Civil Insight: A Technical Magazine Volume 3 | Page 34

Bhatt M.R.
Civil Insight (2019) 29-36
15.0
Resonant Response
Line for (1/2ξ)
Line for (-1/2ξ)
10.0
5.0
0.0
0
10
20
30
40
50
60
-5.0
-10.0
-15.0
Time (sec)
Fig. 5. Response of damped system with ߦ = 0.05 to sinusoidal force of ߱ = ߱ ௡ and initial displacement
and velocity as zero (for longer time period)
25.00
Response (ξ=10%)
Response (ξ=5%)
Response (ξ=1%)
Response (ξ= 3%)
20.00
15.00
10.00
5.00
0.00
-5.00
0
2
4
6
8
10
12
14
16
-10.00
-15.00
-20.00
Time (sec)
Fig. 6. Response of damped system with different ߦ values to sinusoidal force of ߱ = ߱ ௡ and initial
displacement and velocity as zero
3.3) Dynamic response factors for different frequency ratio
For the undamped and damped systems, the dynamic response factor, defined as the ratio of maximum
amplitude in dynamic state to the maximum static amplitude, can be plotted for different values of the
damping ratio coefficiet ߦ. R d , R v , and R a denote the deformation response factor, velocity response factor,
and acceleration response factor respectively. As suggested by Chopra (2007), Clough and Penzien (2003),
and Paz and Leigh (2004), the dynamic response factors R d , R v , and R a are plotted in Fig. 7, Fig. 8, and Fig.
9 respectively using Eqn (6) and Eqn (8).
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