Civil Insight: A Technical Magazine Volume 3 | Page 33

Bhatt M.R.
Civil Insight (2019) 29-36
3.2) Response of damped system at ࣓ = ࣓ ࢔
Considering the fundamental natural period T n is 2 seconds, the natural and forcing frequency will be equal
to ߱ = ߱ ௡ = 3.142 rad/sec. The various parameters assumed for the study are listed in Table 1.
Table 1. Considered various parameters for the response determination
Particular Symbol Considered Value
Initial displacement and Velocity ‫ݑ‬ሺͲሻ= ‫ݑ‬ሶ ሺͲሻ 0
Damping frequency ߱ ௗ 3.142
Damping ration coefficient ߦ 0.05
Natural Period
Natural Frequency
Exponential Factor T n 2
3.142
2.718
߱ = ߱ ௡
e
The responses of the damped system are presented in Fig. 4 and Fig. 5 for shorter and longer time durations
respectively.
15.0
Resonant Response
Line for (1/2ξ)
Line for (-1/2ξ)
10.0
5.0
0.0
0
4
8
12
16
20
24
28
32
36
-5.0
-10.0
-15.0
Time (sec)
Fig. 4. Response of damped system with ߦ = 0.05 to sinusoidal force of ߱ = ߱ ௡ and initial displacement
and velocity as zero
The Fig. 4 and Fig. 5 show the response of visously damped (ߦ = 5%) resonant frequency cases for different
time periods. It can be seen from the figures that the amplitude of the vibration is continously increasing
with time up to some maximum amplitude, and after attaining the peak value the response is not increaseing
with further increase in time. At the steady state 1/2ߦ, the system has the highest amplitude; this implies
that the response is strongly influenced by daping ratio ߦ, as presented in Fig. 6 (Chopra, 2007; Clough &
Penzien, 2003; Paz & Leigh, 2004).
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