Optimal Placement of Viscoelastic Dampers Represented by the Classical and Fractional Rheological Models - Design Optimization of Active and Passive Structural Control Systems - page 70

Figure 11. Peak values of horizontal acceleration of storeys for different configuration of dampers

Example 4: A Ten-Storey Shear Frame

for the frame with dampers concentrated on the
first storey. Identical conclusions can be drawn
from the peak values of acceleration shown in
Figure 11.

In the next numerical example, a ten-storey build-
ing structure, modelled as a shear plane frame
with VE dampers mounted on it is considered.
The bending rigidity of columns varies in se-
quence, for every two storeys:
k

Optimal Placement of Dampers for
Frame Structures: Fractional
Rheological Models of Dampers

= = k 68710 kN/m

1 2

k = = k 54010 kN/m

3 4

The aim of the fourth example is to illustrate
the optimal position of dampers on structure
when dampers are modelled using the fractional
Kelvin model and the fractional Maxwell model.
Moreover, it is shown that results obtained using
the sequential optimization method (which is
a heuristic method) and using the PSO method
are very similar. It justifies that it is possible to
find, using the sequential optimization method, a
solution which is near the global optimum of the
optimization problem at hand.

k = = k 42170 kN/m

5 6

k = = k 28660 kN/m

7 8

Table 5. Natural frequencies ω i for the frame
structure

Natural
Frequency
[rad/sec]

Natural
Frequency
[rad/sec]

Mode
Number

Mode
Number

1 22.690 6 182.399

2 56.534 7 208.638

3 91.909 8 245.147

4 127.472 9 281.524

5 151.769 10 324.052