
-1.40 3.00 -1.60 0.00 0.00 0.00
0.00 -1.60 4.00 -2.40 0.00 0.00
0.00 0.00 -2.40 6.00 -3.60 -4.00
0.00 0.00 0.00 -3.60 7.60 -4.00
0.00 0.00 0.00 0.00 -4.00 4.00
[ [K] - ω
2
[M] ] = 0 =
Misalkan λ =
[A] =
500
2.4-10.3005λ -1.40 0.00 -1.40 3-9.81λ -1.60 0.00 -1.60 4-19.62λ
0.00 0.00 -2.40
0.00 0.00 0.00
-
-
0.00 0.00 0.00
0 0 0 -3.6 7.6 -4
500λ
0 0 0 0 -4 4
-ω2
10.3005 0 0 0 0 0
0 9.81 0 0 0 0
10.30 0.00 0.00 0.00 0.00 0.00
0.00 9.81 0.00 0.00 0.00 0.00
0.00 0.00 19.62 0.00 0.00 0.00
0.00 0.00 0.00 1.96 0.00 0.00
10.3005λ 0.00 0.00 9.81λ 0.00 500 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 19.62λ 0.00 0.00 0.00
0.00 0.00 0.00 1.962λ 0.00 0.00
[A] =
500
0.00 0.00 0.00
-2.40 6-1.962λ 0.00 0.00
-3.60 0.00 -3.60 7.6-0.98 -4.00 -4.00 -4.00 4-1.962λ
(KOFAKTOR )
Determinan [A] = 0
2.4-10.3005λ
0.00 0.00 0.00
(bagian 1) 3-9.81λ -1.60 0.00 0.00 0.00
(bagian 2) -1.60 4-19.62λ -2.40 0.00 0.00
0.00 0.00 -2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
0.00 0.00 0.00 -4.00 4-1.962λ
+
Bagian 1 Bagian 1.1 2.4-10.3005λ
-1.60 0.00 0.00 4-19.62λ -2.40 0.00 -2.40 6-1.962λ -3.60 0.00 -3.60 7.6-0.981λ 0.00 -4.00 -4.00
Bagian 1.2 3-9.81λ
4-19.62λ -2.40 0.00 0.00
-2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
0.00 0.00 -4.00 4-1.962λ
+
BAGIAN 1.1 Bagian 1.1.1
2.4-10.3005λ -1.60
-1.60 0.00 0.00 0.00
-2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
Bagian 1.1.2 4-19.62λ
6-1.962λ -3.60 -4.00
4-19.62λ
6-1.962λ
7.6-0.981λ -4.00
4-19.62λ
6-1.962λ
7.6-0.981λx 4-1.962λ
3-9.81λ
-1.40
-1.40 0.00 0.00 0.00 0.00
-3.60 0.00 7.6-0.981λ -4.00 -4.00 4-1.962λ
+
3-9.81λ
-4.00 4-1.962λ
-2.40
BAGIAN 1.1.1 -4.00 4-1.962λ
+ -16 +
4-19.62λ
-3.60
-3.60 -4.00
4-19.62λ
-3.60
-3.60 x 4-1.962λ
-16
-2.40 -3.60 0.00 0.00 7.6-0.981λ -4.00 0.00 -4.00 4-1.962λ
BAGIAN 1.1.2 3-9.81λ
-2.40
-2.40 0.00 0.00
-3.60 0.00 7.6-0.981λ -4.00 -4.00 4-1.962λ
-2.40
-2.40
7.6-0.981λ -4.00
-2.40
-2.40
7.6-0.981λx 4-1.962λ
-4.00 4-1.962λ
+ -16 +
-2.40
-3.60
0.00 0.00
-4.00 4-1.962λ
-2.40
-3.60
0.00
x 4-1.962λ
0
Bagian 1.2 2.4-10.3005λ
-1.60
-1.60 0.00 0.00 0.00
