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simpler and computationally very efficient compared to the solution of the uncoupled equations in the
fractional derivative model case.
Table 5.1 Comparison of maximum response
Response
Floor 1
Floor 2
Floor3
Floor 4
Relative displacement (m)
No
damper
0.0315
0.0804
0.1242
0.1598
Fractional
derivative
0.0161
0.0338
0.0467
0.0543
Linear
7-para
0.0162
0.0341
0.0472
0.0550
Absolute acceleration (m/s~)
No
damper
6.48
6.10
6.48
10.0
Fractional
derivative
3.28
2.92
3.40
4.14
Linear
7-para
3.26
2.94
3.50
4.32
No
damper
566
590
527
359
Story shear (kN)
Fractional
derivative
290
218
160
79.7
Linear
7-para
291
220
164
82.3
The time histories calculated by the two approaches for displacement and acceleration responses were
very similar, but not exactly the same. A more meaningful comparison is obtained when the maximum
response quantities are compared. In Table 5.1 we compare the maximum values of the floor
displacements, story shears, and floor accelerations calculated by the two approaches. It is noted that
the response values calculated by different approaches are close to each other. Also shown are the
values for the undamped case. The response reducing effect of the dampers is clearly evident. In
Figures 5.2(a) and 5.2(b) we show the floor response spectra of the floors 2 and 4, again obtained by
the two approaches. The difference between the floor response spectra calculated by the two
approaches is minimal at higher frequencies. At lower frequencies, these is some difference, primarily
because of the differences in the match of the frequency dependent moduli, Fig. 5.1. However, this can
be improved. This verifies that the linear higher derivative model can provide an as accurate
description of viscoelastic dampers as the fractional derivative model.
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(a) Floor 2 (b) Floor 4
0.2 1 10 100 0.2 1 10
Frequency (Hz)
Frequency (Hz)
Figure 5.2 Floor spectra of pseudo acceleration at floor 2 and 4
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