94
3 Forced Vibration of Single Degree of Freedom System
Fig. 3.22 Response
variation
3.12 Response to SDF Systems to a General Type
of Forcing Function
A solution of SDF system to a general type of forcing function is sought in this section.
To start with, let us consider an undamped system subjected to an arbitrary external
force F(t). The external force F(t) can be divided into a large number of rectangular
pulses, each having an area F (τ ) dτ as shown in Fig. 3.23. The solution of the
problem is sought by the superimposition of the results obtained from individual
pulses.
In effect, it means finding out solution of one pulse and integrating the results
from time equal to zero to the instant when it is required to find the response.
We shall first consider the effect of a simple pulse having a force F(τ ) and duration
dτ . From the impulse-momentum equation, the velocity imparted to the system is
given by
˙
x τ =
F (τ ) dτ
m
(3.88)
Considering the system to be at rest before the application of the pulse, the equation
of motion is given by (from Eq. 2.11)
Fig. 3.23 General loading
3 Forced Vibration of Single Degree of Freedom System
Fig. 3.22 Response
variation
3.12 Response to SDF Systems to a General Type
of Forcing Function
A solution of SDF system to a general type of forcing function is sought in this section.
To start with, let us consider an undamped system subjected to an arbitrary external
force F(t). The external force F(t) can be divided into a large number of rectangular
pulses, each having an area F (τ ) dτ as shown in Fig. 3.23. The solution of the
problem is sought by the superimposition of the results obtained from individual
pulses.
In effect, it means finding out solution of one pulse and integrating the results
from time equal to zero to the instant when it is required to find the response.
We shall first consider the effect of a simple pulse having a force F(τ ) and duration
dτ . From the impulse-momentum equation, the velocity imparted to the system is
given by
˙
x τ =
F (τ ) dτ
m
(3.88)
Considering the system to be at rest before the application of the pulse, the equation
of motion is given by (from Eq. 2.11)
Fig. 3.23 General loading