-2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
0.00 0.00 -4.00 4-1.962λ
BAGIAN 1.2 Bagian 1.2.1
Bagian 1.2.2 -1.60
6-1.962λ -3.60 -4.00
-1.60
6-1.962λ
7.6-0.981λ -4.00
-1.60
6-1.962λ
7.6-0.981λx 4-1.962λ
-1.60
-3.60 0.00 7.6-0.981λ -4.00 -4.00 4-1.962λ
+
-1.60
-4.00 4-1.962λ
-2.40
BAGIAN 1.2.1 -4.00 4-1.962λ
+ -16 +
-1.60
-3.60
-3.60 -4.00
-1.60
-3.60
-3.60 x 4-1.962λ
-16
0.00 -3.60 0.00 0.00 7.6-0.981λ -4.00 0.00 -4.00 4-1.962λ
BAGIAN 1.2.2 -1.60
-2.40
0.00 0.00 0.00
-2.40
0.00
7.6-0.981λ -4.00
-2.40
0.00
7.6-0.981λx 4-1.962λ
-1.40
(bagian 2) -1.40 0.00 0.00 0.00 0.00
-1.60 4-19.62λ -2.40 0.00 0.00
-3.60 0.00 7.6-0.981λ -4.00 -4.00 4-1.962λ
-4.00 4-1.962λ
+ -16 +
0.00 0.00 -2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
-2.40
-3.60
0.00 0.00
-4.00 4-1.962λ
-2.40
-3.60
0.00
x 4-1.962λ
0.00 0.00 0.00 -4.00 4-1.962λ
Bagian 2 Bagian 2.1 -1.40
Bagian 2.2 -1.40
4-19.62λ -2.40 0.00 0.00
-2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
BAGIAN 2.1 Bagian 2.1.1 -1.40
0
0.00 0.00 -4.00 4-1.962λ
+
-1.40
-1.60
0.00 0.00 0.00 0.00
-2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
Bagian 2.1.2 4-19.62λ
6-1.962λ -3.60
-3.60 7.6-0.981λ
0.00 -4.00
+
-1.40
-2.40
-2.40 -3.60 0.00 0.00 7.6-0.981λ -4.00
-1.40
4-19.62λ
-1.40 -4.00
-4.00
4-1.962λ
-4.00 4-1.962λ
+
-2.40 0.00
-4.00
4-1.962λ
BAGIAN 2.1.1 4-19.62λ
6-1.962λ
7.6-0.981λ -4.00
4-19.62λ
6-1.962λ
7.6-0.981λx 4-1.962λ
-16 +
4-19.62λ
-3.60
-3.60 -4.00
-4.00 4-1.962λ
4-19.62λ
-3.60
-3.60 x 4-1.962λ
-2.40
-3.60
0.00 0.00
-4.00 4-1.962λ
-2.40
-3.60
0.00
x 4-1.962λ
-16
BAGIAN 2.1.2 -1.40
-2.40
-2.40 0.00 0.00
-3.60 0.00 7.6-0.981λ -4.00 -4.00 4-1.962λ
-2.40
-2.40
7.6-0.981λ -4.00
-2.40
-2.40
7.6-0.981λx 4-1.962λ
-4.00 4-1.962λ
+ -16 +
0
Bagian 2.2 -1.40
-1.60
0.00 0.00 0.00 0.00
-2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
BAGIAN 2.2 Bagian 2.2.1 -1.60
0.00 0.00 -4.00 4-1.962λ
Bagian 2.2.2 0.00
6-1.962λ -3.60
-3.60 7.6-0.981λ
0.00 -4.00
+
-1.60
-2.40
0.00 -3.60 0.00 0.00 7.6-0.981λ -4.00
-1.60
0.00
-1.60 -4.00
-4.00
-2.40
4-1.962λ
0.00
-4.00
BAGIAN 2.2.1 0.00
