Optimal Placement of Viscoelastic Dampers Represented by the Classical and Fractional Rheological Models - Design Optimization of Active and Passive Structural Control Systems - page 76

providing the dissipation energy of each
model is approximately equal.

tions of structures will occur when structures are
subjected to very strong earthquakes. In such
a case, analyses of structures in the frequency
domain are not possible or they are very tedious
and only analyses in a time domain could be done.
This fact makes it impossible to use or significantly
complicates the optimization methods presented
above and could drastically increase computa-
tional efforts necessary to obtain the optimal
solution. In particular, objective functions which
are written in terms of transfer functions cannot
be used. Moreover, for example, specification of
a set of accelerograms compatible with the design
spectra is necessary.
In conclusion, reformulation of optimization
procedure for optimal location of dampers on
elastoplastic structures which will be effective and
efficient is desirable and could be the direction of
future works. Other direction of future research
works could be a more thorough examination of
optimization results obtained for structures with
dampers modelled using generalized rheological
models and ones with fractional derivatives. The
influence of uncertainty of structures and damp-
ers parameters on optimal positions and optimal
parameters of dampers has not been analyzed
yet and seems to be an important problem from
a practical point of view.

• The frequency response functions change

very fast in the vicinity of their maximal
value and it is necessary to take into ac-
count small changes of the natural fre-
quencies of vibration when calculating the
maximal values of the frequency response
functions.

The advantage of the optimization methods
used in the chapter is that they are non-gradient
methods and only calculation of the values of the
objective function is required. An advantage of
the PSO method is its ability to solve optimization
problems when the objective function has many
local minima. However, usually many iteration
and many evaluations of the values of the objec-
tive function are necessary. The advantage of
sequential optimization method is its simplicity
and clear physical justification of optimal posi-
tion of dampers. The lack of a formal proof of
convergence of the solution to the global minima
is the main drawback of this method. However,
numerical results reported in the chapter and
previously by Lewandowski (2008) suggest that,
for the considered particular optimization prob-
lems, the method gives us an optimal or nearly
optimal solution, acceptable from the practical
point of view.
The considered optimization methods for
optimal location of dampers could also be used,
without significant changes, to find optimal po-
sitions of dampers on 3D structures. Of course,
3D frames have usually many more degrees of
freedom than planar ones, which means that the
computational effort needed to find an optimal
solution could be substantially greater. Moreover,
additional details, such as specification of accept-
able locations of dampers on the structure, must
be specified in order to reduce the number of
variables in the optimization problem.
In this chapter structures are treated as linear
elastic systems. In reality, elastoplastic deforma-

ACKNOWLEDGMENT

The authors wish to acknowledge the financial
support received from the Poznan University of
Technology (Grant No. DS 11 - 068/11) in connec-
tion with this work. The authors are also thankful
to anonymous referees for their careful reading of
the chapter and their several suggestions, which
have helped improve the chapter.