5.5 Vibration Absorber
167
p
4
−
24,146 × 9.81
60
+
( 24,146 + 41,137) × 9.81
230
p
2
+
24,146 × 41,137 × 9.81
2
60 × 230
= 0
or
p
4
− 6732.33 p
2
+ 6,926,865 = 0
or
p
2
1,2 = 1267.55, 5464.78
or
p 1,2 = 35.60, 73.92 rad/s
5.6 Free Vibration of Two Degrees of Freedom System
with Viscous Damping
Two degrees of freedom damped system with viscous damping has been shown in
Fig. 5.9. The equations of motion of the two masses for free vibration are
m 1 ¨
x 1 + c 1 ˙
x 1 + c 2 ( ˙
x 1 − ˙
x 2 ) + k 1 x 1 + k 2 ( x 1 − x 2 ) = 0
m 2 ¨
x 2 + c 2 ( ˙
x 2 − ˙
x 1 ) + k 2 ( x 2 − x 1 ) = 0
(5.30)
Assuming solutions in the following form
x 1 = Ae
i pt
x 2 = Be
i pt
(5.31)
Fig. 5.9 Two degrees of
freedom system
167
p
4
−
24,146 × 9.81
60
+
( 24,146 + 41,137) × 9.81
230
p
2
+
24,146 × 41,137 × 9.81
2
60 × 230
= 0
or
p
4
− 6732.33 p
2
+ 6,926,865 = 0
or
p
2
1,2 = 1267.55, 5464.78
or
p 1,2 = 35.60, 73.92 rad/s
5.6 Free Vibration of Two Degrees of Freedom System
with Viscous Damping
Two degrees of freedom damped system with viscous damping has been shown in
Fig. 5.9. The equations of motion of the two masses for free vibration are
m 1 ¨
x 1 + c 1 ˙
x 1 + c 2 ( ˙
x 1 − ˙
x 2 ) + k 1 x 1 + k 2 ( x 1 − x 2 ) = 0
m 2 ¨
x 2 + c 2 ( ˙
x 2 − ˙
x 1 ) + k 2 ( x 2 − x 1 ) = 0
(5.30)
Assuming solutions in the following form
x 1 = Ae
i pt
x 2 = Be
i pt
(5.31)
Fig. 5.9 Two degrees of
freedom system