6-1.962λ 0.00 6-1.962λ
7.6-0.981λ -4.00 -4.00 4-1.962λ 7.6-0.981λ x 4-1.962λ
+
0.00
-16 +
-3.60 0.00
-3.60
-3.60 -4.00 -4.00 4-1.962λ -3.60 x 4-1.962λ
-16
BAGIAN 2.2.2 -1.60
-2.40
-2.40
0.00
-3.60 0.00 7.6-0.981λ -4.00 -4.00 4-1.962λ
7.6-0.981λ -4.00 -4.00 4-1.962λ
0.00 7.6-0.981λ x 4-1.962λ
-2.40 maka didapat : Bagian 1 Bagian 1.1 Bagian 1.1.1 Bagian 1.1.2 Bagian 1.2 Bagian 1.2.1 Bagian 1.2.2 Bagian 2 Bagian 2.1 Bagian 2.1.1
0.00 0.00 0.00
= = = = = = = = = =
+ -16 +
2.4-10.3005λ 3-9.81λ 4-19.62λ 6-1.962λ 7.6-0.981λ -2.40 -2.40 7.6-0.981λ -1.60 -1.60 6-1.962λ 7.6-0.981λ -2.40 0.00 7.6-0.981λ -1.40 -1.40 4-19.62λ 6-1.962λ 7.6-0.981λ
-2.40
-3.60 -2.40
-3.60
0.00 -4.00 0.00 4-1.962λ 0.00 x 4-1.962λ
0
4-1.962λ 4-1.962λ
-16.00 4-19.62λ -16.00 -2.40
-3.60 -3.60
-3.60 0.00
4-1.962λ -16.00 4-1.962λ 0.00
4-1.962λ 4-1.962λ
-16.00 -16.00
-3.60 -3.60
-3.60 0.00
4-1.962λ -16.00 4-1.962λ 0.00
4-1.962λ
-16.00 4-19.62λ
-3.60
-3.60
4-1.962λ -16.00
-1.60 -2.40
4-1.962λ
Bagian 2.1.2 Bagian 2.2 Bagian 2.2.1 Bagian 2.2.2
= = = =
A B
= =
-2.40 -1.60 0.00 -2.40
7.6-0.981λ
4-1.962λ
-16.00
-2.40
-3.60
0.00
4-1.962λ
6-1.962λ 7.6-0.981λ 0.00 7.6-0.981λ
4-1.962λ 4-1.962λ
-16.00 -16.00
0.00 -2.40
-3.60 -3.60
-3.60 0.00
4-1.962λ -16.00 4-1.962λ 0.00
Bagian 1 ( bagian 1.1(bagian 1.1.1 + 1.1.2) + bagian 1.2 (bagian 1.2.1 + bagian 1.2.2)) Bagian 2 ( bagian 2.1(bagian 2.1.1 + 2.1.2) + bagian 2.2 (bagian 2.2.1 + bagian 2.2.2))
Maka di peroleh =
1102346.36787654 λ6
-2.40
HITUNGAN MANUAL
A+B
+
821346.65 λ5
+
650276.65 λ4
+
375690 λ3
+
Selanjutnya menggunakan Aplikasi Equaton Solver untuk mencari nilai eigen ( download di app store) Dengan demikian didapat nilai Eigen (λ): λ = λ
2
=
λ3 = λ4 = λ5 = λ6 =
400 *ω2 ω 12 =
492.000
ω 22 =
224.000
ω3
0.00
2 =
22.400
ω 42 =
93.800
ω 52 =
93.824
ω 62 =
186.000
1.23
atau liat online, ada bnyk cara
0.56
Didapatka n dari 0.2345 aplikasi "Equation 0.23456 Solver" 0.056
0.465
ω1/2 ω1 = 22.181073 ω2 = 14.96663
T= 2π / ω
T1 =
0.28326787
T2 =
0.4198129771
ω3 4.7328638 ω4 = 9.68504
T3
1.3275651989
T4 =
0.6487516108
ω1 = 9.686279 ω2 = 13.638182
