38
2 Free Vibration of Single Degree of Freedom System
Fig. 2.20
Force–displacement relation
1
2
m2 ¨
x ˙
x +
1
2
k2x ˙
x = 0
or
m ¨
x + kx = 0
(2.45)
Equation (2.45) is same as Eq. (2.2).
2.6.1 Torsional Vibration of the SDF System
Applying the above energy principle, the free vibration equation for the torsion of
the shaft can be derived.
A vertical shaft with a disc attached at its lower end is shown in Fig. 2.21. The mass
moment of inertia of the shaft is neglected in the analysis. Let ρ be the mass density
of the material, I P be the mass moment of inertia of the disc, D be the diameter of
the disc, d be the diameter of the shaft, L be the length of the shaft, and t be the
Fig. 2.21 Torsional
vibration
2 Free Vibration of Single Degree of Freedom System
Fig. 2.20
Force–displacement relation
1
2
m2 ¨
x ˙
x +
1
2
k2x ˙
x = 0
or
m ¨
x + kx = 0
(2.45)
Equation (2.45) is same as Eq. (2.2).
2.6.1 Torsional Vibration of the SDF System
Applying the above energy principle, the free vibration equation for the torsion of
the shaft can be derived.
A vertical shaft with a disc attached at its lower end is shown in Fig. 2.21. The mass
moment of inertia of the shaft is neglected in the analysis. Let ρ be the mass density
of the material, I P be the mass moment of inertia of the disc, D be the diameter of
the disc, d be the diameter of the shaft, L be the length of the shaft, and t be the
Fig. 2.21 Torsional
vibration