5.2 Free Vibration of Undamped Two Degrees of Freedom Systems
159
Fig. 5.3 Mode shapes of Example 5.1
x 2 = 1.366 D 1 cos 0.518
k
m
t + 1.366 D 2 sin 0.518
k
m
t
− 0.366 D 3 cos 1.93
k
m
t − 0.366 D 4 sin 1.93
k
m
t
The normal mode shape has been given in Fig. 5.3.
5.3 Torsional Vibration of Two Degrees of Freedom System
Consider two rotors having mass moment of inertia I 1 and I 2 respectively. They are
separated by a distance L. Torsional displacements of the two rotors be θ 1 and θ 2
(Fig. 5.4).
Two equations of motion for the system are
I 1 ¨
θ 1 + k (θ 1 − θ 2 ) = 0
I 2 ¨
θ 2 + k (θ 2 − θ 1 ) = 0
(5.12)
Fig. 5.4 A two rotor system
159
Fig. 5.3 Mode shapes of Example 5.1
x 2 = 1.366 D 1 cos 0.518
k
m
t + 1.366 D 2 sin 0.518
k
m
t
− 0.366 D 3 cos 1.93
k
m
t − 0.366 D 4 sin 1.93
k
m
t
The normal mode shape has been given in Fig. 5.3.
5.3 Torsional Vibration of Two Degrees of Freedom System
Consider two rotors having mass moment of inertia I 1 and I 2 respectively. They are
separated by a distance L. Torsional displacements of the two rotors be θ 1 and θ 2
(Fig. 5.4).
Two equations of motion for the system are
I 1 ¨
θ 1 + k (θ 1 − θ 2 ) = 0
I 2 ¨
θ 2 + k (θ 2 − θ 1 ) = 0
(5.12)
Fig. 5.4 A two rotor system