T5
0.6486686308
=
=
=
T6 =
0.4607054992
f = 1/T
F1 = 3.530227 F2 = 2.382013 F3 = 0.753259 F4 = 1.541422 F3 = 1.541619 F4 = 2.170584
-10638 λ2
+
3456.435 λ
+
51
m6= m5= m4= m3= m2= m1= K6= K5= K4= K3= K2= K1=
200 100 200 2000 1000 1050 1000 500 700 800 280 450
0 0 0 0 -K6 K6 0 0 0 -3.6 7.6 -4
0 0 0 0 -4 4
0 0 19.62 0 0 0
0 0 0 0 0 0 0 0 0 1.962 0 0 0 0.981 0 0 0 1.962
0.00 0.00 0.00 0.00 0.98 0.00
0.00 0.00 0.00 0.00 0.00 1.96
=
0
0.00 0.00 0.00 0.00 0.981λ 0.00
0.00 0.00 0.00 0.00 0.00 1.962λ
=
0
=
0
0.00 0.00 0.00 -4.00 4-1.962λ
0.00 0.00 -4.00 4-1.962λ
+
0
0.00 0.00 -4.00 4-1.962λ
=
0
6
m6 K6
5
m6= 1.962 m5= 0.981 m4= 1.962 m3= 19.62 m2= 9.81 m1= 10.3005 K6= 2000 K5= 1800 K4= 1200 K3= 800 K2= 700 K1= 500
m5 K5
4
m4 K4
3
m3 K3
2
m2 K2
1
m1 K1
(K1+K2 -K2 0 0 0 0
[K]=
[K]=
1200 -700 0 0 0 0
-K2 (K2+K3) -K3 0 0 0 -700 1500 -800 0 0 0
0 -800 2000 -1200 0 0
0 0 -1200 3000 -1800 -2000
0 -K3 (K3+K4) -K4 0 0 0 0 0 -1800 3800 -2000
0 0 -K4 (K4+K5) -K5 0 0 0 0 0 -2000 2000
=
500
(bawah)
(atas) (bawah)
(atas)
0 0 0 -K5 (K5+K6) -K6 2.4 -1.4 0 0 0 0
-1.4 3 -1.6 0 0 0
0 -1.6 4 -2.4 0 0
0 0 0 0 -K6 K6 0 0 -2.4 6 -3.6 -4
[ [K] - ω
2
[M] ] {фn} = 0
500
2.4 -1.4 0 0 0 0
-1.4 3 -1.6 0 0 0
0 -1.6 4 -2.4 0 0
0 0 -2.4 6 -3.6 -4
ω2 500
jadi,
ω2
=
500
λ
500
2.4 -1.4 0 0 0 0
-1.4 3 -1.6 0 0 0
0 -1.6 4 -2.4 0 0
0 0 -2.4 6 -3.6 -4
0 0 0 -3.6 7.6 -4
0 0 0 0 -4 4
500
2.40 -1.40 0.00 0.00 0.00 0.00
-1.40 3.00 -1.60 0.00 0.00 0.00
0.00 -1.60 4.00 -2.40 0.00 0.00
0.00 0.00 -2.40 6.00 -3.60 -4.00
0.00 0.00 0.00 -3.60 7.60 -4.00
0.00 0.00 0.00 0.00 -4.00 4.00
[ [K] - ω
2
[M] ] = 0 =
Misalkan λ =
[A] =
500
2.4-10.3005λ -1.40 0.00 -1.40 3-9.81λ -1.60 0.00 -1.60 4-19.62λ
0.00 0.00 -2.40
0.00 0.00 0.00
-
-
0.00 0.00 0.00
0 0 0 -3.6 7.6 -4
500λ
0 0 0 0 -4 4
-ω2
10.3005 0 0 0 0 0
0 9.81 0 0 0 0
10.30 0.00 0.00 0.00 0.00 0.00
0.00 9.81 0.00 0.00 0.00 0.00
0.00 0.00 19.62 0.00 0.00 0.00
0.00 0.00 0.00 1.96 0.00 0.00
10.3005λ 0.00 0.00 9.81λ 0.00 500 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 19.62λ 0.00 0.00 0.00
0.00 0.00 0.00 1.962λ 0.00 0.00
