40
2 Free Vibration of Single Degree of Freedom System
Angular frequency,
p =
k
I P
=
π d 4 G
32L
×
8g
W D 2 =
π Ggd 4
4 W D 2 L
(2.53)
The time period is
T = 2π
4W L D 2
π Ggd 4 = 4
D
d 2
π W L
Gg
(2.54)
Example 2.11 A system having a shaft consisting of two different diameters is shown
in Fig. 2.22. Find the time period of free torsional vibration.
The problem is similar to that of the previous problem, except that the definition
of stiffness is different in this case. If a torque T o is statically applied at the disc level
to produce an angular displacement, then the following relationship is valid
φ =
32T 0 L 1
π d
4
1 G
+
32T 0 L 2
π d
4
2 G
Fig. 2.22 Example 2.11
2 Free Vibration of Single Degree of Freedom System
Angular frequency,
p =
k
I P
=
π d 4 G
32L
×
8g
W D 2 =
π Ggd 4
4 W D 2 L
(2.53)
The time period is
T = 2π
4W L D 2
π Ggd 4 = 4
D
d 2
π W L
Gg
(2.54)
Example 2.11 A system having a shaft consisting of two different diameters is shown
in Fig. 2.22. Find the time period of free torsional vibration.
The problem is similar to that of the previous problem, except that the definition
of stiffness is different in this case. If a torque T o is statically applied at the disc level
to produce an angular displacement, then the following relationship is valid
φ =
32T 0 L 1
π d
4
1 G
+
32T 0 L 2
π d
4
2 G
Fig. 2.22 Example 2.11