Optimal Passive Damper Positioning Techniques: State-of-the-Art - Design Optimization of Active and Passive Structural Control Systems - page 104

Figure 14. Effectiveness of passive dampers (a) uncontrolled frame, (b) controlled frame. Adapted from
Takewaki 2009.

same earthquake with a ductility of 4.0. So in
simple terms, we are attempting to match the ac-
celeration amplitude of the elastic spectra (5%
damping) to the spectra corresponding to a ductil-
ity of 4 by increasing the effective damping. Plots
in Figure 15 depict the above stated objective.
Figure 15 illustrates the elastic response spec-
tra and spectra with ductility equal to 4.0 with the
standard 5% damping. Now the aim is to make
the elastic amplitudes coincide with the amplitudes
of spectra with ductility 4.0 by adding extra damp-
ing. In order to achieve this objective, the damp-
ing ratio is increased and is found that at a damp-
ing ratio of 30%, the amplitudes of elastic spectra
are still slightly higher than the peak amplitudes
of the spectra with ductility 4.
So in effect this study signifies that in order
for the parent frame to remain elastic, for this
particular case, from the very beginning there
needs to be a system of dampers capable of im-
parting more than 25% damping in addition to
the in-structure damping. The whole optimization
algorithms reduce to a series of iterations on this
damping level and in effect in strict mathemati-
cal sense the iterations would need to increase
the overall damping, as a decrease might cause

the algorithms to be invalid (i.e., the frame might
become inelastic and the basic assumption in the
algorithm development is violated). This is an
interesting aspect because since the analysis itself
is in the frequency/state space domain which is
an inherent elastic method, the response evalua-
tions could be deceptive in the sense that it might
not capture the inelastic excursions which might
occur in reality, should the overall damping not
be sufficiently high.

CONCLUSION

A consolidated state of the art review on the optimal
positioning techniques for passive dampers has
been presented. The significance of the optimal
distribution of dampers coupled with the neces-
sity for the use of a more realistic in-structure
damping model is illustrated with the help of a
comparative sensitivity study. It is observed that
different damping models give different responses
highlighting the need for a realistic representation
of the in-structure damping to achieve optimal-
ity in terms of response reduction. Realism of
the basic inherent assumption of linearity of the