[A] =
500
0.00 0.00 0.00
-2.40 6-1.962λ 0.00 0.00
-3.60 0.00 -3.60 7.6-0.98 -4.00 -4.00 -4.00 4-1.962λ
(KOFAKTOR )
Determinan [A] = 0
2.4-10.3005λ
0.00 0.00 0.00
(bagian 1) 3-9.81λ -1.60 0.00 0.00 0.00
(bagian 2) -1.60 4-19.62λ -2.40 0.00 0.00
0.00 0.00 -2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
0.00 0.00 0.00 -4.00 4-1.962λ
+
Bagian 1 Bagian 1.1 2.4-10.3005λ
-1.60 0.00 0.00 4-19.62λ -2.40 0.00 -2.40 6-1.962λ -3.60 0.00 -3.60 7.6-0.981λ 0.00 -4.00 -4.00
Bagian 1.2 3-9.81λ
4-19.62λ -2.40 0.00 0.00
-2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
0.00 0.00 -4.00 4-1.962λ
+
BAGIAN 1.1 Bagian 1.1.1
2.4-10.3005λ -1.60
-1.60 0.00 0.00 0.00
-2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
Bagian 1.1.2 4-19.62λ
6-1.962λ -3.60 -4.00
4-19.62λ
6-1.962λ
7.6-0.981λ -4.00
4-19.62λ
6-1.962λ
7.6-0.981λx 4-1.962λ
3-9.81λ
-1.40
-1.40 0.00 0.00 0.00 0.00
-3.60 0.00 7.6-0.981λ -4.00 -4.00 4-1.962λ
+
3-9.81λ
-4.00 4-1.962λ
-2.40
BAGIAN 1.1.1 -4.00 4-1.962λ
+ -16 +
4-19.62λ
-3.60
-3.60 -4.00
4-19.62λ
-3.60
-3.60 x 4-1.962λ
-16
-2.40 -3.60 0.00 0.00 7.6-0.981λ -4.00 0.00 -4.00 4-1.962λ
BAGIAN 1.1.2 3-9.81λ
-2.40
-2.40 0.00 0.00
-3.60 0.00 7.6-0.981λ -4.00 -4.00 4-1.962λ
-2.40
-2.40
7.6-0.981λ -4.00
-2.40
-2.40
7.6-0.981λx 4-1.962λ
-4.00 4-1.962λ
+ -16 +
-2.40
-3.60
0.00 0.00
-4.00 4-1.962λ
-2.40
-3.60
0.00
x 4-1.962λ
0
Bagian 1.2 2.4-10.3005λ
-1.60
-1.60 0.00 0.00 0.00
-2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
0.00 0.00 -4.00 4-1.962λ
BAGIAN 1.2 Bagian 1.2.1
Bagian 1.2.2 -1.60
6-1.962λ -3.60 -4.00
-1.60
6-1.962λ
7.6-0.981λ -4.00
-1.60
6-1.962λ
7.6-0.981λx 4-1.962λ
-1.60
-3.60 0.00 7.6-0.981λ -4.00 -4.00 4-1.962λ
+
-1.60
-4.00 4-1.962λ
-2.40
BAGIAN 1.2.1 -4.00 4-1.962λ
+ -16 +
-1.60
-3.60
-3.60 -4.00
-1.60
-3.60
-3.60 x 4-1.962λ
-16
0.00 -3.60 0.00 0.00 7.6-0.981λ -4.00 0.00 -4.00 4-1.962λ
BAGIAN 1.2.2 -1.60
-2.40
0.00 0.00 0.00
-2.40
0.00
7.6-0.981λ -4.00
-2.40
0.00
7.6-0.981λx 4-1.962λ
-1.40
(bagian 2) -1.40 0.00 0.00 0.00 0.00
-1.60 4-19.62λ -2.40 0.00 0.00
-3.60 0.00 7.6-0.981λ -4.00 -4.00 4-1.962λ
