68
3 Forced Vibration of Single Degree of Freedom System
Fig. 3.6 Rotating machine
Therefore,
F =
160
3
× 0.01 × 6.53
2
+
150
0.23
× 0.01
2
= 7.39 N
η =
ω
p
= 1
Therefore, the amplitude of the automobile is
x =
F
cω
=
7.39 × 3
6.53 × 160
= 0.021 m = 2.1 cm
3.3 Rotating Unbalance
Many machines, such as a turbine or an electric motor, are reciprocating in nature.
Unbalance in the machines causes vibration excitation, and the unbalance occurs
when the mass centre of the rotor does not coincide with the axis of rotation.
A rotating machine is shown in Fig. 3.6. Total mass of the machine is M. The
unbalance is represented by mass m having an eccentricity e. It is rotating with
angular velocity ω. The machine is constrained to move in the vertical direction
only. The displacement of the mass m from the static equilibrium position at any
instant of time is ( x + e sin ω t).
3 Forced Vibration of Single Degree of Freedom System
Fig. 3.6 Rotating machine
Therefore,
F =
160
3
× 0.01 × 6.53
2
+
150
0.23
× 0.01
2
= 7.39 N
η =
ω
p
= 1
Therefore, the amplitude of the automobile is
x =
F
cω
=
7.39 × 3
6.53 × 160
= 0.021 m = 2.1 cm
3.3 Rotating Unbalance
Many machines, such as a turbine or an electric motor, are reciprocating in nature.
Unbalance in the machines causes vibration excitation, and the unbalance occurs
when the mass centre of the rotor does not coincide with the axis of rotation.
A rotating machine is shown in Fig. 3.6. Total mass of the machine is M. The
unbalance is represented by mass m having an eccentricity e. It is rotating with
angular velocity ω. The machine is constrained to move in the vertical direction
only. The displacement of the mass m from the static equilibrium position at any
instant of time is ( x + e sin ω t).