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Figure 7. Fourier amplitude spectra of the Chi-Chi ground motion records
the plots is that a lower value of µ has a lesser
decay rate for the vibration response.
Qualitatively observing the plots recorded in
Figures 8 and 9 shows that there is a clear distinc-
tion between the responses obtained using non-
viscous models with µ =50.0, µ =5.0 and µ =1.0.
In order to get a better insight, zoomed in plots
are shown in Figures 10 through 13. Figure 10
represents the zoomed in plots for roof displace-
ment and Figure 11 represents roof acceleration
due to the Chi-Chi ground motion. Similarly,
Figures 12 and 13 represent the roof displacement
and roof acceleration responses due to the Sakaria
ground motion.
In all the plots it can be seen that there is a
difference in the response amplitudes between
the viscous and non-viscous models. µ =1.0 rep-
resents highly non-viscous nature and µ =50.0
indicates close to viscous nature. In almost all
cases the response due to classical viscous damp-
ing model is closer to or follows the response with
µ =50.0, justifying the statement made in section
4.3.3, 'a higher value of µ indicates close to vis-
cous characteristics'. It is evident from these plots,
that a smaller value of µ shows lesser decay and
hence higher amplitude of response. The peak
displacement amplitude in the µ =1.0 case is ap-
proximately two times that of the peak displace-
ment amplitude associated with the classical
viscous damping model.
Unfortunately, in reality, very little is known
about structural damping. Free vibration testing
of real buildings indicates that the damping in the
first mode, though not purely viscous, is very
close to viscous and we could say that µ =
(
)
50 0.
represents a realistic behavior, at least in the first
mode. Our intention in plotting the highly non-
viscous µ =
(
)
(
)
.
is to highlight this inherent variability existing in
the modeling. There are other models such as the
frequency independent damping model (described
in section 4.2) which would again give an en-
tirely different set of responses. All these observa-
tions raises a question on the optimality, because
what is optimal in one analysis using a specific
damping model might not be optimal in terms of
response if we use a different damping model. It
has also been shown by earlier studies (Val &Se-
1 0. and close to viscous µ =
50 0
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