-4.00 4-1.962λ
+ -16 +
0.00 0.00 -2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
-2.40
-3.60
0.00 0.00
-4.00 4-1.962λ
-2.40
-3.60
0.00
x 4-1.962λ
0.00 0.00 0.00 -4.00 4-1.962λ
Bagian 2 Bagian 2.1 -1.40
Bagian 2.2 -1.40
4-19.62λ -2.40 0.00 0.00
-2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
BAGIAN 2.1 Bagian 2.1.1 -1.40
0
0.00 0.00 -4.00 4-1.962λ
+
-1.40
-1.60
0.00 0.00 0.00 0.00
-2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
Bagian 2.1.2 4-19.62λ
6-1.962λ -3.60
-3.60 7.6-0.981λ
0.00 -4.00
+
-1.40
-2.40
-2.40 -3.60 0.00 0.00 7.6-0.981λ -4.00
-1.40
4-19.62λ
-1.40 -4.00
-4.00
4-1.962λ
-4.00 4-1.962λ
+
-2.40 0.00
-4.00
4-1.962λ
BAGIAN 2.1.1 4-19.62λ
6-1.962λ
7.6-0.981λ -4.00
4-19.62λ
6-1.962λ
7.6-0.981λx 4-1.962λ
-16 +
4-19.62λ
-3.60
-3.60 -4.00
-4.00 4-1.962λ
4-19.62λ
-3.60
-3.60 x 4-1.962λ
-2.40
-3.60
0.00 0.00
-4.00 4-1.962λ
-2.40
-3.60
0.00
x 4-1.962λ
-16
BAGIAN 2.1.2 -1.40
-2.40
-2.40 0.00 0.00
-3.60 0.00 7.6-0.981λ -4.00 -4.00 4-1.962λ
-2.40
-2.40
7.6-0.981λ -4.00
-2.40
-2.40
7.6-0.981λx 4-1.962λ
-4.00 4-1.962λ
+ -16 +
0
Bagian 2.2 -1.40
-1.60
0.00 0.00 0.00 0.00
-2.40 0.00 6-1.962λ -3.60 -3.60 7.6-0.981λ -4.00 -4.00
BAGIAN 2.2 Bagian 2.2.1 -1.60
0.00 0.00 -4.00 4-1.962λ
Bagian 2.2.2 0.00
6-1.962λ -3.60
-3.60 7.6-0.981λ
0.00 -4.00
+
-1.60
-2.40
0.00 -3.60 0.00 0.00 7.6-0.981λ -4.00
-1.60
0.00
-1.60 -4.00
-4.00
-2.40
4-1.962λ
0.00
-4.00
BAGIAN 2.2.1 0.00
6-1.962λ 0.00 6-1.962λ
7.6-0.981λ -4.00 -4.00 4-1.962λ 7.6-0.981λ x 4-1.962λ
+
0.00
-16 +
-3.60 0.00
-3.60
-3.60 -4.00 -4.00 4-1.962λ -3.60 x 4-1.962λ
-16
BAGIAN 2.2.2 -1.60
-2.40
-2.40
0.00
-3.60 0.00 7.6-0.981λ -4.00 -4.00 4-1.962λ
7.6-0.981λ -4.00 -4.00 4-1.962λ
0.00 7.6-0.981λ x 4-1.962λ
-2.40 maka didapat : Bagian 1 Bagian 1.1 Bagian 1.1.1 Bagian 1.1.2 Bagian 1.2 Bagian 1.2.1 Bagian 1.2.2 Bagian 2 Bagian 2.1 Bagian 2.1.1
0.00 0.00 0.00
= = = = = = = = = =
+ -16 +
2.4-10.3005λ 3-9.81λ 4-19.62λ 6-1.962λ 7.6-0.981λ -2.40 -2.40 7.6-0.981λ -1.60 -1.60 6-1.962λ 7.6-0.981λ -2.40 0.00 7.6-0.981λ -1.40 -1.40 4-19.62λ 6-1.962λ 7.6-0.981λ
-2.40
-3.60 -2.40
-3.60
0.00 -4.00 0.00 4-1.962λ 0.00 x 4-1.962λ
0
4-1.962λ 4-1.962λ
-16.00 4-19.62λ -16.00 -2.40
-3.60 -3.60
-3.60 0.00
4-1.962λ -16.00 4-1.962λ 0.00
4-1.962λ 4-1.962λ
-16.00 -16.00
-3.60 -3.60
-3.60 0.00
4-1.962λ -16.00 4-1.962λ 0.00
4-1.962λ
-16.00 4-19.62λ
-3.60
-3.60
4-1.962λ -16.00
-1.60 -2.40
4-1.962λ
Bagian 2.1.2 Bagian 2.2 Bagian 2.2.1 Bagian 2.2.2
= = = =
A B
= =
-2.40 -1.60 0.00 -2.40
7.6-0.981λ
4-1.962λ
-16.00
-2.40
-3.60
0.00
4-1.962λ
6-1.962λ 7.6-0.981λ 0.00 7.6-0.981λ
4-1.962λ 4-1.962λ
-16.00 -16.00
0.00 -2.40
-3.60 -3.60
-3.60 0.00
4-1.962λ -16.00 4-1.962λ 0.00
Bagian 1 ( bagian 1.1(bagian 1.1.1 + 1.1.2) + bagian 1.2 (bagian 1.2.1 + bagian 1.2.2)) Bagian 2 ( bagian 2.1(bagian 2.1.1 + 2.1.2) + bagian 2.2 (bagian 2.2.1 + bagian 2.2.2))
Maka di peroleh =
1102346.36787654 λ6
-2.40
HITUNGAN MANUAL
A+B
+
821346.65 λ5
+
650276.65 λ4
+
375690 λ3
+
Selanjutnya menggunakan Aplikasi Equaton Solver untuk mencari nilai eigen ( download di app store) Dengan demikian didapat nilai Eigen (λ): λ = λ
2
=
λ3 = λ4 = λ5 = λ6 =
400 *ω2 ω 12 =
492.000
ω 22 =
224.000
ω3
0.00
2 =
22.400
ω 42 =
93.800
ω 52 =
93.824
ω 62 =
186.000
1.23
atau liat online, ada bnyk cara
0.56
Didapatka n dari 0.2345 aplikasi "Equation 0.23456 Solver" 0.056
0.465
ω1/2 ω1 = 22.181073 ω2 = 14.96663
T= 2π / ω
T1 =
0.28326787
T2 =
0.4198129771
ω3 4.7328638 ω4 = 9.68504
T3
1.3275651989
T4 =
0.6487516108
ω1 = 9.686279 ω2 = 13.638182
T5
0.6486686308
=
=
=
T6 =
0.4607054992
f = 1/T
F1 = 3.530227 F2 = 2.382013 F3 = 0.753259 F4 = 1.541422 F3 = 1.541619 F4 = 2.170584
-10638 λ2
+
3456.435 λ
+
51
m6= m5= m4= m3= m2= m1= K6= K5= K4= K3= K2= K1=
200 100 200 2000 1000 1050 1000 500 700 800 280 450
0 0 0 0 -K6 K6 0 0 0 -3.6 7.6 -4
0 0 0 0 -4 4
0 0 19.62 0 0 0
0 0 0 0 0 0 0 0 0 1.962 0 0 0 0.981 0 0 0 1.962
0.00 0.00 0.00 0.00 0.98 0.00
0.00 0.00 0.00 0.00 0.00 1.96
=
0
0.00 0.00 0.00 0.00 0.981λ 0.00
0.00 0.00 0.00 0.00 0.00 1.962λ
=
0
=
0
0.00 0.00 0.00 -4.00 4-1.962λ
0.00 0.00 -4.00 4-1.962λ
+
0
0.00 0.00 -4.00 4-1.962λ
=
0
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